ap physics b review

Advanced Placement Physics

Study Guide and Review

Jansen

Aliso Niguel High School

Fall 2000 - Spring 2001

Comments, corrections, or clarifications: [email protected]

mailto:[email protected]

Table of Contents

1. Physics Overview 1 - 8

2. Kinematics in One Dimension 9 - 10

3. Worksheet: Graphing Motion 11 - 14

4. Kinematics in Two Dimensions 15 - 16

5. Force 17 - 20

6. Circular Motion, Gravity, Satellites 21 - 22

7. Work, Energy, Momentum, & Oscillations 23 - 24

8. Thermal Physics 25 - 30

9. Electricity and Magnetism 31 - 36

10. Worksheet: Circuits 37 - 40

11. Waves and Optics 41 - 46

12. Worksheet: Geometric Optics 47 - 52

13. Modern Physics 53 - 56

14. Worksheet: Radioactive Decay 57 - 58

15. 150 Questions 59 - 62

Advanced Placement Physics Physics Overview

The following does not cover every facet of this introductory college level course. It does contain key information to solve complex problems. The student should refer to the previous review sheets for details on Newtonian Mechanics, Thermal Physics, Electricity & Magnetism, Waves & Optics, and Modern Physics.

The pages that follow focus heavily on major principles that allow a student to recognize the nature of a complex problem and move smoothly between all five strands taught in this course. It pays particular attention to Energy, and also addresses Force, Kinematics, Collisions, Circular Motion, Graphing, Rates, and Electricity and Magnetism. Many items are mentioned repetitively. The information may seem redundant, however you will be asked in exams to use the information in a variety of ways. So some of the same information is presented in a variety of ways.

This document is a review, designed for students familiar with the variables and equations. The important equations to begin a problem are given, but the subsequent substitutions, of minor equations given with the test, is up to the student.

The following equations and facts are not given on the exam, but are essential for your success.

xvt

2 rvT

2

mg Gr

A A B B A A B Bi i f fm v m v m v m v A A B B A B Ai i fm v m v m m v B A B AB A A B Bi f fm m v m v m v /lost dissipated i fK K K

2 21 12 2

i fi fmgh mv mgh mv 212

bottomtopmgh mv 2 21 12 2

kx mv 212

qV mv

And any combination of Work Energy Theorem and Conservation of Energy that might be applicable to the problem.

Adiabatic (fast)

U Q W so

0Q U W

Isothermal (slow) 0U Q W

U Q W so

W work done by engine. Gas expands. W work done on engine. Gas is compressed.

Q heat is added.

Q heat is subtracted.

Work is the area under Force distance. Work is the area under pressure volume e: real or actual efficiency ec: Carnot, ideal, or reversible efficiency

Series circuits: current stays the same Series circuits: voltage adds Parallel circuits: voltage stays the same Parallel circuits: current adds

2

qE kr

2P I R 2VP

R

hcE

Lenses: Rays thru center keep going straight. Rays arriving parallel go thru far focus on convex lenses, and the back trace goes thru the near focus in concave lens.

Mirror: Rays thru 2F bounce straight back. Rays arriving parallel go thru the focus on concave mirrors, and the back trace goes thru the focus on convex mirrors.

Right Hand Rule: Used for positive current. Thumb is +particle / +current, fingers are magnetic field lines, and palm is force. Use left hand for -particles / -current.

V Ir A changing flux induces a current in a wire. The direction of the current is the opposite that specified by the right hand rule. The current induced in the wire generates its own magnetic field, which is opposite to the field that caused the emf.

Study Guide and Review Physics Overview 1

Energy Overview

Energy is a central concept that connects the various strands of physics. Through the Work Energy Theorem and the Principle of Conservation of Energy a host of equations and possibilities help generate solutions.

Work Energy Theorem

Work is a change in any energy

W Energy Work, in the center, is equal to any change in energy around the circle. For example:

212

W K m v so 21cos2

F d m v

gW U mg h so cosF d mg h

W Q mc T so cosF d mc T

EW U qV so cosF d qV

Conservation of Energy

Energy can change forms

i fTotal Energy Total Energy

Any energy around the circle can change into another energy around the circle. For example:

212

m v mg h so 2 21 12 2

i fi fmgh mv mgh mv

212

qV m v A charge accelerated by charged plates

212

m v mc T If the kinetic energy of an object turns to heat

Newtonian Mechanics

Power: If work and energy are important, then any variable that has work / energy in its equation is equally important.

Power is the rate that work is done or that energy is delivered, expended, or used. So from power we can get work and energy, and from work and energy we can get power. One easy way is to set time to 1.0 s. Then power and work / energy have the same value, but different units. If you find the time later in the problem just multiply or divide by the time to solve as necessary.

Modern Physics

Thermal Physics

212

K m gU mghv

cosW F d

212sU k x

Q mc T

Q nc T

E hf

1 2g

Gm mUr

hcE

212cU CEU q V V

12cU Q V

Electricity & Magnetism


MOTION OF A SINGLE OBJECT: Relevant Kinematics, Force, and Energy

Start a problem by asking “What is the object doing?”, then “What is causing it to do that?”. What direction is it moving in (if two find x and y components)? Is it moving at constant v (this includes v = 0)? Is it accelerating? Force? Energy change?

See if energy solves the problem first. Then think force and kinematics.

Most common usage is boxed. But, the most common usage is often a special case. Knowing the overall equations and logic will allow you to solve any scenario.

Situation Kinematics Force Energy Constant Velocity

Need constant velocity

xvt

or x vt

Always think sum of force

0F

Forces are vertical, while motion is horizontal

gF mg

cosNF mg 0o slope

NF mg

Inertia only. No force. No energy needed.

cosW F d Where is the angle between F and d vectors.

cos90oW F d

0W

Accelerating in x

Use Kinematic Equations

x o xv v at

2 2 2x o oxv v a x x

212o o xx x v t at

In projectile motion

o xx v t

There is a sum of force

F ma

x p retardingx xF F F

example

x p frxF F F

A force through a distance.

cosx xW F d Where is the angle between F and d vectors.

cos0oW F d No retarding forces present

W F d This time work is done, so there is a energy.

W Energy

212

W K m v The only thing changing is velocity, so K is changing.

Accelerating in y

y o yv v gt

2 2 2y o oyv v g y y

212o o yy y v t gt

Horizontal projectile or dropped object

212

y gt

y g retarding yF F F

example

y g air resistanceF F F

y yW F h Includes retarding forces

gW F h No retarding forces

gW U mg h Height is changing, so U is changing.

212

W K m v Velocity is changing, so K is changing.

212

mg h m v 2 21 12 2

i f Energy conserved.

FN

d or x Fg

v

Fret

FN

Fg

a

d or x

FP

i fmgh mv mgh mv

Fret

Fg

g h or y


Situation Kinematics Force Energy Inclines

Kinematic Equations Apply

x o xv v at

2 2 2x o xv v a x x o

212o o xx x v t at

y o yv v gt

2 2 2y o yv v g y y o

212o o yy y v t gt

Motion is parallel to slope

Acceleration down the slope is caused by the addition of Fg and FN. The resultant of these two vectors is Fgsin. Since the natural motion is down the slope set that direction as +. In some problems it is useful to reverse this (if the object is going up hill).

sing retardingF F F

cosNF mg

Work and energy can work parallel, in the x, and in the y

W F d Force and distance vectors form similar triangles.

x xW F d Work depends on F and d being parallel.

y yW F d So any pair of parallel vector will solve the problem

212

W K m v

gW U mg h

212

mg h m v 2 21 12 2

i fi fmgh mv mgh mv

Down a curve

Kinematics Fail

The net force is changing as the vectors Fg and FN change. In addition the direction is changing. Acceleration is changing. The Kinematic Equations are designed for changing velocity, but only work for uniform (constant) acceleration.

Force Fails

The net force is changing as the vectors Fg and FN change.

Energy is directionless.

212

W K m v

gW U mg h

212

mg h m v 2 21 12 2

i fi fmgh mv mgh mv

A very important case.

212

bottomtopmgh mv No initial velocity moving to a height of zero.

Pendulum or Swing

h R y 2 2y R

y

x

a

Fret FN

Fg

Less steep, a decreaseing

Steep slope, large a

a = 0 constant velocity from this point on

cosx R

Kinematics Fail

See accelerating down a curve above. The velocity is zero at either end. The velocity is greatest at the lowest point

Force Fails

See accelerating down a curve above. The restoring force is greatest at the ends, as is the acceleration. The restoring force is zero in the middle, and so is the acceleration.


212

W K m v

gW U mg h

212

bottomtopmgh mv If it has no initial velocity and goes all the way down.

At the ends it is all potential no motion, in the middle it is all motion no potential.

h

y x

R


Situation Kinematics Force Energy Object on string, Vertical loop

Tangential Velocity

Instantaneous velocity is tangent to the circlular motion.

2 rvT

Acceleration is toward center, centripetal.

2

cvar

Center seeking.

Force is centripetal, Fc, is the sum of force in circular motion. Toward center is +. Find tension at the top.

c T g F F F

Find tension at the bottom.

c T gF F F

Unlike previous scenarios, the object definitely has velocity at the top.

There is a height difference from top to bottom, but the object has speed at the top as well. And the bottom may not necessarily be the lowest point in the problem

2 21 12 2 fitop top bottom bottomfi

mgh mv mgh mv

Object on string, Horizontal loop

Tangential Velocity

Instantaneous velocity is tangent to the circlular motion.

2 rvT

Acceleration is toward center, centripetal.

2

cvar

Center seeking.

Force is centripetal, Fc, is the sum of force in circular motion. Toward center is +. Find Fc by adding vectors (tip to tail). Then solve for FT.

2 2

T c g F F F

No work is done

cosW F d Where is the angle between F and d vectors.

cos90oW F d

0W

At any instant the direction of motion (tangent to the circle) is perpendicular to the center seeking Fc, the FT, and the Fg.

And for one revolution there is no total displacement from the origin, since a single revolution brings you back to the starting point.

Object turning on flat surface

Tangential Velocity

2 rvT

2

cvar

Why is there circular motion?

Object not sliding off disk, or car turning on a road.

c fr F F

No work is done

See above.

Roller Coaster

Need uniform slope

Kinematics only work on sections that have constant slope.

If the track is curved try energy.

Force centripetal in the loop.

To find the speed needed to have passengers feel weightless at the top of the loop

c gF F

Energy works everywhere, with its directionless advantage.

You can solve for any point A using any other point B. Use the complete equation. The car will usually have both speed and height at every point. An exception is the lowest point on the track, or if it starts with zero velocity at the top of a hill (this is unlikely since roller-coasters don’t stop at the top of each hill). If it has velocity and height at the top you need to include both.

2 21 12 2A A B Bmgh mv mgh mv

v

ac

FT

Fc

Fg

FT

FT Fg

Ffr

Fg


Situation Kinematics Force Energy Spring Kinematics Fail

See Down a curve, and Pendulum above. The velocity is zero at maximum +/- x (amplitude) The velocity is greatest at x = 0

Force Fails

See Down a curve, and Pendulum above. The restoring force is greatest at maximum +/- x (amplitude). The restoring force is zero at x = 0, and so is the acceleration.


212

W K m v

212SW U k x

If it starts at maximum x (amplitude) and it converts all the springs energy into speed of the object pushed / pulled by the spring

2 21 12 2

kx mv 2 2 2 21 1 1 12 2 2 2

i i f fkx mv kx mv

m

m

m

-x +x x=0

Particle accelerated by electric field

Potential difference.

Velocity increases. Positive charges go in the opposite direction. But, + particles are more massive, don’t accelerate as quickly, and have lower final velocities.

The force of the electric field

F qE

Electromagnetism: New forms of energy, but energy is still conserved.

W Energy

212

W K mv

EW U qV

212

qV mv 2 21 12 2

i fi fqV mv qV mv

Charged particle parallel to plates

It acts like a projectile

xox v t

212

y at get a from F

Electric field is perpendicular

Particle is forced toward the plate with opposite sign.

FEq

F qE

F ma ma qE

Work is done in the direction of the electric field.

W F d W qE d

Charged particle in a magnetic field

Path curved by field.

If the field is large enough the particle will follow a circular path.

2 rvT

2

cvar

Forced to center by field.

c BF F

2vm qvBr

No work is done

cos90oW F d

0W

At any instant the direction of motion (tangent to the circle) is perpendicular to the center seeking Fc, and the FB.

v


Collisions Momentum is always conserved in a collision

Know the following equations

A A B B A A Bi i f fm v m v m v m v B 2 objects before, 2 objects after

A A B B A B Ai i fm v m v m m v B 2 objects before, 1 objects after

A B AB A A B Bi f fm m v m v m v 1 objects before, 2 objects after

If there are more than two objects add , C Cm v D Dm v , etc.

If the collisions happen in two dimensions, x and y, turn all vectors into x and y components. Solve for the result in the x direction and then solve for the result in the y direction. Take the final x and y and use Pythagorean Theorem to find the overall resultants.

mv

If the object has momentum it also has kinetic energy.

Total energy is also conserved, but energy changes forms.

Perfectly elastic collision (An idealized unrealistic case)

Kinetic energy is conserved in this rare case.

Use these two equations together (System of 2 equations & 2 varibles).

A A B B A A B Bi i f fm v m v m v m v

2 21 1 1 12 22 2 2 2

i iA A B B A A f B B fm v m v m v m v

Inelastic Collision (The common type)

Kinetic energy is lost or dissipated. There is less kinetic energy after the collision.

/lost dissipated i fK K K

(Note this is the opposite of change in kinetic energy. Change in kinetic energy is Kf – Ki. The value is the same, but the sign is reversed.)

2 2/

1 1 1 12 22 2 2 2

i ilost dissipated A A B B A A f B B fK m v m v m v m v

The kinetic energy lost often turns into heat from the impact

/lost dissipatedK mc T

Circular Motion The key to circular motion is to ask:

“What is causing it to stay in a circle?”

Centripetal means center seeking

The direction of motion is toward the center Any force pointing to the center is a positive force. Any force pointing away from the center is a negative force.

Force Centripetal is the sum of forces in these problems It is not drawn on free body diagrams since it is the net force. Any force (gravity, tension, friction, normal, magnetic, etc.) can contribute to Fc

Possible equations

c gF F To find minimum speed at the top of a roller coaster loop.

c frF F Object is revolving on a horizontal surface, or a car turning.

c TF F If a (horizontal) string spins the object in a horizontal circle.

2 2c T g If an object at the end of a string is spinning through the air

and gravity pulls the string down from the horizontal.

F F F

c T gF F F An object (at the top) spinning at the end of a string in a

vertical circle.

c T gF F F An object (at the bottom) spinning at the end of a string in a

vertical circle.

c NF F Inside an amusement park ride (Gravitron)

c BF F For a charged particle in a magnetic field.

Substitute and solve. 2

cvF mr

Velocity is Tangential The instantaneous velocity is tangent to the circular motion.

2 rvT

T is the period, the time for one revolution.

If the object is released (the force stops working) then the object will move at this velocity in a direction tangent to the circle at the time of the release.



Rates and Graphing A change in a variable as a function of time (in seconds).

In the graphed examples the y intercepts and slopes would depend on where the problem started and on how fast the rate is changing.

Constant Velocity: change in position dvt

Velocity is the slope (derivative) of distance time graph 0v v v

Acceleration: change in velocity va

t

Distance increases (or decreases) in an exponential manner. a a

Acceleration is the slope (derivative) of velocity time graph

a a Areas Under Curves

Velocity is the area (integral) under the acceleration graph. Displacement is the area (integral) under the velocity graph.

*** Work is the area under the force distance curve.

*** Work is the area under the pV (pressure volume curve).

Rates and Graphing

Power: Work (and any form of energy) done in a time t WPt

Remember you can convert directly to work (or energy) from power if you solve the problem using 1 second for time. (Example: 100 W, means 100 J in one second). If you get information about time later in the problem, just multiply by the amount of time to find the actual total work (or energy). Example: If the proceeding 100 W was delivered for 1 minute, then 100 J were delivered each second for 60 s. So 6000 J of work (energy) was done, used, or delivered.

Current: amount of charge moving through a point in a circuit QIt

Current stays the same in a series circuit. All the resistors are in line. It’s like a traffic jam on one road with no alternate routes. All the cars are going the same speed on the entire road, so the amount of cars passing any point in a certain time interval is the same everywhere. Current adds in a parallel circuit. The electrons have multiple pathways to choose from. If 100 C arrive at a fork in the circuit they must split up. Due to conservation of charge, the amount of electrons in the parallel paths must add up to the amount of electrons arriving at the fork.

emf: change in flux (magnetic field thru an area) t

Remember, current can only be generated by a changing flux. So a closed loop of wire must move through the field, or the loop must be getting larger, or the loop must be rotating.

Loop moved thru Bar moved, enlarging loop Loop rotates

cosB At

B v

cosB At

d d d

t t

d

tt

d d

t t

v

t

v

t

Isothermal Line 0,U so Q W

Isobaric Line W p V

V

p

t

t

t

Advanced Placement Physics Kinematics in One Dimension

Kinematics Study of Motion

Distance Total distance traveled from start to finish.

Displacement Straight line distance between the start point and ending point of the problem.

Speed A scalar quantity (no direction specified) that shows the rate that distance d is covered. Instantaneous The speed at an instant in time. Right now. Your speedometer reading when you glance it at. Average The total distance divided by the total time for the entire trip. Constant If the same speed is maintained over the entire trip

Velocity A vector quantity consisting of magnitude and direction. Displacement x divided by time. Acceleration Change in velocity (change in displacement and/or direction)

Kinematic Equations You can only use the constant velocity equation when there is no acceleration. If acceleration is present (Question contains terms such as: starts from rest, final velocity of, accelerates, comes to rest, etc.), then you must use the three Kinematic equations in the highlighted boarder boxes below.

Speed Constant Velocity Average Velocity Acceleration

sdvt

xvt

or x vt ox xv

t

ov vat

2ov vv

Another Way of Looking at Average Velocity One of the four Kinematic Equations. But it is mostly used in conjunction with the above equations to derive the next three equations. Occasionally it is useful in problems.

ov v at

Velocity Rearranged the acceleration equation from above. Useful for determining v, when a and t are given. However, if any three variables are available and the fourth is needed rearrange this as necessary.

212o ox x v t at

Position Key equation to determine distance when a is involved. Used extensively in falling body problems. Its derivative is the velocity equation above.

22 2o ov v a x x When no time is given When v, a, and/or x are known, but no information is given about t, then this can be used to solve for the unknown variable.

xo initial position, x final position, vo initial velocity, v final velocity, a acceleration, t time

Problem Solving Strategy 1. Draw a picture (Mental or on Paper) 2. List known and unknown variables.

a) Caution; some may be extraneous, and are not necessary to solve the problem. b) Often either the starting or ending point is at rest, meaning a value of zero.

3. Do necessary conversions. 4. Choose an equation that can be solved with the known variables.

a) This equation may or may not be the answer you are looking for. b) It may provide a new variable for use in another equation. c) This may lead to a succession of equations.

+ or – ????: “ + ” & “– ” can be used to indicate direction, and/or acceleration (+) or deceleration (–).

–9.8 m/s2 Be careful here. Does this mean the object is decelerating (slowing) or does it mean that the object is moving along a negative (perhaps the y) axis? It would depend on the problem. For an object moving on the x axis it would mean decelerating. For an object falling along the y axis, due to gravity, it means the object is accelerating, but in the downward direction (-+9.8). In forces it is easier to use 9.8 m/s2 as a positive number.

Study Guide and Review Kinematics in One Dimension 9

Falling Bodies Displacement: 0oy Initial position. We can choose the reference frame / coordinate axis.

If the object 0y ends the problem at the same elevation it started at.

If the object y ends the problem at a higher elevation than it started.

y If the object ends the problem at a lower elevation than it started.

Velocity, initial: If it is dropped vo 0 from rest.

If vo fired upward.

If vo fired downward.

Velocity, final: At the moment it reaches maximum altitude, right before falling back to earth. v 0 If it hits something on the way up and never reaches max altitude (Rare problem). v On the return trip. v If it lands at the same elevation that the problem began at. v vo

Acceleration: g m 9 8 2. s

Projectile Motion Motion in two dimensions happens simultaneously.

In the x direction the velocity is constant, with no acceleration occurring in this dimension. In the y direction the acceleration of gravity slows upward motion and enhances downward motion. Both happen simultaneously, however they can be analyzed separately using vector components.

The following review of variables can be overwhelming to memorize. It is much easier if you think it through or draw a pictorial representation.

Angles: All angles are measured from East. Above the horizon is positive, below negative.

Displacement: 0ox 0oy x The x is always positive.

If the object 0y ends the problem at the same elevation it started at.

If the object y ends the problem at a higher elevation than it started.

If the object y ends the problem at a lower elevation than it started.

Velocity, initial: Splits into components, vo coso oxv v , sino oyv v

In every problem, we choose to fire it in the positive x direction. oxv If 0o yv fired horizontally.

If fired at a positive angle (above the horizon). o yv

If fired at a negative angle (below the horizon). o yv

Velocity, final: x oxv v Since there is constant velocity in the x direction, initial and final are the same.

At the 0o yv top of the trajectory

If the object hits something on the way up. Not used in problems very often. o yv

On the return trip. o yv

v Resultant from adding vectors and v . Has an angle not a + or –. vx xo

Acceleration: g m 9 8 2. s

Study Guide and Review Kinematics in One Dimension 10

Graphing Motion Name __________________________

Kinematics WS ___ Date _____________ Per _______

1. A car travels at a constant 20 m/s for 10 s. Fill in the table showing the cars displacement from the origin at the end of each second. Then graph the motion.

t (s) d (m) 1

2

3

4

5

6

7

8

9

10

d

t

2. What is the slope of the curve plotted? __________

3. How does this compare to the velocity, given, in number 1 above?

4. Complete the table showing the cars velocity at the end of each second. Then complete the velocity-time plot.

t (s) v (m/s) 1

2

3

4

5

6

7

8

9

10

v

t

5. Find the area under the curve for the first 5 seconds. __________

6. How does this compare to the displacement, for the first 5 seconds, in number 1 above?

Study Guide and Review Worksheet: Graphing Motion 11

7. The slope of the displacement-time graph is ____________________.

8. The slope of the velocity-time graph is ____________________.

9. The area under the acceleration-time graph is ____________________.

10. The area under the velocity-time graph is ____________________.

Answer the next series of questions using the following displacement-time graph.

11. How far does the object travel during the first 5 seconds (1 to 5 s)? __________

d (m)

5

10

15

20

30 25201510 5 t (s)

12. How far does the object travel during the second 5 seconds (5 to 10 s)? __________

13. How far does the object travel during the third 5 seconds (10 to 15 s)? __________

14. How far does the object travel during the fourth 5 seconds (15 to 20 s)? __________

15. How far does the object travel during the last 10 seconds (20 to 30 s)? __________

16. During which time interval(s) is the object standing still?

17. Does the car ever accelerate in this scenario?

18. Draw the velocity time graph for the above scenario.


Answer the next series of questions using the following velocity-time graph.

20

19. During which interval(s) is the object accelerating? _______________

20. During which interval(s) is the acceleration the greatest? _______________

21. During which interval(s) is the object standing still? _______________

22. During which intervals does the object have the same speed? _______________

23. What is the displacement during interval A? _______________

24. What is the displacement during interval B? _______________

25. What is the displacement during interval C? _______________

26. What is the displacement during interval D? _______________

27. What is the displacement during interval E? _______________

28. Draw the acceleration-time graph for the above scenario.

v (m)

5

10

15

30 25201510 5

C

D

B

E

A

t (s)


Complete the series of graphs: displacement-time, velocity-time, and acceleration-time.

29. 30. 31. 32.


33. 34. 35. 36.

37. 38. 39. 40.

d

t

v

t

a

t

d

t

v

t

a

t

d

t

v

t

a

t

d

t

v

t

a

t

d

t

v

t

a

t

d

t

v

t

a

t

d

t

v

t

a

t

d

t

v

t

a

t

d

t

v

t

a

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d

t

v

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a

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d

t

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a

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d

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a

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Advanced Placement Physics Kinematics in Two Dimensions

X Component Equation Equations Given on Test Y Component Equations

212o ox x v t at

o xx v t

212o ox x v t at 21

2o o yy y v t gt

24.9o yy v t t

x o xv v a t

x o xv v

ov v at y o yv v gt

2 2 2x o oxv v a x x

x o xv v

22 2o ov v a x x 2 2 2y o oyv v g y y

2 19.6y o yv v y

X Variables Common to both X & Y Y Variables

0ox ov 0oy

x y

coso oxv v t sino oyv v

cosx o oxv v v yv

0xa

2 2x yv v v

9.8g

Strategies that work most of the time.

When no time is given. Finding time is the key to all falling body or projectile motion problems

1st solve for v 2 2 2y o oyv v g y y y this can be +/- , but is usually minus

2nd use v from above to get t y o yv v g t y

3rd o xx v t use t from above to solve for range, x

(Alternative: 212o o yy y v t gt , and the quadratic, followed by o xx v t )

When time or range x is given. This makes the problem easy since velocity is constant in the x direction.

1st o xx v t Given time solve for x . Given x solve for time.

2nd 212o o yy y v t gt Once you have time this is easy, and you don’t need the quadratic.

When an object is dropped or fired horizontally 0o yv and yo 0 .

y o yv v g t t becomes v gy

212o o yy y v t gt becomes y g

12

2t

These versions are time savers, particularly the last one, since it now no longer requires the quadratic formula.

Study Guide and Review Kinematics in Two Dimensions 15

PROJECTILE MOTION

Time is ruled by gravity and height. Most problems require y variables and y equations to solve for time. From time distance in the x direction and the final v can be determined.

Study Guide and Review Kinematics in Two Dimensions 16

x

ovo xv v holds true for all projectile motion problems.

o xxv v Horizontal

0o yv

coso oxv v Downward

sino oyv v

coso oxv v Upward

sino oyv v

2 2x yv v v

At top: vy=0, v=vx=vox

vx

-vy

Lands on level ground vy=-voy

Going down

-vy

Going up

+vy

+voy

vox

+ Lands above axis +y Lands on axis y = 0 Land below axis -y

+/-vy means 2 possible t’s at altitudes above ground

tup = tdown for objects returning to ground level

Max. y Solved by setting vy=0

22 2y o oyv v g y y

v

2 2x yv v v

-vy

vx -y

= 0 Vox voy

-voy since down angle means - vo

v

2 2x yv v v

vx

-vy

-y

Advanced Placement Physics Force Force Any push or pull Newton’s 1st Law Law of inertia (Restatement of Galileo’s principle of inertia) Newton’s 2nd Law F maNewton’s 3rd Law Equal and opposite forces. For every action force there is an equal & opposite reaction force.

Forces come in action - reaction pairs.

F Key to all problems. Fx F in x direction on traditional coordinate axis. Fy F in y direction.

F F parallel to a slope (direction of motion). F F perpendicular to slope.

F ma Sum of force is Net Force. You may need to solve for a using the kinematic equations, then solve

for force, or given force you solve for a and then use it in the kinematic equations to find v, x, or t.

Strategy on force Problems: 1. Draw FBD. 2. Set direction of motion. What would the object do if it could? Considered this the positive direction. 3. Using the forces listed below write the F equations relevant to the problem. In what direction is the problem

moving? What matters, the x or the y direction? The parallel or the perpendicular direction? Any force vectors in the FBD pointing in the direction of motion are positive while any vectors the other way are negative.

4. Substitute known equation, (forces like Fg become mg). 5. Substitute for F. Ask yourself what the sum of force should be based on the chart below. Is the object standing still,

moving at constant velocity, or accelerating. Substitute zero or ma for F. 1 v = 0 v = 0 a = 0 F = 0

2 v = +/- a constant value v = 0 a = 0 F = 0

3 v increasing or decreasing v = +/- a constant value a = +/- a constant value F = m a

6. Plug in and solve. (All values including 9.8 are entered as positives. The negative signs were decided when setting up the sum of force equation. Plugging in – 9.8 will just turn a vector assigned as – Fg into a positive. You decided its sign based on the way it was pointing relative to the problems direction of motion. Don’t reverse it now!)

FP Push or Pull.

Fg Force of gravity. gF mg

FT Tension is a rope, string, etc. This force has no equation. You either solve for it, or it cancels, or it’s given. FN Force Normal. A contact force, always perpendicular to the surface. (On a tilted surface use F & F) Ffr Friction force. frF FN Always opposes motion. Static friction: not moving. Kinetic friction: object moving.

Far Force of air resistance. This force has no equation. You either solve for it, or it cancels, or it’s given. Fc Force Centripetal. It is the F in circular motion problems. So Fc can be any force that keeps an object in circular

motion. .c g c N c T c fr c BF F F F F F F F F F etc It can also be two or more of these added together. The direction of motion is toward the center. So any force directed toward the center is positive and any force directed outward is negative.

The key in using any of these equations is to ask yourself: 1. What is causing the circular motion? 2. Then set up the equality. 3. Substitute known equations. 4. Solve.

FB Force due to a magnetic field. This force is perpendicular to the field and perpendicular to the velocity of the particle. So any charged particle will move in a circle. Use the right hand rule for positive charges or positive current, and use the left hand for negative charges or electron current.

Fany subscript that make ssense to solve the problem

Normal force: Gravity pulls the object down the slope and into the slope. If we only consider the motion into the slope (perpendicular), the object has no perpendicular velocity. So the F= 0. Then the surface must push upward, equal and opposite to the perpendicular gravity component. Named the normal force, it is a contact force and operates perpendicular to any surface. It must counter only the component of gravity perpendicular to the surface.

Fg

F FN g cos

F FN g cos Where is the angle between Fg and Fg . It is also the tilt angle

of the surface measured from the ground. Substituting mg for Fg.

F mgN cos Flat surfaces = 0o, F F or F mN g N g

Study Guide and Review Force 17

Friction: opposes motion. Motion is always parallel to a surface, so friction always acts parallel. Static Friction: Friction that will prevent an object from moving. As long as the object is standing still the force of

friction must be equal to the push, pull, component of gravity or other force that attempts to move the object. (If there is no force attempting to cause motion, then there can be no friction).

Static friction is the strongest type of friction since the surfaces have a stronger adherence when stationary. Kinetic Friction: Friction for moving objects. Once an object begins to move breaking static frictions hold, then the

friction is termed kinetic. Kinetic friction is not as strong as static friction, but it still opposes motion. Coefficient of friction: a value of the adherence or strength of friction. k for kinetic friction and s for

static friction.

fr NF F so F mgfr cos

Force Parallel: Motion on a slope is parallel to the slope. Fg and FN are at an angle to each other leaving a gap of magnitude singF when these two vectors are added tip to tail. singF is not a force by itself, it is the sum of

force when Fg and FN are added together. It is not part of the FBD. It describes the motion of the object parallel to the slope, if no other forces are acting on it. What if we sum the forces in the direction of motion (which is parallel to the slope)?

singF is down the slope and positive, since objects generally want

to go down hill (direction of natural motion is positive). Any force opposing the natural downward motion is a retarding force and is negative. So uphill is negative.

F FN g

We need an overall sum of force in the F direction.

sing retardingF F F

What do you use for force retarding? It could be friction Ffr, air resistance Far, a rope holding up the slope FT, someone pushing up the slope FP, or a combination of forces. Substitute the appropriate F and solve.

Friction on the slope: Friction is the retarding force in the scenarios discussed above. 1. No friction.

(What will the object do? Accelerate F = ma)

sing retardingF F F

sin 0gF F

ma mg

sin

sina g

2. v = 0 or v is constant.

(No acceleration F = 0)

sing retardingF F F

0 sin

g frF F cos sinmg mg

cos sin

tan

3. Accelerating with friction present.

(Accelerates so F = ma)

sing retardingF F F

sin

g frF F F sin cosma mg mg

sin cosa g g

sin cosa g

singF

Fg

cos

singF

Fg

NF

singF

Fg

F FN g cos

frF

singF

Fg

F FN g cosfrF

Fg

NF

frF

Fg

NFfrF

singF

Fg

F FN g cos


Complex Force Problems Set direction of motion as positive. If you are not sure what the direction of motion will be take a guess. If the problem returns negative values for the final result, you were wrong, the problem went the opposite of your prediction.

Vertical & Horizontal Tension is the same for both blocks. Rearrange to get equations in terms of tension, then set them equal so tension cancels. Then substitute and solve.

F F FA T frA T

frA B

B

B

F F FB gB

T AF F F T gBF F F

A frA gBF F F F

cosA A Bm a m g m g m a

cosB A

A B

m g m gam m

Pulley If it doesn’t say which is more massive, pick one. In this case I picked B as the heavier object and used this to set the direction of motion. Find what does not change, T, and rearrange in terms of this. Set the equations as equal, substitute and solve.

A T gF F F A B gB TF F F

T AF F FgA T gB BF F F

A gA gB BF F F F

A A Bm a m g m g m aB

B A

A B

m g m gam m

Friction on horizontal surfaces 1. Friction is the only force in the horizontal direction.

frF F

gF F

ma mg a g

2. When friction and the forward force are equal. Object

can be standing still or moving at constant velocity.

P frF F F

0 P frF F

P frF F

PF mg

3. When friction is not strong enough to prevent the object from accelerating anyway.

P frF F F

Pma F mg

PF mgam

Incline I picked mA as moving down the slope, so mB moves up. Tension prevents mA from sliding down the slope and is therefore acting like friction. If there was friction it would be another arrow opposing motion down the slope. Just subtract it as well. Fg and FN are at angles to each other leaving a vector gap of Fgsin (see previous page)

sing retardingF F F

sinA gA TF F F B T gBF F F

sinT gA AF F F T B gBF F F

singA A B gBF F F F

sinA A Bm g m a m a m gB

sinA B

A B

g m ma

m m

+FN

-Ffr

-Fg

+FT mA

Direction of Motion A

+ B

-FT

+Fg

mB

-FTB +FTA

+FgB

B A

B A -FgA

+FT

Fg

FN -FT

mA

Direction of Motion

+

mA mB -Fg

F mN B

-Ffr

mA

Fg

+FN

-Ffr

m

-Fg

+FP A

+FN

-Ffr

m

-Fg

+FP A



Vertical Circular Motion A ball at the end of a string is swung in a vertical circle. Any force pointing to the center is positive centripetal force, while force vectors pointing away from the center are negative centripetal force. Sum the forces. Look for the force that is the same, and set up an equality.

c g T tF F F op

F

c g T bottomF F F

T top c gF F T bottom c gF F F

2

T topvF m mr

g

2

T bottomvF mr

mg

r

Horizontal Circular Motion A penny on a circular disk rotating horizontally. What keeps it from flying off? Friction. Something must be keeping it going in a circle.

Otherwise it would move in a straight line. Friction is the only candidate. No force is pushing it out of the circle (If friction let go the penny would move due to inertia in a direction tangent to the disk. It would not move out from the center of the circle, since no such force is present in this problem.) Force centripetal is the sum of forces for circular motion.

c fF F

2vm mr

g

v gr or

2vrg

Magnetic Field Force on a charged particle

A charged particle moving in a magnetic field will experience a force causing it to follow a curved path and be deflected from its original course. If the force is strong enough the particle can be made to follow a circular path.

sinBF qvB

q is the charge on the particle. See constants table. v is the velocity of the particle. B is the magnetic field strength. is the angle between the velocity and magnetic field.

Force on a current carrying wire

The magnetic field can also move a current carrying wire. The wire can jump.

sinBF BI

B is the magnetic field strength. I is the current in the wire.

is the charge on the particle is the angle between the velocity and magnetic field.

The Right Hand Rule is used to determine the direction of deflection of the charged particles in the top scenario and the direction of movement of the wire in the bottom scenario. How do you choose the right equation?

q is for charged particles, and length of wire.

Lawn Mower

Pushing with 90 N at 45o

Constant speed. 0 F

Solve for the Retarding Force

.x P rxF F F et

.0 P retxF F

. 90 cos45 63.6oret PxF F N N

Solve for the Normal Force

y P NyF F F gF

N y P yF F F gF

22020 90 sin 45 16 9.8oNF N kg m s N

Solve for Fp to accelerate from rest to 1.5 m/s in 2.5 s

26.05.2

05.1 smtvv

atavv o

o

xxxxxx

NsmkgmaF xx 6.96.0162

You need this force to accelerate, but you still need to overcome the retarding force.

.x P rxF F F et

.P xx

9.6 63.6 73.2retF F F N N N

But you aren’t pushing in the x direction. You need the push at 45o to generate 73.2 N in the x direction.

cos 45oP pushxF F 73.2 104

cos 45 0.707P x

push o

F NF N

Fg

FT bottom

FT top Fg

F

Fret

Fg

N FP

FP

FN

Fret

Fg

Advanced Placement Physics Circular Motion, Gravity, & Satellites Frequency: How often a repeating event happens. Measured in revolutions per second. Time is in the denominator.

Period: The time for one revolution. 1Tf

Time is in the numerator. It is the inverse of frequency.

Speed: Traveling in circles requires speed since direction is changing. Velocity: However, you can measure instantaneous velocity for a point on the curve. Instantaneous velocity in any

type of curved motion is tangent to the curve. Tangential Velocity.

Projectile Motion Circular Motion Satellite Motion

The equation for speed and tangential velocity is the same 2 rvT

Acceleration: Centripetal Acceleration. Due to inertia objects would follow the tangential velocity. But, they don’t. The direction is being changed toward the center of the circle, or to the foci. In other words they are

being accelerated toward the center. 2

cvar

Centripetal means center seeking.

Force: Centripetal Force. If an object is changing direction (accelerating) it must be doing so because a force is acting. Remember objects follow inertia (in this case the tangential velocity) unless acted upon by an external force. If the object is changing direction to the center of the circle or to the foci it must be

forced that way. c cF ma 2

cvF mr

1. As always, ask what the object is doing. Changing direction, accelerating, toward the center, force centripetal. 2. Set the direction of motion as positive. Toward the center is positive, since this is the desired outcome. 3. Identify the sum of force equation. In circular motion cF is the sum of force. cF can be any of the previous forces.

If gravity is causing circular motion then c gF F . If friction is then c frF F . If a surface is then c NF F .

4. Substitute the relevant force equations and solve. For cF substitute 2vmr

Gravity 1 22g

m mF Gr

and F mg g combined are mg G m mr

1 22

simplified is 2

mg Gr

r is not a radius, but is the distance between attracting objects measured from center to center. Is the problem asking for the height of a satellite above earth’s surface? After you get r from the equation subtract earth’s radius. Are you given height above the surface? Add the earth’s radius to get r and then plug this in. Think center to center.

Inverse Square Law: If r doubles (x2), invert to get ½ and then square it to get ¼. Gravity is ¼ its original value so Fg is ¼ of what it was and g is ¼ of what it was. So multiply Fg by ¼ to get the new weight, or multiply g by ¼ to get the new acceleration of gravity. If r is cut to a (x 1/3), invert it to get 3 and square it to get 9. Multiply Fg or g by 9.

Apparent Weight: This is a consequence of your inertia. When an elevator, jet airplane, rocket, etc. accelerates upward the passenger wants to stay put due to inertia and is pulled down by gravity. The elevator pushes up and you feel

heavier. Add the acceleration of the elevator to the acceleration of gravity g apparentF mg ma . If the elevator is going

down subtract g apparentF mg ma . If the elevator is falling you will feel weightless 0g apparentg a so F . This same

phenomenon works in circular motion. Your inertia wants to send you flying at the tangential velocity. You feel pressed up against the side of the car on the outside of the turn. So you think there is a force directed outward. This false non-existent force is really your inertia trying to send you out of the circle. The side of the car keeps you in moving in a circle just as the floor of the elevator moves you up. The car is forced to the center of the turn. No force exists to the outside. However, it feels like gravity, just like your inertia in the accelerating elevator makes you feel heavier. You are feeling g’s similar to what fighter pilots feel when turning hard. It is not your real weight, but rather what you appear to weight, apparent weight.

Study Guide and Review Circular Motion, Gravity, & Satellites 21

Kepler’s Three Laws of Satellite Motion 1. Satellites move in elliptical orbits. The body they orbit about is located at one of the two foci. 2. An imaginary line from the central body to the orbiting body will sweep equal areas of space in equal times.

3.

2 3

1 1

2 2

T rT r

Compares the orbit of one satellite to another (i.e. you can use the earth’s orbit to solve for any

other planet’s orbit. Remember, in this case r is not the radius of earth, but rather the earth sun distance.

Rotation All parts of an object are rotating around the axis. All parts of the body have the same period of rotation. This means that the parts farther from the central axis of rotation are moving faster. So if we look at some of the tangential velocities diagramed at the right, we see that they are in all directions and vary in magnitude. So we need a new measurement of velocity. Collectively all the velocities are known as the angular velocity, which is a measure of the radians turned by the object per second. Because the period is the same for the various parts of the rotating object, they move through the same angle in the same time. In rotation the parts of a rotating body on the outside move faster. They need to travel through the same number of degree or radians in the same amount of time as the inner parts of the body, but the circumference near the edge of a spinning object is longer than close to the center. So the outer edge must be moving faster to cover the longer distance in the same time interval. (This differs from the circular motion of the planets, which are not attached, and therefore not a single rotating body. The planets move in circular motion individually. Here the inner planets move faster. The planets closer to the sun must move faster in order to escape the gravity of the sun. They also travel a shorter distance and therefore have the shortest period of orbit).

All the equations for an object in circular motion hold true if we are looking at a single point and only a specific point on a rotating object.

Rotating objects have rotational inertia and an accompanying angular momentum, meaning that a rotating object will continue to rotate unless acted upon by an unbalanced torque, & a non-rotating object will not rotate unless acted upon by an unbalanced torque.

Torque: The force that causes rotation. In rotation problems we look at the sum of torque (not the sum of force). But it is exactly the same methodology.

sinrF

Strongest when the force is perpendicular to the lever arm (since sin 90o equals one).

Balanced Torque: The sum of torque is zero. No rotation.

Unbalance Torque: Adding all the clockwise and counterclockwise torque does not sum to zero. So there is excess torque in either the clockwise or counterclockwise direction. This will cause the object to rotate.

1. As always, ask what the object is doing. Is it rotating or is it standing still? 2. Set the direction of motion as positive. It will either rotate clockwise or counterclockwise. If you pick the wrong

direction your final answer will be negative, telling you that you did thing in reverse. But, the answer will be correct nonetheless. If it is not moving pick one direction to be positive, it really doesn’t matter. But the other must be negative, so that the torque cancels.

3. Identify the sum of torque equation.

clockwsise counterclockwsise or counterclockwsise clockwsise 4. Substitute the relevant force equations and solve (examples assume clockwise was positive direction)

Rotating you get some + / - sin sinclockwsise counterclockwsise

rF rF

Not Rotating 0 sin sinclockwsise counterclockwsise

rF rF

Angular momentum: Depends on mass (like regular momentum) and it also depends on mass distribution. As an ice skater brings their arms closer to the body they begin to spin faster, since the mass has a shorter distance to travel.

Angular momentum is conserved. The radius gets smaller, but angular velocity increases (vice versa as the skater moves arms outward). A galaxy, solar system, star, or planet forms from a larger cloud of dust. As the cloud is pulled together by gravity its radius shrinks. So the angular velocity must increase. These objects all begin to spin faster and faster. That is why we have day and night.

Study Guide and Review Circular Motion, Gravity, & Satellites 22

Advanced Placement Physics Work, Energy, Momentum, and Oscillations

Understanding the relationships between All Forms of Energy, Conservation of Energy, and Work Energy Theorem are extremely essential for success on the AP Exam. The review here is very limited, since this critical information is given substantial emphasis in the course overview. Often energy is either the only way to progress in an AP Free Response problem, or it is the easiest (quickest) way to solve the problem. Students who have a thorough understanding of energy will achieve success on the AP Exam and arrive at college as a more accomplished physics student.

Energy is conserved: It cannot be created or destroyed, but it can change forms.

Can energy be lost? No! Lost energy goes to the environment. A car (system) looses energy due to air resistance, so air molecules (environment) gain energy and move faster. Energy is conserved.

When we did kinematics, problems might have started at 205.65 m from where we were standing. But, to make it easier we said the problem started at 0 m. For energy pretend the system has zero internal energy initially. Then only worry about the other forms of energy. We can then solve for how much the internal energy changes in the problem.

Work An object or problem has a certain amount of energy starting the problem (potential energy due to position and/or kinetic energy due to motion). Remember were pretending internal energy is zero. Think of work as the energy that is added (+W) to the system or subtracted (-W) from the system. If you add a force to something that is standing still it will begin to move a distance. This requires positive work, the product of the force used and distance moved.

W Fs cos Force applied over a distance. Force and distance must be parallel. Note: this does not mean the x axis which cos usually goes along with. is the angle between direction of motion and applied force.

Work is the Area Under the Force Distance Curve: This is the integral of the force distance function in a calculus based course. But, our functions will be simple enough to allow us to use geometry to find the area.

Kinetic Energy K mv12

2 Energy of moving matter. Note that doubling mass doubles kinetic

energy, but doubling velocity quadruples kinetic energy. So you car at 60 mph is 4 times more lethal than at 30 mph.

Potential Energy Gravitational Depends on height. Consider the lowest point in the problem to be zero

height. This isn’t correct, but who wants to add the radius of the earth to every number in the problem. Radius factors out at the end anyway.

U mgh

Electric Energy of a particle experiencing an electric potential. U qVE

Spring U kS 12

2x Energy of a compressed spring with spring constant k.

Capacitor U QV CVC 12

12

2 Energy of capacitor.

Energy of Photons E h pc Used in modern physics

Work Energy Theorem Work put into a system = the change in energy of the system. If you do work on a system you add energy (+W). If the system moves to a lower energy state (dropping a bowling ball on your toe), then the system does work on the environment (-W). It can transfer energy to the environment. The bowling ball has –W while your toe gets +W (toe gets energy) W U EW U sW U W K W Qheat energy etc.

But, what if the energy changes from zero to some amount or from some amount to zero.

W U W U E W Us W K W Qheat energy etc.

Work and work-energy theorem are great for changes in energy, when energy moves from one thing to another or is added or subtracted. But what if a system doesn’t exchange energy with the environment or another system. What if it has certain types of energy in the beginning of the problem, but it has a different amount of each energy at the end?

Study Guide and Review Work, Energy, Momentum, & Oscillations 23

Conservation of Energy Energy cannot be created or destroyed, but can change form and be transferred.

Study Guide and Review Work, Energy, Momentum, & Oscillations 24

f

f

The big picture: i i i i f f fInternal Energy K U Any other energy Energy K U Any other energy However, the problem may only talk about two forms of energy.

As an example: If the problem only involves Potential Energy and Kinetic Energy

then substitute known equations i i fU K U K mgh mv mgh mvi i f f 12

12

2 2

Here are some other possibilities: The first is accelerating charges, the second is for springs.

qV mv qV mvi i f f 12

12

2 2 12

12

12

12

2 2 2kx mv kx mvi i f 2f etc.

The following formulas are specific short cuts usually applied when there are two extremes in the problem.

Gravity mgh mv12

2 A mass m starts at the highest point and ends at the lowest point, or vice versa.

Electric qV mv12

2 When a charge q is accelerated by charged plates with a potential difference V.

Spring 12

12

2kx mv 2 If a compressed spring extends to the equilibrium position, or vice versa.

Electrons h m 12

2v When energy of a photon is transferred to an electron, or vice versa.

Collisions E E E Ei i f1 2 1 2 f Can be used by itself and with conservation of momentum below.

K K K K Ki i f f dissipated1 2 1 2 b gd i In collisions total energy is conserved, but kinetic energy is not.

Unlike momentum, kinetic energy can decrease in collisions which are not perfectly elastic. But where does it go? The deformation of colliding bodies turns into heat (internal energy). So if you take the Kinetic energy at the start, it will equal the kinetic energy at the end plus the amount of kinetic energy dissipated. The energy dissipated is conserved: transfers to internal energy.

Power: Rate at which work is done. Powerful machines do more work in the same time, or the same work in less time.

P Wt

P Fv Work or Energy delivered as a rate of time.

It involves work. Making this another of the very important concepts. As an example you can go from energy to work to power then to voltage and current P IV

Energy and time: Think Power when you see energy and time, Joules and seconds.

Momentum inertia in motion. Measure of how difficult it is to stop an object. p mvImpulse Trade off between time taken to stop and force needed to stop. Ft p Conservation of Momentum Total momentum before a collision must match total momentum after. Not given

on the AP exam. One object might be standing still at the start or after. Completely Elastic Collision: Bounce off completely. m v m v m v m vi i f1 1 2 2 1 1 2 2 f

m v m v v m mi i f1 1 2 2 1 2 b g Inelastic Collision: The objects stick together, mass adds, one velocity.

Oscillations Period T

f

1 Time for one revolution, measured in seconds

Frequency The number of revolution, turns, vibrations, oscillations, rotations per second. Springs

Restoring force displace a spring and it will return to equilibrium, center. F k x k is the spring constant, the minus sign is not mathematical

Period of a spring T mks 2 Depends on mass of object attached to spring and k.

Pendulum Tgp 2 Depends on length of the pendulum and g.

Advanced Placement Physics Thermal Physics

Temperature: Average KE of the particles. Depends on average speed only of particles (atoms or molecules) A bucket of water at 50o has the same temperature as a cup of water at 50o

Thermal Energy: Average KE and the mass of the particles Depends on speed and the mass of the particles. A bucket at 50o has more thermal energy than a cup at 100o. Bucket of $50 bills has more money than a cup of $100’s. While the particles are going faster in the cup, there are so many more in the bucket.

Heat: Transfer of energy between objects that have different temperatures. The direction of heat flow depends on temperature. From hot objects (more energy) to cold objects (less energy).

Thermal Expansion: As objects are heated the molecules move faster and they expand. This is why the liquid in a thermometer rises when heated. It is how a thermostat works. It is why there are gaps in sidewalks, bridges, & railroad tracks. It is why they don’t fill bottles to the top, they might explode if the liquid expands to much.

o T Gives the change in length. The original length is multiplied by o , the coefficient of linear expansion,

and the change in temperature.

How long will a 5 m section of steel railroad track expand ( 612 10 , from table 13-1, p 343) to if it is heated from 15o to 25oC?

65 12 10 25 15 0.0006o T m so it will be 5 0.0006 5.0006m m m

Kinetic Molecular Theory: Gas molecules collide with each other and their surroundings.

1. Large number of gas molecules (N) moving in random directions and a variety of speeds. 2. They are far apart, with the separation distances being vast compared to the diameter of each particle. 3. Molecules obey laws of mechanics. They attract each other, but we ignore this since the speeds and KE are huge. 4. Collisions with each other and container walls are assumed to be perfectly elastic. Conservation of p and KE.

The higher the temperature the faster the molecules move. The particles vary in speed, so we can only measure an average. Half will be going faster and half slower than the average. Average KE is a reflects thisspeed.

32 BKE k T Average KE = 3/2 (Boltzman’s Constant, 1.38x10-23)(Temperature in degrees Kelvin)

We can calculate the speed of the molecules on average

3 3Brms

k T RTvM

The Root Mean Square Velocity = Square root of [(3)(1.38x10-23)(Temp in Kelvin)/(mass)]

Gas Laws Pressure: P F Area Measured in 2N m called a Pascal. Collisions against an object are felt as pressure.

Universal Gas Law: PV nRT (Static cases) or PVn T

PVn T

1 1

1 1

2 2

2 2

(Changing cases)

Pressure is measured in Pascals 51 101300 1 10atm Pa Pa 21 1Pa N m

Volume is measured in meters cubed 31000 1L m

Gas constant 8.31 Jmol K

Static cases: One container under a specific set of conditions.

What is the temperature of 30 mol of gas at 4 atm of pressure occupying 200 L?

PV nRT 5 34 10 0.200 30 8.315Pa m mol J mol K T

Study Guide and Review Thermal Physics 25

Changing cases: One container under changing conditions, or gas moved from one container to another.

Boyle’s Law: Pressure and Volume are inversely proportional. As one goes up the other goes down.

200 L of gas at 4 atm of pressure is moved to a 400 L container, what is its new pressure? (n and T aren’t mentioned, so they must stay the same, and must cancel)

PVn T

PVn T

1 1

1 1

2 2

2 2

1 2PV PV 5 324 10 0.200 0.400Pa m P m 3

Charles’ Law: Temperature and Volume are directly proportional. As one goes up the other goes up.

200 L of gas at 273 K are heated to 373 K, what is the new volume? (P and n aren’t mentioned, so they must stay the same, and must cancel)

PVn T

PVn T

1 1

1 1

2 2

2 2

1 2

1 2

V VT T

3

20.200273 373

m VK K

Combined Law: 200 L of gas at 3 atm and 273 K are moved to a 400 L container and heated to 373 K. What is the pressure? (n isn’t mentioned, so they must stay the same, and must cancel)

PVn T

PVn T

1 1

1 1

2 2

2 2

1 1 2 2

1 2

PV PVT T

5 323 10 0.200 0.400

273 373Pa m P m

K K

3

or

23 2 4273 373

atm L P LK K

Heating and cooling curve Heat: Q Specific Heat Capacity: c, Ability to absorb or retain heat heat.

Q mc T

Latent Heat: L, energy required to break intermolecular forces causing a phase / state change.

Q mL

Latent Heat of Fusion: LF, energy required to melt a solid. Latent Heat of Vaporization: LV, energy required to turn a liquid into a gas.

When phase / state is changing temperature cannot rise since the energy is required for the change.

1

2 3

4

5 6 7 8 9

10

-100

-50

0

50

100

150

200

250

TIME

TEMPCelcius

1-2 Solid Q c m Tsolid

2-3 Melting/Freezing nQ mLfusio

3-4 Liquid Q c m Tliquid

5-9 Vaporizing/Condensing n Q mLvaporizatio9-10 Gas Q c m Tgas

How much energy does it take to melt 200 g of ice at 00C and heat it to 60oC? It has to start as a solid, so it starts at point 2 on the graph. Melting is fusion so L is the Heat of Fusion for water from table 14-2, p. 377. Then it rises in temperature, so it must end around point 4. It is a liquid so you need the specific heat, c, of liquid water in table 14-1, p. 373. (Every substance has different melting plateau, different vaporizing plateau, and different specific heats. Also each substance has different specific heats for the three principle states of matter. This values must be given in chart form or be stated in the problem.)

Melting: Q mLfusion 50.200 3.33 10 66600Q kg J kg J

Heat: Q c m Tliquid 4180 0.200 60 0 50160o o oQ J kg C kg C C J

Total is 66600 50160 116760J

If you start with a solid below the freezing plateau (point 1) and go to a gas above the vaporization plateau (point 10) you must do all five equations using the correct specific heats for all three states and the correct latent heats for fusion and vaporization. The plateaus vary since all substances have different melting/freezing and vaporization/condensation points. The above graph is for water only. You have to use the tables.


Thermodynamics System and environment: Think of the amount of energy in universe as constant. But, energy can be added

to or subtracted from a system (engine, etc.). Energy comes from or goes to the greater universe (environment). Energy can transfer between systems. A ball colliding with another can transfer energy to that ball. Energy can change forms. If you calculate potential energy that energy can change into kinetic energy, electrical energy, thermal energy, etc.

Internal Energy All matter has some amount of energy. Objects feel warm to the touch (internal energy: due to heat content or thermal energy of the object) caused by vibration of atoms that make up the object. If energy is added to an object it can start moving or become hotter. If energy is subtracted it can slow down or become colder. Or it can be a combination of motion and heat. Most of the beginning problems we do are done pretending that no energy is lost to the environment in the form of friction and air resistance. We often assume the energy stays in one form or that 100% is transferred when energy changes form. In real life energy is lost to the environment. Also objects become a little hotter in collisions increasing internal energy. 100% of the energy put into problems will not be available to cause motion, electricity, or power a heat engine. So many of the problems are not realistic. They ask for a theoretical unattainable maximum assuming no energy loss or perfect energy transfer.

Heat Transfer Conduction: Objects touch transferring energy Convection: Fluids (gases & liquids) carry heat as they flow. Hot air or water rise, carrying heat. Convection

currents. Radiation: Electromagnetic radiation, as in infrared frequencies of light. Why does a thermos have an inner

container separated from the outer by a vacuum? Why is the inside reflective?

Zeroth Law of Thermodynamics: Two objects, each in thermal equilibrium with a third object, are in thermal equilibrium with each other.

Internal Energy: It is the sum total of all the energies of the individual molecules that make up a system. Internal energy is the potential thermal energy that all objects contain. U

First Law of Thermodynamics: Statement of conservation of energy.

U Q W : the change in the system’s internal energy. Q : heat added. W : the work done by system. U+Q means heat is added to the system, while -Q means heat is given out by the system. +W means work is done by the system, while -W means work is performed on the system.

Adiabatic: If no heat enters or leaves system, then system is said to be perfectly isolated from its environment. Process that happens so rapidly so that heat does not have time to flow in or out of the system. If a gas filled cylinder is compressed very rapidly, heat won’t have time to escape.

Q U 0 W

W

Change in internal energy is the negative of work done

Isothermal: If temp of the system does not change during process A good approximation is one that proceeds so slowly that temperature rise is negligible. Compress a gas filled cylinder very slowly so that molecules don’t speed up and temperature does not rise.

0U Q Heat added equals the work done.

Isobaric: If pressure is kept constant during the process.

W P V Work to raise a piston in a gas cylinder. W Fd W P Area distance P V

Second Law of Thermodynamics: First Law is a statement of conservation of energy. A ball with PE falls so energy becomes KE. Then it hits the ground causing the molecules to vibrate. The KE is transferred to internal energy and the ball comes to a stop. Have you ever seen the reverse? If internal energy caused the ball to rise energy would still be conserved, so why isn’t it reversible.

“Heat flows naturally from a hot object to a cold object; heat will not flow spontaneously from a cold to a hot object.”


Heat Engines Mechanical energy can be obtained from thermal energy, only when heat is allowed to flow from a high temperature to a low temperature. Example: steam engines, internal combustion engines, and human respiration. Remember thermal energy is not heat (heat is the transfer of energy because of a temperature difference). A piece of cold wood has high thermal energy (fuel) that can be burned. This is true for gasoline and the food you eat. If this energy can be tapped it can do work. But there is always a by-product: heat rising above a fire, the hot exhaust of a car, and human body heat are the by-products.

Efficiency: ratio of useful work done to the heat input.

W

QC

QH

Low Temperature, TC

High Temperature, TH 1H C C

H H H

Q Q QWeQ Q Q

Carnot Efficiency: an unattainable maximum theoretical efficiency.

Carnot imagined a gas cylinder moved from hot to cold and expanding and contracting. He also imagined that all the processes could be done reversibly. He imagined this because it happened so slowly that equilibrium was maintained throughout. Real processes happen fast and involve turbulence thus making reversal along the same path impossible. He showed that even under these ideal circumstances 100% efficiency is impossible.

1H C Cc

H H

T T TeT T

Second Law Revisited No device is possible whose sole effect is to transform an amount of heat completely into work.

Refrigerator

W

QC

QH

Low Temperature, TC

High Temperature, TH

(Heat Pump diagrammed to the right) Pumps heat away from one area to another. You do work to make this happen. The work comes from electrical energy. But, what’s happening to QH? It’s getting bigger. So overall a refrigerators actually produce heat. As an example, in the process of lowering the inside air volume 40 degrees they may raise an equal volume of outside air by 100 degrees. If you fan yourself to keep cool, you do work and generate even more heat.

Entropy

A measure of how much energy or heat is unavailable for conversion to work. This is why heat is sometimes called the graveyard of energy. As Carnot showed not all the heat energy in even a perfect engine can be used to do work.

Entropy is thought of as disorganization. As we use more energy we get more heat as a by-product. Look at oil. It is composed of large well organized molecules. When we burn it to produce work, we get smaller less organized molecules and heat. The small gas by-products of combustion, CO2 and H2O, are more difficult to burn and extract further work from. Gases are less organized than liquids, which are less organized than solids. Perhaps all highly organized molecules will turn into small atoms of gas evenly distributed throughout the universe and they may eventually reach an even average temperature. If there is no heat difference there can be no work. So life and machines can’t exist. This is called the heat death of the universe.

Second Law Re-Revisited Natural processes tend to move toward a state of greater disorder (entropy).

The entropy of an isolated system never decreases. It can only stay the same or increase. And entropy can only really stay the same for idealized (reversible) processes. So it always increases.

The total entropy of any system and the environment increases as a result of any natural process.


pV Diagrams

Fig. 1

Lower temperature

Higher temperature

Isothermal Line

V

p

Boyles Law: Pressure and volume are inversely proportional. This is a part of the ideal gas law and was derived when the number of moles and the temperature remained constant.

1 1 2 2

1 1 2 2

p V p Vn T n T

1 1 2 2p V p V

Isothermal: If temperature is constant the process is termed isothermal. (iso: same, isothermal: same temperature). So a hyperbolic curve is generated under conditions of constant temperature. Pressure and volume are indirectly proportional. Moving up or to the right from the isotherm increases temperature. Moving left or down decreases temperature.

Fig. 2

Temp. Increasing Isobaric line

Work p

V

Isobaric Same Pressure: generated under conditions of constant pressure.

FpA

If we multiply pressure by a change in volume F VA then

32

F V m F dA m

and since W F d , then W p V .

Work is f iV V W p , the area under the pV curve (shaded area Fig.2).

Work is the area under any pV curve. But it would require calculus to accurately solve for the area under the isothermal line in Fig 1. So many of the processes in this class will be represented by straight lines to facilitate the computation of work, heat added, and change in internal energy.

Fig. 3

Isovolumetric line

Temp. Decreasing

V

p

Isovolumetric (Isochoric) Same Volume. An isovolumetric line is generated under conditions of constant volume (Fig. 3). There is no work done, since there is no area under the curve.

The Full Cycle ABCA A to B: p is constant, so this is an isobaric process. The temperature

increases by going to the right, so is positive. Plug T T into the

Q nc

Fig. 4 V1

p2

C

B A

V

Work

p1

T where is used, Q n . Then Q must also be positive

(heat is added) to make this step take place. The temperature increase also causes an increase in . The volume is increasing while the gas expands,

so W is positive. W p , . Work is the area under the AB curve. (Shaded area, Fig. 2)

pc

Pc T

2 2V

W pU

V 1V

B to C: Isovolumetric, V is constant. The equation VQ nc T

U

applies.

Temperature is decreasing, so is negative. Q must also be negative to

make this step take place. If temperature decreases, then

T decreases

(negative). VcU n T also applies. The pressure drops even though volume stays the same. The drop in

internal energy means the molecules of gas slow down. And slower molecules exert less pressure. W 0 . The area under the curve is zero.

C to B: Isothermal, so . As a result 0T Q nc T and VU nc T

Q both become irrelevant. The First Law

of Thermodynamics simplifies to WU Q W . Work is the area under the CA curve and it is

negative, since the gas is compressed.

ABCA: The Net Work done is the stripped area bounded by ABCA (Fig. 4). Upon returning to A the temperature is the same as it was at the start, so for the cycle. So W0U Q for the whole cycle.


Carnot Engine pV Diagram

2Vo

po

2po

B

D C

A

Isothermal Curve at TH

QH

QIsothermal Curve at TC

Vo

A to B: Isothermal (Done slowly: Heat added has time to convert into work without raising internal energy of the gas)

Lies along the isotherm. Temperature is constant. AT 0U U Q W so ABW Q

Work is positive since the gas is expanding. The gas pressure starts out high and this pressure causes the volume to expand. If this process is done slowly the temperature of the gas does not change.

1 1 2 2

1 2

p V p VT T

2 o o o op V p V

T T

2 This process is HQ , so AB HW Q .

B to C: Adiabatic (Done rapidly: Short time period prevents heat from being added, so Internal energy turns to work) Drops from the AT isothermal line to the . So temperature and internal energy are both decreasing. But no heat is

added.

BT

0 Q so U Q W BCW U . Work is positive since the gas is expanding. All the

work comes from internal energy. If work is increasing, then internal energy must be decreasing. The gas pressure starts out high and this pressure causes the volume to expand. But while the gas pressure appears

to be cut in half to 2op the volume moves from to about . Plugging in to the ideal gas law shows that

temperature cannot be the same.

2 oV

3 oV

?????

2 2o o o

A isothermal

3 op V pT T

V

C to D: Isothermal (Logic is similar to AB above, but work will calculate negative, gas is being compressed.) Lies along the isotherm. Temperature is constant. BT 0U and CDW Q . The gas pressure starts out

low and this pressure causes the volume to compress. This process is , so CQ CD CW Q .

D to A: Adiabatic. (Logic is similar to BC above, but work will calculate negative, gas is being compressed.)

Rises from isothermal line to the BT AT . So temperature and internal energy are both increasing. But no heat is

added. 0Q so DAW U . All the work goes into increasing the internal energy of the gas.

The Cycle ABCDA: This is a heat engine. The Net Work done in the entire cycle is the sum of the areas under the AB, BC, CD, and DA curves. AB and BC are positive work since the gas expands doing work by the system. CD and DA are negative work since work is done on the engine and the gas is compressed. In other words, the Net Work is the area enclosed by ABCDA. If it returns to the same temperature at A, then during the entire process

and W , the net work must have come from the net heat added 0U Q H CW Q Q . This would be for a

reversible ideal engine (Carnot ) which does not exist. The ideal efficiency for this reversible, Carnot, engine is

H Cc

H

T TeT

The real efficiency is H C

H H

Q QWeQ Q

with HQ being generated during the AB process on the

HT isotherm and being generated during the CD process on the . CQ CT

Refrigerators: Run in reverse. Counterclockwise. ADCBA. Follow the steps above backwards and change the signs.


Advanced Placement Physics Electricity and Magnetism

Electrostatics: Not moving. Deals a lot with point charges, small q. Can calculate the force between two point charges and the strength of the electric field created by point charges. If there are a number of charges you simply do the calculations for each charge separately and then add the results, the principle of superposition. However, never plug in minus charges for q. Always plug in the positive magnitude for the charge whether positive or negative. Use the signs on the charges to tell you if they are moving right (positive) or left (negative). Assign each completed calculation of F or E the appropriate sign and then add the F’s for the total force or add the E’s for the total electric field strength.

1 22E

q qF kr

1 22

q qF kr

EFEq

EF Eq 2

qE kr

2

qE kr

Remember small q is for a point charge, like a small group of electrons or protons, or even an oil drop. Large Q (similar to heat energy, so watch out) is for lots and lots of charge, like that stored on charged plates.

Gravitational Fields Electric Fields

* 1 22g

m mF Gr

* 1 22E

q qF kr

gF mg * EE

FE Fq

qE Combine the above equation to create an new equation

1 22

m mmg Gr

Combine the above equation to create an new equation

1 22

q qqE kr

Simplify

2

mg Gr

Simplify

2

qE kr

Fg, Force of gravity is felt in a gravitational field. m, mass causes gravitational fields g is a way to assess the strength of the gravity field. Double mass: F (force) and g (field strength) double. g Distance follows the inverse square law.

Double r: Fg (force) and g (field strength) are 1/4. Halve r: F (force) and g (field strength) are quadrupled. g

FE, Force of electrostatics, is felt in an electric field. q, charge, causes electric fields. E is a way to assess the strength of the electric field. Double charge: F (force) and E (field strength) double. E Distance follows the inverse square law.

Double r: FE (force) and E (field strength) are 1/4. Halve r: F (force) and E (field strength) are quadrupled. E

Superposition What is (a) the force of gravity and (b) the acceleration of gravity on a 1000 kg space ship located half way between the earth and the moon? Both are pulling on it so find each F and g separately.

(a)

Study Guide and Review Electricity & Magnetism 31

1 2m m 2gF G

r

245.98 1011

28

10006.67 10 10.2

1 2 3.84 10gF earth N

2211

28

7.4 10 10006.67 10 0.13

1 2 3.84 10gF moon N

As drawn: earth pulls left, negative

moon pulls right, positive.

Add left, so toward earth.

(b)

10.2 0.13 10.07N N N

2

mg Gr

2411 2

28

5.98 106.67 10 0.0102

1 2 3.84 10earthg m s

2211 2

28

7.4 106.67 10 0.00013

1 2 3.84 10moong m s

As drawn: earth pulls left, negative

moon pulls right, positive.

Add 20.0102 0.00013 0.01007 m s left, so toward earth.

Superposition What is (a) the force of electricity on a +1 C charge located half way between a –3 C charge and a +2 C charge separated by 2 m? (b) What is the electric field strength at this location due to the – 3 and +2 C charges only? Both are pulling on it so find each F and g separately.

(a) 1 22E

q qF kr

9 92

3 19 10 27 10

1 2 2E

C CF N

m

9 92

2 19 10 18 10

1 2 2E

C CF N

m

As drawn: –3 charge attracts +1 charge to left, negative.

+2 charge repels +1 charge to left, negative.

Add left toward –3.

(b)

9 927 10 18 10 45 10N N 9 N

2

qE kr

9 93 2

39 10 27 10

1 2 2from

CE N C

m

9 92 2

29 10 18 10

1 2 2from

CE N C

m

As drawn: –3 attracts positive test charge left, negative. +2 repels positive test charge left, negative.

Add 9 9 927 10 18 10 45 10 N C left toward –3.

E M

-3 +2


Gravitational Field acts downward. Gravity Field forces masses to move. Point A has less potential energy than point B. To lift it from A to B you must increase energy, add

energy. You must do + W Work energy theorem says that W = Energy. Moving from A to B increases U. The increase (change) in U equals the work. U = 0 at the ground, the lowest point.

Release the mass at B. Mass accelerates toward ground. The velocity increases so, K increases while U decreases. The mass can do work on the way down.

Electric Field is based on a positive test charge Electric Field acts away from positive & toward negative.

Electric Field forces charges to move. Point A has less potential energy than point B. To move it from A to B you must increase energy, add

energy. You must do + W Work energy theorem says that W = Energy. Moving from A to B increases U. The increase (change) in U equals the work. U = 0 at the ground, the lowest point.

Release the charge at B. Charge accelerates toward negative, away from positive. The velocity increases so, K increases while U decreases. The charge can do work along the way.

Mass falls down, and needs work to go up. But, Electricity has positives and negatives. Negative charges are the opposite. Work is needed to move them toward ground. They have higher UE closer to the negative plate. They do work on their way to the positive plate.

Similarities causes gravity m measure of field strength g distance above ground h

q causes electricity

E measure of field strength d distance above ground

Gravitational Potential Energy

Gravity field is very weak and its change is irrelevant. gU mg h

h gU mg

Work Energy Theorem W Energ y

d

W mg h

Electric Potential Energy

Electric field is very strong and changes with distance. EU qE

EU q Ed

Work Energy Theorem W Energ y W q Ed

gU m g h

dNo equivalent ? g h

EU q Ed

Electric Potential * V E VEd

* EU qV

From above U q

From above

Combine

Simplify

E Ed

2

qE kr

2EqU q k dr

* 1 2E

q qU k r

2

qE kr

VE d

2

V qkd r

qVr

k * i

i i

qV kr

Electrostatic Equation Summary 1 2

2Eq qF kr

EFEq

1 2E

q qU qV kr

VEd

i

i i

qV kr

2

qE kr

(not given)

Remember superposition can be used with a number of these even though only one is shown with a sum symbol.

+

Ground h= 0

B

A g AU mgh

g BU mgh

A

Ground d = 0

+ + + + + + + + + +

B +

?EU

- - - - - - - - - - -

Voltage: It is a way to express the difference (change) between potential energies of two charged plates or two parts of an electrical circuit.

Confusing Terms Electric Field E Electric Potential Energy Potential Energy U Electric Potential Potential Difference Potential V

The variable Voltage V, measured in the units V, for Volts

What’s the pattern? If it contains the word energy it is U. If it contains the word potential without the word energy it is V. Also watch out for the big V for voltage and the small v for velocity. Sometimes you use them in the same problem.

Electric Field Lines An imaginary way to view the electric field, similar to the elevation lines on a map. On maps, steep slopes are indicated by lines close together. In a similar fashion a concentration of electric field lines indicates higher field strength. The lines are based on the direction a positive test charge will go, so field lines leave positive charges and enter negative charges. Field lines leave and enter surfaces perpendicular to the surface. On the figure at the right the electric field lines are closest between the two plates. They are also virtually parallel in the center of the diagram.

Equipotential Lines: Lines of equal electric potential energy, U. If a charge is moved along an equipotential line it does not change its potential energy. If you hike in the mountains along the contour lines you always stay at the same height above sea level, so you don’t change your gravitational potential energy. The equipotential lines are perpendicular to the field lines. The two dotted lines in the diagram are two examples of the many possible equipotential lines.

Faraday Cage Any enclosed metal structure, even one made of chicken wire, acts as a Faraday Cage. Charges pile up on the outer surface of the metal enclosure. Due to a combination of q and r at any point within the box, cylinder, sphere, etc. the electric field is zero inside. E = 0. This is why you are not electrocuted in a car or airplane if it is struck by lightening.

Capacitors or charged plates: Use large Q. Capacitors are a way to store electrical charge. They will hold an electrical charge as long as a voltage (potential difference) is applied to create the static electric build up on the plates, or until the plates are discharged by providing a path for the electrons to flow from one plate to the other. Think of Capacitance, C, as the capacity of the capacitor to hold the charge. So it is the amount of charge divided by the potential difference that creates the charge build up. Since the charges would prefer to stay on the ground, U = 0, and they have been moved against the electric field to a higher U, work must have been done by some kind of electrical pump to put them there. If work was done and they’d like to fall back to the ground (negative plate) then they have potential energy, Uc, (C for capacitor).

C QV

U QV CVc 12

12

2

You can think of electricity as water. If you pump water up to a water tower it has high potential energy. If you turn off the pump it will flow back to the ground. A capacitor is an electrical water tower where charge is stored temporarily until it is needed. So if the electrical circuit needs to flush all its toilets simultaneously the capacitor discharges. It is refilled for the next big flush. Q is then the amount of water pumped into the tower. V is the potential difference between the height of the tower and ground level.

Why is while EU qV 12cU Q V ? As you move more electrons from one plate to the other the capacitor it becomes

more charged. The first electron moves easily. But the second is repelled by the first, and the third by the first two. It becomes harder and harder to put more and more electrons on the plate since repulsion becomes higher and higher. Also the positive plate becomes more electron challenged, and pulls the electrons overloading the negative plate back to it. So the amount of charge moved starts out high and declines to zero. Average the highest with zero and you get half. If you pump water up to a water tower it goes fast at first. But, the weight of the water filling the tower begins to make it harder to pump, until the force of the water in the tower pushing down equal the force of the pump pushing up. Average the fast pumping at the start with zero pumping at the end, and you get half.

Point charges are not affected, since they are autonomous and not physically attached to another plate.


Current: The flow of electricity. Current, I, is assumed to be positive due to an old convention (Thanks a heap Ben!). We now know that the electrons actually flow, but we still refer to current as positive. So if we want to talk about actual electron flow we must say electron current or negative current, etc. The word current by itself implies positive current flow. Positive current flow follows the direction of the electric field, so this negative flow is counter to the electric field.

I Qt

It’s a rate (divided by time). But, it is unlike velocity where we measure the distance the car went. Instead we

stand still and count how many charges, Q (charge represents an amount of charged particles), go by. Big Q since we’re counting lots-o-charge.

Resistance: When current flows the wires have internal properties that slow the current. When water flows down a stream it runs into rocks, sand, salmon on their way to their grave, etc. These act like friction slowing the water down. Resistance is like friction countering the forward progress of the electrons. Conductors slow the current very little, while insulators have a lot of resistance and slow it drastically. In addition to the wires, all appliances, and even the sources of electricity have resistance. There are also actual resistors built into circuits to help control the amount of electrical flow to exact quantities in various parts of the circuit.

RArea

Resistance is a function of resistivity, , wire length, , and cross sectional area.

Resistivity, , is like the coefficient of friction. It is given since it is derived by experimentation. Different materials

have different natural resistances. Gold has very low resistance, copper is pretty good, and plastic is not so hot.

So let’s worry about length and cross section of wire.

What kind of water pipe would provide the least friction, allowing water to pass through more easily? a. long and narrow b. long and wide c. short and narrow d. short and wide

Look at the equation above. Try to make R as small as possible, by changing and Area. Make length small and area big, so the answer is d. The longer the wire the more resistance it has. And resistance is like friction. What type of energy does some of the KE turn into when an object is slowed by friction? Heat. What kind of energy is produced when charges are slowed down by resistance? Heat. What do you feel when you touch an electrical component, like a stereo? It gets hot. Heat loss is disadvantageous. You’re losing valuable energy, wasting money on you electrical bill, and increasing entropy. So minimizing resistance is usually a good thing. But, sometimes you need to create resistance if you have components that can only handle certain amounts of power, energy, voltage, etc. In addition the wires themselves act like resistors. One goal in circuit design is to shorten the wires between components to minimize power loss and heat. How much energy is lost to heat in the high tension wires from Hoover Dam to California?

Two important equations for circuits, and two equations (not given) but that can be derived from these.


V IR P IV 2 P I R 2VP

R

DC Circuits: Direct Current, meaning it travels in one direction only following the electric field lines. The battery or power supply pumps charges creating a potential difference (voltage) between the ends of the circuit. You have a positive terminal (positive plate) which is a region of high potential energy. At the other end of the circuit (wires and components) is a negative terminal (negative plate) which is a region of low potential energy. Positive current (positive charges) want to fall toward the ground through the potential difference toward the negative plate. This is the direction of the electric field. So the potential difference between the positive and negative plates creates the electric field that guides the charges through the circuit. (Just remember the electrons really flow, so its all backwards. But, mathematically you get the same numbers).

Water Analogy: A pump (battery or generator) pumps water (charge) from the ground (negative plate) up to the top of the water theme park (positive plate) The water (charge) wants to follow the gravitational field (electric field) back to the ground. But we’ve constructed a series of tubes (wires) for the water (charge) to pass through on the way to the ground. Because the water (charge) is losing potential energy as it falls, and because energy must be conserved, the potential energy must be turning into another form of energy. It is turning into the kinetic energy of the water (charge). If the water (charge) is run through a paddle wheel (appliance, light bulb, etc.) it can turn the wheel thus doing useful work (browning toast, lighting up you desk lamp). Unfortunately, some of the water is slowed going through the wheel (appliance, lamp, etc.) and this friction (resistance) creates heat. Also our contractor who built the park used inferior materials that impede (high resistivity) the flow of water (current). So the water (charge) is slowed in the tubes (wires) as well. Fortunately the contractor did note that the paddle wheel (appliance, lamp, etc.) was very small and fragile. And while the plan placed the paddle wheel (appliance, lamp, etc.) in a very steep section of pipe (high potential difference) where the flow of water (current) was very high the contractor installed a metal grating (resistor) in front of the paddle wheel (appliance, lamp, etc.) to slow the amount of water flow (current) to a level that the paddle wheel (appliance, lamp, etc.) could handle.

Circuits Containing Resistors Series: All resistors are in line. Resistors are like sections of wire, designed to slow current. Let’s examine the resistivity of two sections of wire placed in series, or end to end.

RArea

is doubled, but cross sectional area stayed the same. So R doubles. If there were three wires R would triple. This

makes sense. Lets pretend they make your commute on the freeway longer, but they didn’t build more lanes to widen the road. So you experience the same traffic (resistance) for two or three times as long.

So in series Resistance adds s ii

R R or 1 2 3 ...sR R R R

Now let’s examine the resistivity of two sections of wire placed in parallel, or next to each other.

RArea

stays the same, but cross sectional area doubles. It’s more complicated than above. Area is in the denominator. If area doubles R is cut in half. If there were three wires R would be cut in third. This makes sense since the current and a bigger pipe to flow through. Its like they expanded the freeway from four lanes to 8 or even 12. You travel the same distance as before but now have less traffic congestion.

So in parallel 1 1

p iiR R or

1 2 3

1 1 1 1 ...pR R R R

Please don’t solve for 1/R. Remember to invert you final answer.

Current and Voltage in Circuits: Think of current as traffic and resistors as less lanes Series Current stays the same (resistors in line slow traffic in the whole circuit)

1 2 3 ...SI I I I

Voltage adds (cars are all pushed down a single path) 1 2 3 ...SV V V V

Parallel Current adds (current can choose paths, but the total must split between paths available)

Voltage stays the same (cars have an equal pressure down any path) 1 2 3 ...SI I I I

SV V1 2 3 ...V V

Circuits containing Capacitors The rules for capacitors are opposite the rules for resistors. But similar problem solving techniques apply. 1 1

s iiC C P i

iC C

Magnetism Similar to electricity, in that unlike poles attract. Different in that, separate poles cannot exist by themselves. Magnetism and Electricity are interconnected. Electric fields can influence magnets, and magnetic fields can influence moving charged particles and current carrying wires.

B is a measure of magnetic field strength, analogous to E for electric fields, and g for gravitational fields.

F qvBB sin charged particles (small q, point charge) traveling (velocity, v) in a magnetic field (B)

F BIB sin influence of a magnetic field (B) on a current (I) carrying wire of a certain length ()

Right Hand Rule Fingers (plural) represent the magnetic field lines (plural). Thumb represents the charged particles velocity, or the direction of current flow in a wire. You want

to hitchhike with the charged particle or current flow in the wire. Palm, represents the direction of force. A slap from the palm of the hand is a force.

All are perpendicular to each other. The force on a charged particle in a magnetic field is always perpendicular, so no work is done in this case. They ask this on just about every AP test somewhere.

A charged particle flying in a magnetic field will move in a circular path.

What is causing the circular motion? FB . So C BF F m vr

qvB2


If magnetism can causing a current carrying wire to move, then could moving a current carrying wire in a magnetic field cause current to flow?

Electromagnetic Induction: A loop of wire moving in a magnetic field experiences a change in flux. B Area Flux: The strength of a magnetic field moving through an area of space, such as a loop of wire.

To generate electricity you need a changing flux. Take a loop of wire and move it through or rotate it in a magnetic field. The area is the area of the loop of wire.

avg

m

t

Induction: The changing flux, means the charged electrons in the wire are experiencing a changing

magnetic field. This causes them to be deflected, and since they are bound by the wire in the loop they travel down the wire. The minus sign in this equation is a reminder that the moving electrons create their own magnetic field (Moving charge is the basis of electromagnetic fields), and that this field is opposite in direction to the magnetic field causing the flux. This is Lenz’s Law. It means you use the right hand rule as before, but you reverse the direction of current flow in you final answer. Remember you only do this reversal in electromagnetic induction.

If you have a bar moving along two wires through a magnetic field you can use the following equation

B v is the length of the bar, and is the velocity of the bar. vThis is derived using the formulas above.

avg

m

t

B Area avgB Area

t

avgB d

t

avgdBt

B v

Electromotive Force, emf: Induction actually creates electromotive force , which really isn’t a force. Every device that generates electricity has resistance, known as internal resistance. So in a way emf is the amount of voltage you could produce if there were no internal resistance in a battery, power supply, generator, or wire loop creating electricity.

So the equation for voltage induced is actually V emf resistance internal .

But, in the problems you are given internal resistance will usually be negligible, so voltage and emf are essentially the same. In AP B this is normally the case. But, not in college. 0V emf

If it is not zero, just use you’re rules for series and parallel and treat the internal resistance as an ordinary resistor that happens to be right next to the battery or power supply.

Watch these. Q vs. q E in electricity is electric field, later it is energy. UE is the electric potential energy or potential energy V is the potential difference, electric potential, potential, or voltage V vs. v The magnetic field does no work on charged particles since everything is perpendicular. Work, however is very useful

EW U q V 21 12 2cW U QV CV

P IV Wt

2 WP I Rt

2V WP

R t

And a whole bunch of combined equations that I can’t even begin to list.

Conservation of energy They love questions with charged particles moving between charged plates.

E f E ff fU K U K 2 21 12 2

qV mv qV mv

212

qV mv If it is not moving at the beginning and then uses up all the PE converting it entirely into KE


Circuits Name _________________________

Resistors & Capacitors WS ___ Date ______________ Per _______

V I R

Battery V A

R1 V 2.00 A 4.00

R2 V A 6.00

R3 V A 8.00

1.

V I R

Battery 12.00 V A

R1 V A 2.00

R2 V A 4.00

2.

V I R

Battery V A

R1 V 2.00 A

R2 V 3.00 A 12.00

R3 V 1.00 A

3.

V I R

Battery 12.00 V 2.00 A

R1 V A 6.00

R2 V A 4.00

R3 V A 15.00

4.

V I R

Battery 24.00 V A

R1 8.00 V A

R2 V 4.00 A

R3 V 2.00 A

5.

R1

R

R3

RR

RRR

R

R

R

Study Guide and Review Worksheet: Circuits 37

V I R

Battery 50.00 V 5.00 A

R1 V 2.00 A

R2 25.00 V A

R3 10.00 V A

R4 V 3.00 A

6.

V I R

Battery V A

R1 12.00 V A 2.00

R2 V A 4.00

R3 24.00 V A 4.00

R4 V A 8.00

7.

V I R

Battery 46.00 V A

R1 V 3.00 A

R2 V 4.00 A

R3 V A 6.00

R4 V 3.00 A

R5 V 7.00 A

8.

R

R

R

R

R3

R5

R1

R2

R4

R5

R1

R2

R3


V I R

Battery V A

R1 V A 20.00

R2 10.00 V A

R3 V A 4.00

R4 V 1.00 A

R5 V 5.00 A 5.00

R6 V A 6.00

9.

V I R

Battery 30.00 V A

R1 6.00 V 3.00 A

R2 V 2.00 A

R3 V A 3.00

R4 V 1.00 A

R5 8.00 V A

R6 V A

10.

V I R

Battery V 12.00 A

R1 V A

R2 18.00 V 2.00 A

R3 V A 3.00

R4 V A 4.00

R5 V A 2.00

R6 V 8.00 A

R7 6.00 V A

11.

R

RR4

R6

R1

R2

R3

R3

R4

R5

R1

R2

R6

R1

R5

R6

R2

R3

R


12. The battery generates 24 V of emf and has an internal resistance of 1.0 . R1 = 4 , R2 = 2 , R3 = 4 , and R4 = 6 .

a. What is the current through R2? __________


b. What is the voltage through R4? __________

c. How much power does R1 consume? __________

d. What is the voltage produced by the battery? __________

13. The following circuit contains four capacitors, each with 120 nF of capacitance. What is the total capacitance between points A and B? __________

14. The following circuit contains four capacitors, each with 50 nF of capacitance. What is the total capacitance between points A and B? __________

B

A R1

Rr

R

R

A B

B A

Advanced Placement Physics Waves and Optics

Energy: E Waves transport energy.

Vibration / oscillation: Something must be vibrating / oscillating in order to create a wave. Medium: Waves must travel in a medium with one important exception. Electromagnetic waves are the only type of wave that do not require a medium at all.

Frequency: f Number of vibrations, oscillations, cycles, revolutions, etc. that take place each second.

Period: 1T f Time for one complete vibration / oscillation.

Wavelength: The length on a single wave. Measure to the same point on the next wave.

Velocity: v f Wave velocity depends on the elasticity of the medium. Sound travels faster in metal

than in water and faster in water than in air. Light, however, is unusual. It is fastest in a vacuum and slows slightly in air, and to a greater extent in water.

Amplitude: A Maximum displacement from the equilibrium position (midline on the graph).

Transverse Wave: Particles vibrate in a direction perpendicular to the wave direction & velocity. Longitudinal Wave: (also Compression, or Shock ) Particles vibrate in a direction parallel to wave direction & velocity. Sinusoidal: When a vibrations displacement is graphed against time a sinusoidal function is plotted. It is the

graphical representation for any wave phenomenon, and looks like a transverse wave. However, any wave, even longitudinal waves, follows the same sinusoidal pattern.

Pulse: A single wave.

Wavelength

Amplitude

Continuous Wave: A series of equal pulses equally spaced moving together. Standing wave: When a continuous wave strikes a barrier and reflects back on itself it will create an interference

pattern (see interference below). If the phase (see phase below) of the reflected wave is exactly opposite to the incoming wave they will superimpose creating a standing wave.

Node: A point on a standing wave that does not move at all.

Amplitude

Wavelength

Speed depends on the mediums elasticity. When a wave travels from one medium to a different medium the speed & wavelength change. However the frequency remains the same. Interference: When two or more wave meet, the amplitudes add.

In phase: Waves are in phase when they have the same wavelength and the crests are aligned.

Out phase: Waves are out of phase when they the crest on one wave aligns with the trough of another.

Constructive Interference: If the waves are in phase you add them to construct a larger amplitude.

Destructive Interference: If the waves are out phase you add them to destroy the amplitude. The waves shown have the same amplitude and wavelength, but any kind of wave can interfere, so different amplitudes and wavelengths can result in many unique new wave functions.

Sound: The speed of sound in air at 25o C is 343 m/s (often rounded to 340 m/s). The speed of sound changes with temperature since the density and elasticity of air change as temperatures fluctuate.

Pitch: Frequency Loudness: Amplitude

Sound waves can originate from vibrating strings or in tubes. This is the basis for musical instruments. There are two types of tubes: those open at both ends & those closed at one end.

Study Guide and Review Waves and Optics 41

Strings: Only multiples of ½ wavelengths can fit on a vibrating string that is held fixed at each end.

node wavelength

Open Tubes: Same as strings, multiples of ½ waves. But the waves look a little different, since the ends aren’t fixed. Closed Tubes: Closed tubes hold multiples of ¼ waves.

1/2 wavelength 1/4 wavelength 2/2 wavelength 1/2 wavelength

Adjustments to the velocity equation. The simplest case is the minimum number of wavelengths. So we will work with the fundamental, strings or open tubes that have a ½ wavelength, and closed tube holding ¼ wavelength.

Normal wave velocity v f

Strings: 2v f L If ½ wavelength fits on the string, then 2 2String Length L .

Open tubes: 2v f L If ½ wavelength fits in the tube, then 2 2Tube Length L .

Closed tubes: 4v f L If ¼ wavelength fits in the tube, then 4 4Tube Length L .

To adjust for more than ½ wavelengths in strings & open tubes, and ¼ wavelengths in closed tubes you divide L by the

number of nodes. Example: This tube contains two nodes. 2Lv fn

More on velocity: Sound also follows the normal velocity equation v d t . You can time the distance to lightening by

counting the seconds between the flash and the thunder. But, if you’re timing sound that makes a round trip (like an echo, or sonar) you have to divide your final answer by 2.

Resonance: Everything has a natural vibration frequency. If you can match the natural vibration and add more wave energy at the right frequency and wavelength you can shatter the object. Breaking a crystal glass with your voice, or the Tacoma Narrows Bridge are examples.

Light: Travels in packets of energy, called Photons.

Electromagnetic Radiation: It can travel through a vacuum since it is a self-supporting electromagnetic phenomenon. It consists of two perpendicular waves, one electric and one magnetic. The electric field wave generates a magnetic field wave that is perpendicular to it, and the magnetic field wave generates an electric field wave perpendicular to it. After they are emitted by the source they recreate each other and support each other allowing EM waves to travel through a vacuum free of their original source and without a medium. We see only visible light, which is a very small portion of the entire electromagnetic spectrum. The entire spectrum from weakest to strongest is:

Radio Waves Microwaves Infrared (IR) Visible Ultraviolet (UV) X-Rays Gamma Rays Long wavelength Short Wavelength Low frequency High frequency Low energy High energy

In a vacuum they travel at 3x108 m/s. When they strike an object they can interact with the object in four principle ways.

Absorb: The wave energy is transferred to the object and its internal energy U goes up, as the does the temperature.

Scattering: The incoming light can be absorbed briefly, exciting the electrons in the atoms. The excited electrons move to higher energy states, but quickly move down to lower energy levels. The electrons may drop to various intermediate energy levels on their way back to the ground state, thus emitting photons with new frequencies.

Transmit: The waves may pass through an object, like visible light through glass or x-rays through your body.

Reflect: They may bounce off of the object.

To see light the waves must be aimed straight into our eyes to excite the photo-receptors at the back of our eyes. The colors we see are the waves of light that reflected off of the object or that were scatted by the object. The colors that are not present are the ones that either passed through the object or were absorbed by the object. Grass is green because it absorbs red and blue light needed for photosynthesis, and it reflects the unnecessary green wavelengths. The sky is blue due to scattering of the white light from the sun by particles in the earth’s atmosphere.


Diagramming Waves Sinusoidal: If you look at a wave from the side you see a sinusoidal pattern. Wave Front: If you look at waves from above you see the crests moving parallel to each other. Ray: The easiest method. You use one or more vectors to indicate the direction the waves are moving in. Even though light radiates radially from a source in rays, light arriving from a distant source arrives very nearly parallel. So for simplicity the waves of light are assumed parallel. A distant source does not need to be very far away for visible light since the wavelengths are measured in nanometers.

Wave Fronts Rays or or

Reflection Law of reflection i r . The angle of incidence and angle of reflection are measured in relation to the normal. A

normal is a line perpendicular to the surface (as in Force Normal which is perpendicular to the surface). It is normally shown as a dashed line. To simplify the diagram a single ray of light is shown as opposed to wave fronts of light. Each individual ray follows the law of reflection.

Single Ray, smooth surface Parallel rays, smooth surface Rough surface, Diffuse reflection On a smooth surface such as a mirror the incident parallel rays of light reflect parallel and the image formed is identical to the object. But on a rough surface the incident parallel rays are sent in all directions and the image may be diffuse (fuzzy), or not form at all.

r i

Converging Spherical Mirror

The law of reflection holds. You need a normal perpendicular to the surface. A perpendicular line to a sphere will pass through its center. When incident parallel rays arrive from a distant light source the angle of reflection will equal the angle of incidence. The normal bisects this angle. Therefore, the rays of light will converge on a point half way between the curved surface and the center. The point of convergence is called the

focus or focal point. 2F r and 2C F

C = 2F F

Transmitting Light The speed of waves is dependent on the medium the wave travels in. Electromagnetic waves are the only waves capable of traveling in a vacuum. And unlike other waves they travel fastest in a vacuum and are slowed by other

mediums. The speed of light in a vacuum is 83 10c m s . To compare the speed of light in different mediums

an Index of refraction was devised, cnv

. This index is a comparison value (other comparison values in the

course have been the coefficient of friction, coefficient of linear expansion, and resistivity.). If the speed of light in glass is slowed to 2x108, the index of refraction is 1.5. The index of refraction for light in a vacuum is 1.00. So the

index can never be less than one. The index of refraction for air is 1.0003, which rounds to 1.00airn .

Refraction Light Traveling through mediums with different densities v f

From a less dense to more dense medium From a more dense to less dense medium Light moves slower Light moves faster The frequency is unchanged The frequency is unchanged So wavelength is shorter So wavelength is longer So light bends toward the normal So light bends away from the normal


Snell’s Law

1 1 2sin sinn n 2 Given the speed in one or both mediums the indices of refraction can

be determined. Or one or both angles can be determined experimentally. With three pieces of information the fourth can be determined mathematically. The diagram to the right shows light moving from a less dense medium to a more dense medium. n1 and 1 go with the incident medium while n2 and 2 go with the refracted medium.

Total Internal Reflection A special case of Snell’s Law. If the incident angle is of a certain size it will result in a 90o angle of refraction. This incident angle is called the critical

angle c . At incident angles larger

than the critical angle the light reflects back into the substance. So the light at the critical angle or greater is totally internally reflected.

1 1 2sin sinn n 2

1 2sin sin 90ocn n

If medium one is the incident ray then 1 is the critical angle and 2 is 90o.

1 2sin cn n 2

1

sin cnn

Lenses and Mirrors Mirrors reflect light and lenses transmit light. They both fall into two main categories. Converging lenses and mirrors converge parallel rays of light on the focal point. Diverging lenses and mirrors diverge parallel rays of light away from the focus. The shapes of lenses and mirrors fall into two main categories, convex and concave. Concave has a cave shape.

Converging Lense Diverging Lense Converging Mirror Diverging Mirror Convex Lense Concave Lense Concave Mirror Convex Mirror Note: Converging and Diverging are the important terms. The shapes are secondary. The terms converging and diverging dictate the information needed to do the mathematical steps outlined on the next page.

Images: Two types of images are formed by light interacting with lenses and mirrors. To find the location and diagram the size of an image you draw the rays of light and look for their intersection. When rays of light converge it is easy. You follow the path of the light, the forward ray trace. But, when rays diverge (separate) the forward ray traces will not intersect. So you must draw a back ray trace to the other focus. The forward trace is drawn as a solid line, while the back ray trace is drawn as a dotted line.

Real Image: Can be projected on a screen. Results from the intersection of forward ray traces & is always inverted.

Virtual Image: Cannot be projected on a screen. Results from the intersection of back ray traces & is always upright.

Ray Tracing: See the worksheet on ray tracing for details on all the special cases of the lenses and mirrors. Ray tracing follows a set of rules. There are many variations, but I believe the list below will cover most if not all cases.

Rules for Lenses: Remember light goes through the lens. Rays arriving parallel to the midline, either converge on the far focus or diverge from the near focus. Rays that go through the center of the lens keep going straight.

Rules for mirrors: Remember light bounces off the mirror. Rays arriving parallel to the midline, either converge on the near focus or diverge from the far focus. Rays drawn through the object and the focus, go out parallel. Rays that go through the center of curvature bounce (C = 2F) bounce straight back.

n2

n1

2

1

Less dense medium o 90

c

is larger than c. Rays are reflected


Geometric Optics

2rf The center of curvature is located at 2f. So the focal point is half of the radius.

1 1 1

o if s s Shows the geometric relationship between the focal length, object distance, image distance.

i

o o

h sMh s

i Relates the magnification to the height of the object and image, and the distance to each.

The equations are simply a matter of identifying correct variables and solving. Conversions to base units are not even necessary. In the first equation all variables have the same units and you are merely adding them. The only conversions needed are in cases where you lack unit agreement. In optics centimeters are commonly used. Millimeters may be seen on occasion. In the second equation units cancel providing they are the same.

However, you must know when the variables are positive and when they are negative.

f Converging lenses and mirrors are positive. Diverging lenses and mirrors are negative.

os Object is always positive, so the object distance is positive.

is Positive if the forward ray traces intersect to create the image. Negative if generated by back ray traces.

oh Object is always positive, so the object height is positive.

ih If the image is upright, the image height is positive. If the image is inverted, the image height is negative.

M Plugging in a positive image height into the formula results in positive magnification. Plugging in a negative

image height results in negative magnification. Remember negative M does not mean the image is smaller. It means the image is upside down. 0.5x is a smaller image and upright, while –2.0x is a larger image, but it is inverted.

Real: A real image is formed by positive ray traces. Positive ray traces are where the light goes, so this image can be projected on a screen.

Virtual: A virtual image is formed by back ray traces. It appears on the opposite side of the lens or mirror from the lights path. So it cannot be projected on a screen.

Patterns A general rule: If the forward light rays touch the focus or image they are positive.

Object distance and height: The object is always positive.

Image height and magnification: Look at the image, up is positive and down is negative.

These always go together

Converging Real positive si inverted negative hi negative M Diverging Virtual negative si upright positive hi positive M

Remember the terms convex and concave are secondary. Focus on the terms converging and diverging. The patterns are based on the nature of the lens or mirror, whether it is converging or diverging.

Diffraction When light hits the edge of a barrier it will bend around it. If the barrier is small compared to the wavelength of light the light will pass the barrier uninterrupted. Like water flowing around a buoy. But, if the barrier is large compared to the wavelength of light the waves will bend around the edge of the barrier in a circular fashion. Imagine water waves hitting the end of a jetty, or going through a hole in a jetty.


Huygen’s Principle: Every point on a wave front can be considered as a source of tiny wavelets that spread out in the forward direction at the speed of the wave itself. The wave front is formed by the constructive interference of the circular wavelets.

So, if the barrier has a hole in it, the particles of the wave create new circular wave fronts when they exit on the other side. This is why you get the circular patterns shown on the previous page.

The particles of light that create this diffraction pattern are the photons. Each photon generates circular wave fronts that constructively interfere to generate linear wavefronts.

Slit Width: If waves move thru an opening or slit the circular wave pattern is more pronounced when the slit is small.

Young’s Double Slit Experiment Uses monochromatic light source to since white light consisting of all the colors would result in a rainbow refraction. Light showed the same characteristic pattern as water waves and is evidence that light behaves as a wave.

Light from two slits interferes with each other. As a result you get dark and light bands if the pattern is shown on a screen.


Needs to travel ½ wavelength to match other wave

Reflected rays constructively interfere

Interference Fringes sind m mm Lx

d

d is the distance between the slits.

m is the fringe number. m = 0 is the central maximum. It is also the path difference in wavelengths.

Whole numbers are used for the bright Constructive Interference Fringes. m = 0.0, 1.0, 2.0, 3.0, etc.

Half numbers are used for the dark Destructicve Interference Fringes. m = 0.5, 1.5, 2.5, 3.5, etc.

is the angle from the midline (from the middle fringe)

L is the distance from slits to the screen.

xm is the distance from the midline (center fringe) to the fringe being measured.

Thin Films: Reflection revisited. Most people are familiar with the rainbow effect seen when a thin oil or soap film is floating on top of water. The thickness of the film, and the density of the substances work together to cause this effect.

A reflected ray will change phase by 180o when going from a medium with a low n to a medium with a high n. If oil is suspended on water. Light moving from air to oil hits a higher n and is reflected with a 180o phase change.

Light moving from oil to water hits a smaller n and its phase isunaltered.

?

a

For what wavelengths in the visible spectrum will the intensity be a maximum in the reflected beam

Maximum intensity occurs when waves reflecting off the oil and those reflecting off the water join and constructively interfere. The waves reflecting off the oil have their phase changed by 180o. Those reflecting off the water follow the same wave pattern out as they did in. To meet with the rays reflecting off the oil they need

to go ½ a wavelength (or a multiple of ½) and then rebound traveling back the same distance. So they must travel total of 1, 2, or 3, … wavelengths (m wavelengths). So if the film is 1x10-7 m thick, what wavelengths will results in maximum intensity.

7 72 2 1 10 2 10 200thickness of film m nm

Any multiple of 200 nm will result in maximum intensity.

200m nm where m is an integer. The rainbow effect depends on where you are standing in relation to the light source. Remember refraction is also happening for the light entering the oil. And the colors are separating with blue bending more. And the oil may not have the exact same thickness everywhere. So a rainbow pattern is seen, which depends on a combination of all these factors.

Dark

Light

Dark

Light

xm

L

m =2

m = 1

m = 0

d

L

Geometric Optics Name _________________________

Ray Tracing WS ___ Date ______________ Per _______

f so si ho hi M

f so si ho hi M

f so si ho hi M

Study Guide and Review Worksheet: Geometric Optics 47

f so si ho hi M

f so si ho hi M

f so si ho hi M


Geometric Optics Name _________________________

Ray Tracing WS ___ Date ______________ Per _______

1. Complete the tables below with the correct signs, + or – , and choose the correct terms.

f so si ho hi M Converging or Diverging

Real or Virtual

Convex or Concave

Converging Lens, Object outside f

Converging Lens, Object at f

Converging Lens, Object inside f

Converging Mirror, Object outside f

Converging Mirror, Object at f

Converging Mirror,

Object inside f

Diverging Lens, Object outside f

Diverging Lens, Object inside f

Diverging Mirror, Object outside f

Diverging Mirror, Object inside f

2. Which variables have the same sign in all cases above?

3. What does the sign of the focal point depend on?

4. When an image is real, what else can be said about it? (There are quite a few)

5. When an image is virtual, what else can be said about it? (There are quite a few)

6. What are the main differences between converging and diverging?

7. What are the differences between lenses and mirrors?

Study Guide and Review Geometric Optics 48

Advanced Placement Physics Modern Physics

Electromagnetic Radiation: In the previous review sheet we discussed the electromagnetic spectrum.

Maxwell: Derived a famous series of four equations that could completely describe electromagnetic effects. His equations, which were a compilation of the work of many other famous scientists, showed the existence and predicted the speed of these waves. However, you won’t need the equations now. You can enjoy this chapter of physics in college. Atomic Theory Thompson: Designed the Cathode Ray Tube (CRT), the basis for TV and computer monitors. In the partially

evacuated tube he had two electrical terminals, thus creating an electric field. When a potential difference was created between the electrodes (plates) he witnessed an eerie beam that came from the negative (cathode) plate and went to the positive plate. He surmised the existence of negative particles that must have come from inside the atom. So the atom was no longer recognized as the smallest entity in the universe. These particles were called electrons.

n.

Milikan Oil Drop: He charged oil drops with these negative particles. He then sprayed the oil drops between two charged plates. He could adjust the potential difference between the plates until the oil drops were suspended in mid air. This means that the force up =the force down. So the electric force up = the gravity force dow mg Eq

so mgqE

By finding the mass of the oil drop and noting the strength of t

electric field he could calculate the excess charge on the oil drop. He performed the experiment many times. He noted that the charge was always a multiple of 1.6x10

he

-19 C and he never found a value smaller than this. So heconcluded that this is the charge on the electron. After all charge comes in quanta, or whole number quantities. There are no half electrons.

Rutherford: Fired alpha particles at gold foil. Around the foil he placed a screen sensitive to alpha particles. He thought the heavy and fast alpha particle would fire right through the foil. While most did, he did note that many rebounded from the foil. He likened this to shooting a cannon at tissue paper and having the shell bounce back. He postulated that the atom was mainly empty space, but that there was a small dense nucleus comprised of positive particles (protons) located at the center. The empty space would account for most alpha particles passing through. The positive nucleus would explain how the positive alpha particles were bounced back. He did calculations based on the various trajectories of the alpha particles, and he was able to predict the relatively small size of the nucleus. His model of the atom was similar to the solar system (planetary model) with the nucleus (sun) at the center and the electrons (planets) orbiting at a great distance.

Einstein: Postulated that light has a particle nature, and travels in packets of energy known as photons.

Planck: Found the energy of a photon. E hf . The energy of a photon is Planck’s constant (h) x frequency.

Emission Spectrum: It was noted that when gaseous elements were placed in a tube at near vacuum and a potential difference was placed at the ends of the tube (Thompson CRT) different colors were seen. When shot through a diffraction grating the colors showed up as discrete lines with dark areas in between. Formulas were worked out for Hydrogen, the simplest element and the placement of the lines fit a mathematical pattern.

Bohr: He predicted that the atom was similar to Rutherford’s model, but Bohr added the concept of energy levels. The fact that atoms only emitted certain frequencies of light implied that the electrons could only occupy certain discrete energy levels. And these electrons could never be in between these energy levels. When photons strike an atom, the electrons (normally in the ground state) of the atom absorb the energy. These electrons (excited) now have higher energy and thus move to higher energy levels within the atom. When the electrons returned to the ground state photons are emitted since the electrons loose energy. But the electrons may drop to a variety of levels on the way back to the ground state. This explains the many colored lines in the emission spectrum and the calculations matched those of the emission spectrum. The Bohr Model of the atom is outdated & incomplete, but it is still used to visualize the atom.

Debroglie: Felt that since light can act as both a particle (photon) and a wave, perhaps electrons (a particle) can have a

wave property as well. He calculated the wavelengths of electrons h p and found that theoretically an electron in

the lowest energy level has one electron wavelength in a standing matter wave. An electron in the second energy level completes two wavelengths, etc. This resulted in the Wave Mechanical Model of the Atom. So the electrons were not jumping from energy levels as Bohr had surmised, rather they were changing wavelength when bombarded by photons.

Study Guide and Review Modern Physics 53

Heisenberg: Postulated that you can never know both the location and the momentum of an electron simultaneously. His Uncertainty Principle states that you cannot find an electron or predict what it will do, since if you shoot photons at electrons to see what their doing the photons interact with the electrons changing their location and / or their speed.

Schrodinger: Performed the calculations to narrow down the possible locations that electrons may be found in an atom. These statistical shells that electrons occupy are the basis of the current Electron Shell Model of the Atom.

Einstein: Found the mass energy equivalence 2E m c . Even though a photon is really mass-less energy it

does have a mass equivalence. So if its energy can be converted to a mass value, then the photon can be given a

mathematical momentum. So Planck’s equation is updated. E hf pc

Energy Level Calculations: Bohr’s model has been updated, but the energy levels still hold mathematically.

If a photon of the right frequency and energy were to strike the lone electron in hydrogen while it is in the ground state, the electron would then acquire all of the photons energy. The photon is absorbed by the atom. The energy of the photon determines how much energy the electron receives and thus determines the energy level that the electron is boosted to. Perhaps the electron would receive enough energy to be excited to the 3

B

rd energy level as shown in process A. This excited electron would be unstable and would eventually return to the ground state, but not necessarily in one leap. It could conceivably drop all the way back releasing a photon of the same frequency and energy as the one that struck the electron boosting it out of the ground state. Or it might drop to the 2nd energy level first (B), and then finally drop back to the 1st energy level (C). This two-step return will result in two photons that have different frequencies, and these photons are also different from the photon that hit the electron initially. Photons are emitted from the atom. Here are some of the energy levels of a hydrogen atom. The atom is small, so energy is measured in electron volts.

Drawing a circular atom is tedious. The following covers the same scenario as detailed above, but includes the mathematical steps and an additional step D. Remember this is only one scenario, there are many energy levels.

A: Absorption of a photon. The hydrogen atom is bombarded with light of frequency, 4.14x10-15 Hz.

15 154.14 10 2.92 10 12.1E hf eV s Hz eV

As a result an electron in the ground state, -13.6 eV is boosted to the second energy level, -1.5 eV. In this case it drops to the first energy level and then drops back to the ground state. Lot’s of possibilities exist.

B: Emission of a photon. The electron falls to the first energy level, a drop of 1.9 eV. This corresponds to a frequency of,

15 141.9 4.14 10 4.59 10f E h eV eV s Hz

A photon of light is emitted from the atom with this frequency. This generates a distinct band of light on the emission spectrum.

C: Emission of a photon. Next the electron falls back to the ground state, a drop of 10.2 eV. This corresponds to a frequency of,

15 1510.2 4.14 10 2.46 10f E h eV eV s Hz

A photon of light is emitted and this generates a distinct band of light on the emission spectrum.

D: Ionization. If a photon strikes a hydrogen atom electron in the ground state with more than 13.6 eV the electron receives enough energy to leave the atom entirely. The hydrogen atom lacking its electron becomes an ion. Therefore, this energy is referred to as the ionization energy. (Also called the work function. See below.)

Photoelectric Effect: Young’s Double Slit Diffraction experiment provided evidence that light exhibited wave properties. The photoelectric effect provided evidence of lights particle behavior. If light is shined on certain photoelectric materials a current can be induced. This requires the light to have enough energy to knock electrons out of the atoms, so a current can flow. This is the basis of solar energy. This process requires a certain minimum energy, known as the work

function . So if a photon E hf strikes a photoelectric material some of its energy is required to move the electron

D

C

B

A

-1.5 eV

-0.00 eV

-0.85 eV

-3.4 eV

-13.6 eV Ground State

C A


completely out of the atom. This is the energy needed to ionize the atom. The kinetic energy given the electrons is the

energy left over after the ionizing energy, work function, is subtracted from the photons energy. maxK hf


Nuclear Physics Nucleons: Proton Positive charge +e = 1.6 x 10-19 C mp = 1.6726 x 10-27 kg

Neutrons Neutral charge q = 0 mn = 1.6749 x 10-27 kg ???? Mass difference between a proton & a neutron (1.6749 x 10-27 - 1.6726 x 10-27 = 2.3 x 10-30)

It is almost the mass of an electron. A neutron is made of a proton and an electron that have fused. This explains

why the neutrons are neutral. As for the mass not quite adding up, see . 2E mc

Atomic Mass Number (A) = # Nucleons AZ X or just 12 12

6C CAtomic Number (Z) = # Protons Neutron Number (N = A-Z) = # Neutrons

Isotopes: Same # of Protons, different # of Neutrons 126C

136C

146C

Unified Atomic Mass (u) C-12 = 12.00000 u 1.00000 u = 1.66054 x 10-27 kg E = m c2 100000 u = 931.5 MeV

Binding Energy: Total mass of a stable nucleus is less than the component protons and neutrons He: 4.002602 u Added separately: 4.032980 u When He is formed some mass turns into energy: E = m c2, Mass Defect = m = 28.30 MeV

Total Binding Energy: Mass difference, amount of energy required in order to break the nucleus apart.

Average Binding Energy per Nucleon: Divide Total binding energy by the number of nucleons Highest for Iron: Requires the most energy to split this nucleus, most stable Hydrogen: Used in fusion, Energy drops from Fe to H. Binding energy released: Powers stars Uranium: Used in fission, Energy drops from Fe to U. Binding energy released: Nuclear power & bombs

Strong Nuclear Force: Force holding nucleons together

Radioactivity: Disintegration / decay of unstable nucleus. Certain isotopes are unstable and emit rays (radiation). The Electric Force acts over entire nucleus. It results from the repulsion of all the protons. Neutron are not involved

in the electric force. The Strong Force is a short-range force. It holds the individual nucleons together. Both neutrons and protons attract

due to this force. So adding more neutrons can help hold the nucleus together, since they do not contribute to the repulsive electric

force. There is however an ideal amount of neutrons, not too many and not too few that each nucleus needs in order to be stable. If this number is out of balance the nucleus can deteriorate spontaneously.

The larger the nucleus the greater the electric force. The distances become too large for the strong force to hold the nucleons together. The balance of force favors electric force.

Transmutation: Occasionally parts of the nucleus are repelled out with great force and speed. When part of the nucleus is ejected the Parent nucleus changes into a Daughter nucleus

Alpha Decay: Results when an Particle, He nucleus 42 He is spontaneously ejected from the nucleus. The

nucleons comprising the alpha particle are strongly bonded to each other and they eject as a single packet.

226 222 488 86 2Ra Rn He

Beta Decay: Results when there are too many neutrons compared to the ideal number required to maintain the

electric / strong force balance. A neutron is a proton and an electron that have been fused together. So if there are too many neutrons one of them can split, forming a new proton (adding to atomic number) and a nuclear electron, known as a

- particle 01e . This particle has a very low mass and picks up all the energy of this transmutation. It is ejected at an

extreme speed. Being smaller and faster than the alpha particle it has more penetrating power and is thus a more

hazardous form of radiation. 14 14 06 7 1C N e v . One by product of this reaction is a positron (anti-electron). The

existence of this anti-matter particle lead scientists to postulate the existence of a fourth fundamental force, the Weak Nuclear Force. Don’t worry about the positron on this exam.

Gamma Rays: Electrons around the nucleus can be found in excited states. It turns out that nucleons can exist in excited states as well. If a nucleon drops to a lower energy state a tremendous energy is released, since the energy differences in the nucleus are huge. This results in the emission of extremely high energy photons.


Law of Conservation of Nucleon Number: Total # of nucleons remains constant

Half Life: Length of time for half of the sample to decay. See worksheet that follows this section.

Nuclear Reactions: Nucleus is struck by a particle. Causes transmutation Enrico Fermi: Neutrons most effective projectile particle. No charge, not repelled.

Fission Hahn and Strassmann: Bombardment sometimes made smaller particles Meitner and Frisch: Realized that Uranium split in two Liquid drop model: Neutron added to nucleus increases energy. Increases motion of individual nucleons.

Abnormal elongated shape. Short range Strong Force is weakened. Electric Repulsive Force dominates. 2 Fission Fragments result. Also some free neutrons are given off. Tremendous amount of energy released. Fission fragment plus neutron are substantially lower in energy than original U 235

Chain Reaction: 2 to 3 neutrons freed collide with other 235U Self Sustaining Chain Reaction: Nuclear Reactor

Moderator: Need slow neutrons, with the right speed

Enriched Uranium: To increase probability of 235U fission

Critical Mass: Mass of fuel large enough to compensate for lost neutrons

Multiplying Factor: 1 or more neutrons must go to next reaction.

Subcritical: Less than one neutron goes on

Supercritical Control Rods: Cadmium or Boron. Absorb neutrons

Delayed Neutrons: Come from fission fragments

Core: Fuel plus moderator. 2 - 4 % 235U

Problems Thermal pollution: Disposal of radioactive fission fragments. Radioactive interaction with structural

components. Accidental release of radioactivity into atmosphere. Leakage of radioactive waste. Life time of 30 yrs due to build up of radioactivity. Earthquakes. Limited supply of fissionable materials

Breeder Reactor: Some neutrons produced are absorbed by 238U. 239Pu is produced, and is fissionable. So the supply of fuel can increase 100 times. However, Plutonium is highly toxic and can readily be used in bombs, and it involves a graphite moderator, as was used in Chernobyl.

Fusion: Building up nuclei Sum of energy of nucleus is less than sum of energy of its component parts Elements may be result of fusion in stars Proton Proton Cycle

11

11

12H H H e v

0.42 MeV

11

12

23H H He 5.49 MeV

23

23

24

11

11He He He H H 12.86 MeV

4 2 211

24H He e v 2

Carbon Cycle: Similar method in hotter stars, can make heavier elements

Thermonuclear Device: Fusion Devices Stars are under tremendous gravity Creates tremendous pressure High pressure means high temperature High temperature means particles collide violently

On earth high temperatures and densities not easily achieved Fission Bomb can ignite Fusion Bomb: Thermonuclear Device or H bomb

Plasma Need high density as well as temperature. Ordinary materials cannot contain plasma Magnetic Confinement: Tokamak Reactor. Break even point: Output equals input Inertial Confinement: Pellet of deuterium and tritium. Struck simultaneously by several lasers


Radioactive Decay Name _________________________

Nuclear Physics WS ___ Date ______________ Per _______

Half Life: Length of time for half of the sample to decay

146C Carbon – 14, with 2 extra neutrons is radioactive. It decays into Nitrogen – 14, a

process that has a 5730 yr half life. So after 5730 years half of any existing sample of Carbon – 14 is left and the other half turned into Nitrogen –14. In another 5730 years half of the half is remaining, and so on.

1. Start with 1.024 kg of Carbon 14. Fill in the rest of the chart below

½ lives Years C 14 (kg) N 14 (g)

0 0 1.024 0

1 5730 0.512 0.512

2 11460

3

4

5

6

7

8

9

10

2. On a piece of graph paper plot the mass of Carbon – 14 versus Time.

3. Describe the appearance / math function seen in the graph.

4. The half-life for U 238 is 4.5x109 years.

a) If five half-lives have gone by how many years have gone by?

b) If you start with 240 grams of U 238 and end up with 60 grams, how many years have gone by?

c) If you start with 240 grams of U 238 and 1.8 x 1010 years go by, how much U 238 is left?

d) If you start with 562 g and six half lives go by how many grams are left? (Look at all those years, and how much is left. That’s how long it takes to change this much to Thorium. Wait till you see what happens to it next. Check out side two of the worksheet. Any idea what all the fuss is about when it comes to nuclear waste?)

Study Guide and Review Worksheet: Radioactive Decay 57

Decay Series

Decay of one radioactive isotope often produces another radioactive isotope, and then another, and so on. The chart shows one path for the decay of Uranium 238. The half-life times are given for your information. Remember half the sample decays each half-life, then half of that, then half of that, etc. So it takes billions and billions of years for this stuff to disappear. That’s why the earth’s core is hot. When this stuff decays it releases energy.

5. Fill in the chart below to show the decay of U 238.

Isotope Decay Time Result

92238U 4.5 x 109 yrs. 90

234Th

90234Th 24 days 91

234Pa

91234Pa 6.7 hr 92

234U

92234U 2.5 x 105 yrs 90

230Th

90230Th 7.5 x 104 yrs

1600 yrs 86222Rn

86222Rn 3.8 days 84

218Po

84218Po 3.1 min

1.6 s 83214Bi

83214Bi 20 min 84

214Po

84214Po 1.6 x 10-4 s

22 yrs

5 days 84210Po

84

210Po

138 days 82206Pb

6. On the back of the graph paper used in number 2 above, plot this decay series with mass number on the vertical axis and atomic number on the horizontal axis.

Study Guide and Review Worksheet: Radioactive Decay 58

One Hundred and Fifty Questions

1. What two entities comprise a vector? 2. What do you do with any vector that is not on either the x or y axis? 3. How are velocity and speed different? 4. What is the slope of the distance time graph? 5. What is acceleration? 6. What is the area under the velocity time graph? 7. What is the slope of the velocity time graph? 8. What is the y intercept of the velocity time graph? 9. What is the area under the acceleration time graph? 10. What is the horizontal acceleration of projectiles? 11. What dimension controls time in falling body and projectile motion problems? 12. When two objects are launched horizontally 13. What equation describes the distance that a dropped object falls t seconds after it started moving? 14. What equation describes the distance that a horizontally launched projectile falls t seconds after it started moving? 15. What equation describes the speed of a dropped object t seconds after it started moving? 16. What equation describes the speed in the x direction of a projectile t seconds after it started moving? 17. What equation describes the speed in the y direction of a projectile t seconds after it started moving? 18. A projectile follows the path in Fig. 1.

At what points does it have the same speed? C

B D 19. A projectile follows the path in Fig. 1.

At what point is its horizontal speed the greatest? 20. A projectile follows the path in Fig. 1.

What is the direction of acceleration at points A, B, C, D, and E? (Zero, up, down, right, left?) 21. A projectile follows the path in Fig. 1. What is the direction of the vertical speed at point C? 22. What is implied when an object is not accelerating in the x direction? 23. What is implied when an object is not accelerating in the y direction? 24. When is sum of force (net force) zero, and when is it non-zero? 25. What force is always present, and what is its equation? 26. How is sum of force (net force) depicted in a FBD? 27. When is a normal force present, what is its direction? 28. What is the component of Fg down a slope? 29. What is the general equation for motion down a slope and how does it change if the object is going up the slope? 30. In circular motion, how is tangential velocity calculated? 31. What is centripetal acceleration and force? 32. What is the direction of acceleration of the object, in Fig. 2,

at points A, B, C? (Zero, up, down, right, left?) 33. What is the direction of velocity of the object, in Fig. 2,

at points A, B, C? (Zero, up, down, right, left?) 34. How is Fc represented in a FBD? 35. Mathematically what does Fc represent and how is Fc calculated? 36. Which vectors are positive and negative in circular motion? 37. What are some possibilities that can create Fc? 38. What is the work done on an object moving in a circle? Why? 39. If you double the mass of one planet, triple the mass of another, and move them twice as far apart, what happens to

the force of attraction between them? 40. What is the derived equation for the acceleration of gravity in terms of m and r2 ? 41. How can total momentum be calculated? 42. What is the difference between elastic and inelastic collisions? State the relevant equations for each. 43. What is impulse, and how does it relate to both momentum and force? 44. What is a key requirement in order for work to be done? 45. Work is the area under which curve? 46. What is work energy theorem and what is its significance?

Fig 2

C

B

A

E A Fig 1

Study Guide and Review 150 Questions 59

47. What is conservation of energy and what is its significance? 48. What is the energy equation if you see a height difference between two points in the problem? 49. What is the energy equation if you see a particle accelerated perpendicular to two charged plates, or the problem

states that the particle is accelerated through a potential difference? 50. What is Kinetic Energy lost and how is it calculated? 51. What is the energy equation for the change in temperature if it results from a loss in KE? 52. What is the energy equation if a force (friction) through a distance results in heat and thus a change in temperature? 53. What is the relationship that describes the rate that work is done, or that energy is used? 54. In a pendulum or spring, what are the displacement, velocity, Us and K at the equilibrium position? 55. In a pendulum or spring, what are the displacement, velocity, Us, and K at maximum displacement? 56. What do the period of pendulums and springs each depend on? 57. What is temperature? 58. What is internal energy? 59. What is heat? 60. What is meant by the terms system and environment? 61. What are the two forms of the ideal gas law? 62. What is latent heat, and why does the temperature stay the same when state changes occur? 63. What is specific heat capacity? 64. What is the first law of thermodynamics? 65. What is an isothermal process, and what is its impact on the first law of thermodynamics? 66. What is an adiabatic process, and what is its impact on the first law of thermodynamics? 67. What is the area under any pV curve? 68. Under what conditions is work positive and negative? 69. Under what conditions is heat positive and negative? 70. What is the net work done by an entire process? 71. What is the second law of thermodynamics? 72. Describe the relationship between QH, Qc, and W in a heat engine? 73. What is the difference between a heat engine and a refrigerator? 74. How can you tell when an engine is a Carnot Engine? 75. Under what conditions does entropy increase? 76. What are 2 key differences between electric force and gravitational force? 77. In electricity, what takes the place of m and g? 78. If you have two charges, and you double one charge and triple the other, and move them twice as far apart, what

happens to the force of attraction / repulsion between them? 79. What is the derived equation for the electric field in terms of q and r2 ? 80. What is the difference between q and Q? 81. What do the terms: potential difference, electric potential, potential energy, and electric potential energy mean? 82. What is the potential energy of a charge in an electric field? 83. Why is the potential energy of a capacitor half of the electric energy in the preceding problem 84. What are three ways to increase the capacitance of a capacitor? 85. What forces charges to move? 86. What indicates the ease with which charges can be moved? 87. What do batteries and generators produce? 88. What is the actual movement of charges, and how is it measured? 89. What causes resistance, and how does a wires composition, length, thickness, and temperature effect resistance? 90. What are the relationships between voltage, current, resistance, and power? 91. What stays the same in a series circuit, and what adds? 92. What stays the same in a parallel circuit and what adds? 93. What is the path of a charged particle in a magnetic field, and how is the force on the creating the path calculated? 94. What is the work done on a charged particle by the magnetic field? Why? 95. What is the force on a current carrying wire? 96. What is electromagnetic induction? 97. What is needed for electromagnetic induction to occur?


98. What is the difference between emf and voltage? State the relevant equation. 99. How does the right hand rule work in electromagnetic induction? 100. What is the difference between a motor and a generator? 101. What are the differences and similarities between transverse and longitudinal waves? Give examples of each type. 102. What is the relationship between speed, frequency, and wavelength? 103. What is the relationship between energy, frequency, and wavelength in any wave? 104. How are wavelength and amplitude measured on a sinusoidal wave? 105. What are the wavelengths for strings, open tubes, and closed tubes? 106. What cause an electromagnetic wave, and what makes the wave propagate indefinitely even in a vacuum? 107. What is the order of the electromagnetic spectrum, including the order of the color composing visible light? 108. What is the difference between reflection, refraction, and diffraction? 109. What is the law of reflection? 110. What is Snell’s Law? 111. What is Fermat’s Principle? 112. What happens at the critical angle? 113. When light goes from a less to a more dense medium what changes and how does it change? 114. What doesn’t change (speed, frequency, or wavelength), when light moves from one medium to another? 115. What conditions are necessary to change the reflected rays phase by 180o? 116. What shapes are converging in lenses and in mirrors? 117. What shapes are converging in lenses and in mirrors? 118. What are the two rules for ray tracing in lenses that work all the time? 119. What are the three rules needed for mirrors, since not all three work every time? 120. What do you do if your forward ray traces are diverging? 121. When are f, so, si, ho, hi, and M positive.

122. When are f, so, si, ho, hi, and M negative.123. What is the difference between a real and virtual image, and how is each formed? 124. What is Huygen’s Principle? 125. Describe Young’s experiment and state its significance. 126. What does the pattern look like in a Young Double Slit diffraction pattern? 127. What does the pattern look like in a single slit diffraction pattern? 128. What was Thompson’s discovery? Describe the apparatus and experiment. 129. What was Milikan’s discovery? Describe the apparatus and experiment. 130. What was Rutherford’s discovery? Describe the apparatus and experiment. 131. What is the Bohr Model of the atom? 132. What is the photon energy equation? 133. What is mass energy equivalence? 134. What does light absorption involve? 135. What does light emission involve? 136. What is ionization energy and how does it compare to the work function? 137. What is the photoelectric effect? 138. What is the difference between atomic number and mass number? 139. How do you find the number of neutrons in an atom? 140. What is an isotope? 141. What are binding energy, total binding energy, and average binding energy? 142. What is the strong force? 143. What causes radioactivity? 144. What is transmutation? 145. What are the three types of radiation? Describe each including its composition and origin. 146. What is half-life, and how does 512 g of a radioactive substance change thru 10 half lives? 147. What is the difference between fission and fusion? 148. How hard will you study for the AP Exam? 149. What will your score be on the test? 150. Are you in control or just along for the ride?


What if?

A projectile is launched horizontally: 212o o x ox xx v t v v v y gt

A mass is spun vertically on a string: c T g c T gtop bottomF F F F F F

An object moves horizontal, on a flat surface: cF force causing circular motion

A mass is spun horizontally on a string, and it is hanging down: 2 2

T c gF F F 2

You see a height difference: 212

bottomtopmgh mv

The term energy or work (units J) are used with time (units s): WPt

Kinetic Energy is lost: lost initial finalK K K

Kinetic Energy lost turns into heat: lostK mc T

The process is isothermal (slow), so temperature is not changed: U O U Q W W Q

The process is adiabatic (fast), so heat is not added: Q O U Q W W U

You see a charge particle moving perpendicular to two charged plates: 212

endstartqV mv

A charged particle is accelerated by an electric field: 212

endstartqV mv

A charged particle enters a magnetic field: 2vm qvr B

Tips and Strategies Try energy first.

Energy is directionless and has the advantageous of working throughout all five major subject areas. It is the universal thread tying it all together. You must be flexible and adaptable here.

Try force second. If an object is not moving in one or more dimensions then force may be the answer. What are the forces acting on the object and in what direction are they acting. Are they canceling or resulting in acceleration?

If you see a vector at an angle, split it into the x and y directions. Analyze each direction independently.

What is the object doing in the relevant direction?

Is it standing still or does it have constant velocity, then 0F

There must be equal & opposite forces in the direction (horizontal or vertical) that you are analyzing.

Is it accelerating, then F ma

So the forces in the direction (horizontal or vertical) that you are analyzing are out of balance.

Last try kinematics.

When you get stuck: Think Conservation of energy Work Energy Theorem Power


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