physics 113 syllabus physics 113-a fall 2010 prof. jed macosko office: olin 215, lab: olin 213...

PHYSICS 113 SYLLABUS

Physics 113-A Fall 2010Prof. Jed Macosko

Office: Olin 215, Lab: Olin 213Phone: 758-4981

e-mail: macoskjc@wfu.edu

OFFICE HOURSTF 2:30-3:30 pm R 10-11 am, 215 Olin

Feel free to drop by any time and I’ll try to accommodate you.

Physics 113 is the first course in a two-semester sequence in calculus-based general physics. It does require the use of calculus and simple vector calculations.

SCHEDULE

- Lectures: Mon, Wed, Fri 11:00 – 11:50 am -Each student must also enroll for one laboratory session. - Lab sessions begin the week of Monday, August 30. (see which day and time your particular lab session will be)

TEXT AND MATERIALS

The text is the eighth edition of Physics for Scientists and Engineers by Serway & Jewett. You’ll need an i-Clicker ($36) for class and the lab manual (~ $10) for lab from the bookstore.

EXAMS AND GRADING

There will be one final exam and three 50-minute, in-class midterm exams given at the dates listed below. Homework problems will be assigned for each chapter (due two lecture days later) and they will be also be graded.

Homework: 20%

Laboratory: 13%

Worst test score: 10%

Intermediate test score: 14%

Best test score: 19%

Final exam: 20%

Homework notebook: 1%

Class participation (i-clickers): 3%

First class: Aug. 25, 2010Last day to drop class: Sept 29, 2010

Exam 1: Monday, Sept. 20, 2010Exam 2: Wednesday, Oct. 20, 2010Exam 3: Monday, Nov. 22, 2010Final: Tuesday, Dec. 7, 2009, 2:00 pm

93 1/3 G 100, A;

90 G < 93 1/3, A;

86 2/3 G < 90, B+;

83 1/3 G < 86 2/3, B;

80 G < 83 1/3, B;

76 2/3 G < 80, C+;

73 1/3 G < 76 2/3, C;

70 G < 73 1/3, C;

66 2/3 G < 70, D+;

63 1/3 G < 66 2/3, D;

60 G < 63 1/3, D;

G < 60, F.

HOMEWORK AND PROBLEM SOLVING

Homework and problem solving is a very important part of learning in a course in physics. Approximately 5-10 questions or problems per chapter will be assigned as homework. We will use WebAssign. Homework is due two lectures after it has been assigned. No late homework is accepted. Some problems may also re-appear on the exams and the final.

POSTINGS

Homework, exam solutions and other material relating to the course will be posted on the web site for the class:

http://www.wfu.edu/~macoskjc/Courses/113Fall10.htm

This class does not use CourseInfo or Blackboard.

WebAssign http://www.webassign.net/ will be implemented for standard homework assignments. You have nine attempts to get the answers right (Demo follows).

ATTENDANCE

It is expected that students attend all scheduled classes and laboratory sessions. Attendance at the three exams and the final is required - absence will result in a zero grade unless an official excuse is presented. Excuses should be reported to me in advance or as soon as possible.

Monday Tuesday Wednesday Thursday Friday Saturday Sunday

Aug. 24

Introduction

Chapter 1

Aug. 25 Aug. 26

Chapter 2

Motion in 1D

Aug. 27 Aug. 28

Aug. 29

Ch. 2: 1-D motion

Last day of “free” Drop/Add

Aug. 30 Aug. 31

Chapter 3

Vectors

Sept. 1 Sept. 2

Chapter 3

Vectors

Sept. 3 Sept. 4

Sept. 5

Chapter 4

Motion in 2D

Sept. 6 Sept. 7

Chapter 4

Motion in 2D

Last day to add courses

Sept. 8 Sept. 9

Chapter 5

Force & Motion I

Sept. 10 Sept. 11

Sept. 12

Chapter 5

Force & Motion I

Sept. 13 Sept. 14

Chapter 6

Force & Motion II

Sept. 15 Sept. 16

Catch-up & Review

Sept. 17 Sept. 18

Sept. 19

Midterm 1

Chapters 1-6

Sept. 20 Sept. 21

Chapter 7

Energy Transfer

Sept. 22 Sept. 23

Chapter 7

Energy Transfer

Sept. 24 Sept. 25

Sept. 26

Chapter 8

Potential energy

Sept. 27 Sept. 28

Chapter 8

Potential energy

Last day to drop class

Sept. 29 Sept. 30

Chapter 9

Linear Momentum and Collisions

Tentative outline of class (date numbers are wrong!)

Oct. 1 Oct. 2

Oct. 3

Chapter 9

Linear Momentum and Collisions

Oct. 4 Oct. 5

Chapter 10

Rotation

Oct. 6 Oct. 7

Chapter 10

Rotation

Oct. 8 Oct. 9

Oct. 10

Chapter 11

Angular Momentum

Oct. 11 Oct. 12

Chapter 11

Angular Momentum

Oct. 13 Oct. 14

Fall Break

Oct. 15 Oct. 16

Oct. 17

Catch-up and review

Oct. 18 Oct. 19

Midterm 2

Chapters 7-11

Oct. 20 Oct. 21

Chapter 12

Static Equilibrium

Oct. 22 Oct. 23

Oct. 24

Chapter 13

Universal Gravitation

Oct. 25 Oct. 26

Chapter 13

Universal Gravitation

Oct. 27 Oct. 28

Chapter 14

Fluids

Oct. 29 Oct. 30

Oct. 31

Chapter 14

Fluids

Nov. 1 Nov. 2

Chapter 15

Oscillations

Nov. 3 Nov. 4

Chapter 15

Oscillations

Nov. 5 Nov. 6

Nov. 7

Chapter 16

Waves I

Nov. 8 Nov. 9

Chapter 16

Waves I

Nov. 10 Nov. 11

Chapter 17

Waves II

Nov. 12 Nov. 13

Nov. 14

Chapter 18

Waves III

Nov. 15 Nov. 16

Catch-up & Review

Nov. 17 Nov. 18

Midterm 3

Chapters 12-18

Nov. 19 Nov. 20

Nov. 21

Chapter 19

Temperature

Nov. 22 Nov. 23

Thanksgiving break

Nov. 24

Thanksgiving

Nov. 25

Thanksgiving break

Nov. 26 Nov. 27

Nov. 28

Chapter 19

Temperature

Nov. 29 Nov. 30

Chapter 20 Thermodynamics

Dec. 1 Dec 2

Catch-Up & Review

Dec. 3 Dec. 4

Dec. 5 Dec. 6

2 PM (section B)

Dec. 7 Dec. 8 Dec. 9 Dec. 10 Dec. 11

Dec. 12

Winter break

Part 1: Mechanics• Concerned with the motion of objects (larger than atoms; slower than speed of light)

• Conservation of energy

• Conservation of momentum

• Rotation of objects

• Oscillations

• Thermodynamics

Chapter 1:

Physics and Measurement

Reading assignment (reading quiz this Friday!): Chapter 1 (and 2.1-2.6)

Homework:

Problems: Chapter 1: OQ3, 7, 10, 24, Chapter 2: OQ13

Due: Monday Aug. 30, 2009, 1 minute before midnight

Check out WebAssign: http://www.webassign.net/

In mechanics the three basic quantities are:

• Length (we will use the unit meter; 1 m; Paris, 1792)

• Mass (we will use the unit kilogram; 1 kg; Paris, 1792)

• Time (we will use the unit second; 1 s)

And combinations of these units (e.g. unit of velocity: m/s)

• These are units of the SI (Système International) system that is used throughout the world in the Sciences.

Changing units

We need to apply conversion factors (a ratio of units that are equal to one) to get the right units

A snail crawls along with a speed of one inch per minute.

What’s its speed in m/s?

See appendix for conversion factors

Black board example 1.1

A significant figure is a reliably known figure. Give answers in significant figures. black board examples.

Significant figures

When adding or subtracting numbers, the number of decimal places in the result should equal the smallest number of decimal places of any term in the sum.

When multiplying several quantities, the number of significant figures in the final answer is the same as the significant figures in the least accurate of the quantities being multiplied. (Same for division)

Factor Name Symbol

1024 yotta Y

1021 zetta Z

1018 exa E

1015 peta P

1012 tera T

109 giga G

106 mega M

103 kilo k

102 hecto h

101 deka da

10-1 deci d

10-2 centi c

10-3 milli m

10-6 micro µ

10-9 nano n

10-12 pico p

10-15 femto f

10-18 atto a

10-21 zepto z

10-24 yocto y

The 20 SI prefixes used to form decimal multiples and submultiples of SI units (from NIST).

DNA has a diameter of 2x10-9 m. How many nanometer is that?

The building blocks of matter

• All matter consists of atoms (greek: atomos = not sliceable)

• All atoms consist of a nucleus surrounded by electrons

• Nuclei consist of protons and neutrons. The sum of neutrons and protons in the nucleus of a particular element is called the atomic mass of the element. The number of protons is called the atomic number.

• Protons and Neutrons consist of Quarks (six different varieties)

Atomic force microscope

image of gold surface

Atomic mass of an element: average mass of one atom in a sample of the element.

Unit of the atomic mass: 1u = 1.66·10-27 kg

One atom of the carbon-12 isotope (12C) has a mass of 12 u.

Density:

Density = _______________

For example:

Aluminum: 2.7 g/cm3

Lead: 11.3 g/cm3

Density of matter depends on:

• The atomic _____ of the individual atoms

• How tightly atoms are packed

Gold, which has a mass of 19.32 g for each cubic centimeter of volume, is the most _________ metal and can be pressed into a thin leaf or drawn out into a long fiber.

(a) If 1.000 oz of gold, with a mass of 27.63 g, is pressed into a leaf of 1.000 µm thickness, what is the area of the leaf?

(b) (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.500 µm, what is the length of the fiber?

Black board example 1.3 (problem 20)

Density:

Density = mass/unit volume

For example:

Aluminum: 2.7 g/cm3

Lead: 11.3 g/cm3

Density of matter depends on:

• The atomic mass of the individual atoms

• How tightly atoms are packed

Gold, which has a mass of 19.32 g for each cubic centimeter of volume, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber.

(a) If 1.000 oz of gold, with a mass of 27.63 g, is pressed into a leaf of 1.000 µm thickness, what is the area of the leaf?

(b) (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.500 µm, what is the length of the fiber?

Black board example 1.3 (problem 20)

Dimensional analysis

Dimensions (In this case we mean the units of a physical quantity) can be treated as algebraic quantities.

• Always do a dimensional analysis when solving problems.

Newton's law of universal gravitation is represented by the following equation.

F = GMm/r2

Here F is the gravitational force, M and m are masses, and r is a length. Force has the SI units kg · m/s2. What are the SI units of the proportionality constant G?

Problem solving:• Always make sure you use the right units (conversion may be necessary)

• Always do an order of magnitude estimation (Ask yourself: “Does the number I’m getting make sense?).

Review: • Length, mass, time

• SI units

• Dimensional analysis, conversion of units

• Order-of-magnitude estimates

• Significant figures

Announcements:

• Questions about WebAssign?

• My office hours: TF 2:30-3:30 pm, R 10-11 am

•Labs start next week Bring ThinkPads to lab

•And now…for our reading quiz!!!

1. The slope of the curve in the position vs. time graph for a particle’s motion

___ 1. the particle’s speed.

___ 2. the particle’s acceleration.

___ 3. the particle’s average velocity.

___ 4. the particle’s instantaneous velocity.

___ 5. not covered in the reading assignment

2. Is it possible for an object’s instantaneous velocity and instantaneous acceleration

to be of opposite sign at some instant of time?

___ 1. yes

___ 2. no

___ 3. need more information

3. Without air resistance, an object dropped from a plane flying at constant

speed in a straight line will

___ 1. quickly lag behind the plane.

___ 2. remain vertically under the plane.

___ 3. move ahead of the plane.

TUTOR & HOMEWORK SESSIONS

This year’s tutors: Xinyi Guo, Stephen Baker, and Wei Li,

All sessions will be in room 101 (lecture room).

Tutor sessions in semesters past were very successful and received high marks from students.

All students are encouraged to take advantage of this opportunity.

5-7 5-7 5-7 5-7 5-7

• In this chapter we will only look at motion along a line (one dimension).

• Motion can be forward (positive displacement) or backwards (negative displacement)

Chapter 2: Motion in One Dimension

Reading assignment: Finish Chapter 2

Homework 2: (Due Wednesday, Sept. 2)

Chapter 2: 1, 9, 11, 37, 60

Remember: Homework 1 is due this Monday, Aug. 30.

An object goes from one point in space to

another. After it arrives at its destination, its

displacement is:

1. either greater than or equal to

2. always greater than

3. always equal to

4. either smaller than or equal to

5. always smaller than

6. either smaller or larger

than the total distance it traveled.

Conceptual question 2.1

Displacement and

total distance traveled

Displacement of a particle: Its change in position:

12 xxx x

2 final position

initial position

Don’t confuse displacement with the total distance traveled.

Example: Baseball player hitting a home run travels a total distance of 360 ft, but his displacement is 0 ft!!

Displacement is a vector: It has both, magnitude and direction!!

Total distance traveled is a scalar: It has just a magnitude

A person initially at point P in the illustration stays there a moment and then moves along the axis to Q

and stays there a moment. She then runs quickly to R, stays there a moment,

and then strolls slowly back to P. Which of the position vs. time graphs below correctly represents this

motion?

Conceptual black board example 2.2

Velocity and speed

Average Velocity of a particle:

12, tt

xv xavg

x: displacement of particle

t: total time during which displacement occurred.

Average speed of a particle:

Velocity is a vector: It has both, magnitude and direction!!

Speed is a scalar: It has just a magnitude

time total

distance total eedaverage sp

The position of a car is measured every ten seconds relative to zero.

A) 30 m

B) 52 m

C) 38 m

D) 0 m

E) - 37 m

F) -53 m

Find the displacement, average velocity and average speed between

positions A and F.

Blackboard example 2.1

Instantaneous velocity and instantaneous speed

Instantaneous velocity is the derivative of x with respect to t, dx/dt!

Velocity is the slope of a position-time graph!

The instantaneous speed (scalar) is defined as the magnitude of its velocity (vector)

A particle moves along the x-axis. Its coordinate

varies with time according to the expression x

= -4t + 2t2.

0 0.5 1 1.5 2 2.5 3 3.5 4

time (s)

(a) Determine the displacement of the particle in the time intervals t=0 to t=1s and t=1s to t=3s.

(b) Calculate the average velocity during these two time interval.

(c) Find the instantaneous velocity of the particle at t=2.5s.

(d) Is the velocity constant or is it changing?

Acceleration

When the velocity of a particle (say a car) is changing, it is accelerating. (Decelerating/braking = negative acceleration).

12, tt

va xxx

The average acceleration of the particle is defined as the change in velocity vx

divided by the time interval t

during which that change occurred.

The instantaneous acceleration equals

the derivative of the velocity with respect to time (slope of a velocity vs. time graph).

Because vx

= dx/dt, the acceleration can also be written as:

Units: m/sec2

Find the appropriate

acceleration graphs

parabola

Conceptual black board example 2.3

Relationship between acceleration-time, velocity-time, and displacement-time graphs.

A train car moves along a long straight track. The graph shows the position as a function of time for this train. The graph shows

that the train:

1. speeds up all the time.

2. slows down all the time.

3. speeds up part of the time and slows down part of the time.

4. moves at a constant velocity.

The graph shows position as a function of time for two trains running on parallel tracks. Which is true:

1. At time tB

,both trains have the same velocity.

2. Both trains speed up all the time.

3. Both trains have the same velocity at some time before tB

4. Somewhere on the graph, both trains have the same acceleration.

Peer Instruction question:

4. can’t determine without knowing throw velocity

• In this chapter we will only look at motion along a line (one dimension).

• Motion can be forward (positive displacement) or backwards (negative displacement)

Chapter 2: Motion in One Dimension-continued

Reading assignment: Chapter 3

Homework 3 (due Saturday, Sept. 4, 2010):

(Chapter 3) OQ4, 5, 9*, 29, 51

(note: problem 5 is asking for r, not x and y)

1. The slope of the curve in the position vs. time graph for a particle’s motion

___ 1. the particle’s speed.

___ 2. the particle’s acceleration.

___ 3. the particle’s average velocity.

___ 4. the particle’s instantaneous velocity.

2. Is it possible for an object’s instantaneous velocity and instantaneous acceleration

to be of opposite sign at some instant of time?

___ 1. yes

___ 2. no

___ 3. need more information

Can the instantaneous velocity v of an

object at an instant of time ever be

greater in magnitude than the average

velocity, over a time interval containing

the instant? Can it ever be less?

A) v is always less than or equal to .

B) v can be less than , but not greater.

C) v can be greater than , but not less.

D) v is always greater than or equal to .

E) v can be greater than or less than .

If an object's average velocity is nonzero over some time interval, does this mean

that its instantaneous velocity is never zero during the interval?

If the velocity of a particle is nonzero, can its acceleration be zero?

If the velocity of a particle is zero, can its acceleration be nonzero?

Review from Friday:

• Displacement x, velocity v, acceleration a

• a = dv/dt = d2x/dt2, and v = dx/dt.

• x is slope of v-graph, v is slope of a-graph.

4. can’t determine without knowing throw velocity

One-dimensional motion with constant acceleration

atvv 0*Velocity as function of time (2-13)

)(2 02

02 xxavv Velocity as function of position (2-17)

Derivations: Book pp. 41-42

1attvxx *Position as function of time (2-16)

Position as function of time and velocity (2-15)tvvxx )( 02

General Problem-Solving Strategy

Conceptualize __________________________________

Categorize__________________________________

Analyze __________________________________

Finalize __________________________________

See the movie in your mindSee the movie in your mind

Pick the example that matches

See the movie in your mind

Do the algebra to isolate the variable

Make sure units and magnitude are reasonable

GRAPH IT! (if possible)

Black board example 2.7 (see book)

Spotting a police car, you brake a Porsche from a speed of 100 km/h to speed

80 km/h during a displacement of 88.0 m at a constant acceleration.

(a) What is your acceleration?

(b) How long did it take to slow down?

Notice that acceleration and velocity often point in different

directions!!!

A car traveling at constant speed of 45.0 m/sec passes a trooper hidden behind a billboard. One

second after the speeding car passes the billboard, the trooper sets out from the billboard to

catch it, accelerating at a constant rate of 3.00 m/s2.

(a) How long does it take her to overtake the car?

(b) How far has she traveled?

Freely falling objects

In the absence of air resistance, all objects fall towards the earth with the same constant acceleration (a = -g = -9.8

m/s2), due to gravity

A stone thrown from the top of a building is given an initial velocity of 20.0

m/s straight upward. The building is 50 m high. Using tA

= 0 as the

time the stone leaves the throwers hand at position A, determine:

(a) The time at which the stone reaches its maximum height.

(b) The maximum height.

(c) The time at which the stone returns to the position from which it

was thrown.

(d) The velocity of the stone at this instant

(e) The velocity and and position of the stone at t = 5.00 s.

Conceptualize __________________________________

Categorize__________________________________

Analyze __________________________________

Finalize __________________________________

Review (warning: “summaries” can atrophy your mind!)

• Know x, v, a graphs. x is slope of v-graph, v is slope of a- graph.

• For constant acceleration problems (most problems, free fall):

• Equations on page 34-35 (const. Acceleration & free fall).

• Free fall

atvv 02

1attvxx

If I hurl a watermelon straight up at 10 m/s off the top of Wait Chapel and then hurl another

watermelon straight down at 10 m/s, which one will have a greater velocity when it hits the ground.

Assume no air resistance.

A)The first watermelon

B)The second watermelon

C)They will hit with equal velocities

D)Not enough information

• In this chapter we will learn about vectors, (properties, addition, components of vectors)

• Multiplication will come later

Chapter 3: Vectors

• WebAssign ok?

• Everything all right in lab?

• Questions?

Reading assignment: Chapter 3.3-3.4

Homework 4 (due Monday, Sept. 6, 2010):

Chapter 3: AE1-5, 64, 62 (AE=active exercise)

Note: a max of 10 points will be given, even when HWs have more possible points (e.g. HW4 is has 15

possible pts)

Remember: Homework 2 is due tonight at 11:59 pm

If an object's average velocity is nonzero over some time interval, does this mean

that its instantaneous velocity is never zero during the interval?

Which of the following is a vector?

A)force

B)the height of a building

C)the volume of water in a can

D)temperature

E)the ratings of a TV show

F)the age of the Universe

Is it possible to add a vector quantity to a scalar quantity?

Review:

• Know x, v, a graphs. v is slope of x-graph, a is slope of v- graph.

• For constant acceleration problems (most problems, free fall):

• Equations on page 36-7 (const. Acceleration & free fall).

• Free fall

atvv 02

1attvxx

Conceptualize __________________________________

Categorize__________________________________

Analyze __________________________________

Finalize __________________________________

Freely falling objects

In the absence of air resistance, all objects fall towards the earth with the same constant acceleration (a = -g = -9.8

m/s2), due to gravity

Vectors: Magnitude and direction

Scalars: Only Magnitude

A scalar quantity has a single value with an appropriate unit and has no direction.

Examples for each:

Vectors: Displacement, Velocity, Acceleration, Force

Scalars: Mass, Time, Distance, Speed, Density, etc.

Motion of a particle from A to B along an arbitrary path (dotted line).

Displacement is a vector

Coordinate systems

Cartesian coordinates:

Vectors:

• Represented by arrows (example displacement).

• Tip points away from the starting point.

• Length of the arrow represents the magnitude

• In text: a vector is often represented in bold face (A) or by an arrow over the letter.

• In text: Magnitude is written as A or A

These four vectors are equal because they have the same magnitude and point the same

direction

Adding vectors:

Draw vector A.

Draw vector B starting at the tip of vector A.

The resultant vector R = A + B is drawn from the tail of A to the tip of B.

Graphical method (triangle method):

The vectors a, b, and c are related by c = b + a. Which diagram below illustrates

this relationship?

2) II.

3) III.

4) IV.

5) None of these

A vector of magnitude 3 CANNOT be added to a vector of magnitude 4 so that the

magnitude of the resultant is:

1) zero

Adding vectors:

Draw vector A.

Draw vector B starting at the tip of vector A.

The resultant vector R = A + B is drawn from the tail of A to the tip of B.

Graphical method (triangle method):

Adding several vectors together.

Resultant vector

R=A+B+C+D

is drawn from the tail of the first vector to the

tip of the last vector.

Adding several vectors together.

Resultant vector

R=A+B+C+D

is drawn from the tail of the first vector to the

tip of the last vector.

Associative Law of vector addition

A+(B+C) = (A+B)+C

The order in which vectors are added together does not matter.

Negative of a vector.

The vectors A and –A have the same magnitude but opposite direction.

A + (-A) = 0

Subtracting vectors:

A - B = A + (-B)

The vector –2 is:

1) longer than 2

2) shorter than 2

3) in the same direction as 2

4) in the direction opposite to 2

5) perpendicular to 2

A car travels 20.0 km due north and then 35.0 km in a direction 60° west of north as shown in the figure.

Find the magnitude and direction of the car’s resultant displacement.

We cannot just add 20 and 35 to get resultant vector!!

Chapter 3: Vectors

• WebAssign ok?

• Everything all right in lab?

• Questions?

Homework 4 (due Monday, Sept. 6, 2010):

Chapter 3: AE1-5, 64, 62 (AE=active exercise)

Note: a max of 10 points will be given, even when HWs have more possible points (e.g. HW4 is has 15

possible pts)

Remember: Homework 2 is due tonight at 11:59 pm

Chapter 3: Vectors

• Vector components

• Unit vectors

• Polar coordinates

Reading Assignment: Chapter 4.1-4.3

Homework 3 (due Wednesday, Sept. 8, 2010):

Chapter 4: OQ3, 1, 7, 30, 34*

Outline

A vector A lies in the xy plane. For what orientations

of A will both of its components be negative?

a) A is between 0° and 90°

b) A is between 270° and 360°

c) A is between 90° and 180°

d) A is between 180° and 270°

For what orientations will its components have

opposite signs?

a) first quadrant

b) second quadrant

c) third quadrant

d) fourth quadrant

e) both b and d

Can the magnitude of a vector have a negative value?

Under what circumstances would a nonzero vector lying in the xy plane ever have

components that are equal in magnitude?

A) The vector is parallel to any axis.

B) The vector is oriented at 45° to any axis.

C) The vector is parallel to the +x or +y axis.

D) The vector is parallel to the -x or -y axis.

Multiplying a vector by a scalar

The product mA is a vector that has the same direction as A and magnitude mA.

The product –mA is a vector that has the opposite direction of A and magnitude mA.

Components of a vector

22yx AAA

The x- and y-components of a vector:

The magnitude of a vector:

The angle between vector and x-axis:

Vectors A and B lie in the xy plane. We can deduce that A = B if:

1) Ax2 + A

y2 = B

x2 + B

2) Ax + A

3) Ax = B

x and A

/Ax = B

5) Ax = A

y and B

The signs of the components Ax

and Ay

depend on the angle and they can be positive

or negative.

Examples)

Unit vectors

• A unit vector is a dimensionless vector having a magnitude 1.

• Unit vectors are used to indicate a direction.

• i, j, k represent unit vectors along the x-, y- and z- direction

• i, j, k form a right-handed coordinate system

The unit vector notation for the vector A is:

A = Ax

i + Ay

Vector addition using unit vectors:

We want to calculate: R = A + B

From diagram: R = (Ax

i + Ay

j) + (Bx

i + By

R = (Ax

)i + (Ay

The components of R:R

2222 )()( yyxxyx BABARRR

The magnitude of a R:

The angle between vector R and x-axis:

Vector addition using unit vectors:

Once again, dad doesn’t know where he is going. He drives the

- east for a distance of 50 km,

- then north for 30 km

- and then in a direction 30° east of north for 25 km.

(a) Sketch the vector diagram for this trip.

(b) Determine the components of the car’s resultant displacement R for the trip. Find an expression for R in terms of

unit vectors.

(c) Determine magnitude and direction (angle) of the car’s total displacement R.

• If A = (6 m)î – (8 m)j then A has magnitude:

• 1) 10 m

• 2) 20 m

• 3) 30 m

• 4) 40 m

• 5) 50 m

Polar Coordinates

A point in a plane: Instead of x and y coordinates a point in a plane can be represented by its polar coordinates r and

ytan 22 yxr

The Cartesian coordinates of a point in the x-y plane are

(x,y) = (-3.50, -2.50).

Find the polar coordinates of this point.

• In this chapter we will learn about the kinematics (displacement, velocity,

acceleration) of a particle in two or three dimensions.

• Uniform Circular Motion

• Superposition principle

Chapter 4, part 1:

Reading assignment: Chapter 4 (4.4-4.6)

Homework 6: (due Saturday, Sept. 11, 2011):

Chapter 4: all AE's, 4AF's, 9, 69

The figure shows the velocity and acceleration of

a particle at a particular instant in three situations.

(1) In which situation is the speed of the

particle increasing?

(2) In which situation is the speed of the

particle decreasing?

(3) In which situation is the speed not

changing?

A B C D

None of these three

Displacement in a plane

The displacement vector r:

if rrr

Displacement is the straight line between the final and initial position of the particle.

That is the vector difference between the final and initial position.

kzjyixr ˆˆˆby given is r vector The

Average Velocity

Average velocity v:

Average velocity: Displacement of a particle, r, divided by time interval t.

Instantaneous Velocity

Instantaneous velocity : Limit of the average velocity as t approaches zero. The

direction v is always tangent to the particles path.

The instantaneous velocity equals the derivative of the position vector with respect to

The magnitude of the instantaneous velocity vector is called the speed (scalar)

Average Acceleration

Average acceleration:

Average acceleration: Change in the velocity v divided by the time t during which the

change occurred.

Change can occur in direction and magnitude!

Acceleration points along change in velocity v!

Instantaneous Acceleration

Instantaneous acceleration: limiting value of the ratio

as t goes to zero.

Instantaneous acceleration equals the derivative of the velocity vector with respect to

Two- (or three)-dimensional motion with constant acceleration a

Trick 1:

The equations of motion we derived before (e.g. kinematic equations) are still

valid, but are now in vector form.

Trick 2 (Superposition principle):

Vector equations can be broken down into their x- and y- components. Then

calculated independently.

jvivv yx

Position vector: Velocity vector:

Two-dimensional motion with constant acceleration

tavv if

Velocity as function of time

1tatvrr iif

Position as function of time:

tatvyy

tatvxx

A melon truck brakes right before a

ravine and looses a few melons.

The melons skit over the edge

with an initial velocity of vx = 10.0

(a) Determine the x- and y-components of the velocity at any time and the total velocity at any

(b) Calculate the velocity and the speed of the melon at t = 5.00 s.

(c) Determine the x- and y-coordinates of the particle at any time t and the position vector r at

any time t.

(d) Graph the path of a melon.

Uniform Circular Motion

Motion in a circular path at constant speed.

• Velocity is changing, thus there is an acceleration!!

• Acceleration is perpendicular to velocity

• Centripetal acceleration is towards the center of the circle

• Magnitude of acceleration is

• r is radius of circle The period is:

An airplane makes a gradual 90° turn while flying at a constant speed of 200

The process takes 20.0 seconds to complete. For this turn the magnitude of the

average acceleration of the plane is:

1) zero

2) 40 m/s2

3) 20 m/s2

4) 14 m/s2

5) 10 m/s2

Relative Motion

Moving frame of reference

A boat heading due north crosses a

river with a speed of 10.0 km/h.

The water in the river has a speed

of 5.0 km/h due east.

(a) Determine the velocity of the boat.

(b) If the river is 3.0 km wide how long does it take to cross it?

A cart on a roller-coaster rolls down the

track shown below. As the cart rolls beyond

the point shown, what happens to its speed

and acceleration in the direction of motion?

1. Both decrease.

2. The speed decreases, but the acceleration

increases.

3. Both remain constant.

4. The speed increases, but acceleration

decreases.

5. Both increase.

• In this chapter we will learn about the kinematics (displacement, velocity, acceleration) of a particle in two or

three dimensions.

• Projectile motion

• Relative motion

Chapter 4, part 2:

Homework 7: (due Monday, Sept. 13, 2010):

Chapter 5: 8AE's, 4AF's, CQ13, 12, 13, 30*

Figure 4-24 shows three situations in which identical projectiles are launched from the ground

(at the same level) at identical speeds and angles. The projectiles do not land on the same

terrain, however. Rank the situations according to the final speeds of the projectiles just before

they land, greatest first.

1) (a) > (b) > (c)

2) They all have the same final speed.

3) (c) > (b) > (a)

4) (a) > (c) > (b)

A ball thrown vertically upward reaches a maximum height of 30.

meters above the surface of Earth. At its maximum height, what is

the speed of the ball?

A) 9.8 m/s

B) 3.1 m/s

C) 24 m/s

D) 0.0 m/s

E) None of the above

An archer uses a bow to fire two similar arrows with the same string force. One

arrow is fired at an angle of 60° with the horizontal, and the other is fired at an

angle of 45° with the horizontal. Compared to the arrow fired at 60°, the arrow fired

at 45° has which of the following properties:

1) longer horizontal range

2) shorter flight time

3) longer flight time

4) shorter horizontal range

5) Both 1 and 2

Projectile motion

Two assumptions:

1. Free-fall acceleration g is constant.

2. Air resistance is negligible.

- The path of a projectile is a parabola (derivation: see book).

- Projectile leaves origin with an initial velocity of vi.

- Projectile is launched at an angle i

- Velocity vector changes in magnitude and direction.

- Acceleration in y-direction (vertical) is g.

- Acceleration in x-direction (horizontal) is 0.

gtvv yiyf

1tatvyy yyiif

xixf vv

tvxx xiif

Acceleration in x-direction is 0. Acceleration in y-direction is g.

(Constant velocity) (Constant acceleration)

Projectile motion

Superposition of motion in x-direction and

motion in y-direction

The horizontal motion and vertical motion are independent of each other; that is, neither motion affects the other.

Simultaneous fall demo

Which ball will hit the ground first?

• Straight drop• Straight out• Both released at

the same time

A battleship simultaneously fires two shells at enemy ships.

If the shells follow the parabolic trajectories shown, which ship gets hit first?

3) Both hit at the same time.

4) Need more information.

1. hits the criminal regardless of the value of vo

> vmin

2. hits the criminal only if vo

is large enough (vo

> nvmin

, where n “large enough”)

3. misses the criminal.

Consider the situation depicted here. A bullet is

accurately aimed at a dangerous criminal

hanging from the gutter of a building. The target

is in range of the bullet’s minimum velocity, vmin

The instant the gun is fired and the bullet moves

with a speed vo, the criminal lets go and drops

to the ground. What happens? The bullet

Hitting the bull’s eye. How’s that?

Just to re-iterate:

A rifle is aimed horizontally at a target 30 m away. The bullet hits the target 1.9 cm below the aiming point.

(a) What is the bullets time of flight

(b) What is the bullets speed as it emerges from the rifle?

A ball is tossed from an upper-story window of a building. The ball is

given an initial velocity of 8.00 m/s at an angle of 20° below the

horizontal. It strikes the ground 3.00 s later.

(a) How far horizontally from the base of the building does the ball strike the ground?

(b) Find the height from which the ball was thrown.

(c) How long does it take the ball to reach a point 10 m below the level of launching?

• In this chapter we will learn about the relationship between the force exerted on an object

and the acceleration of the object.

• Forces

• Newton’s three laws.

Chapter 5: Force and Motion – I

Homework : (due Wednesday, Sept. 15, 2010)

Chapter 5: AE11, 24, 20, 33, 42, 71

1. Which of these laws is not one of Newton’s laws?

___ 1. Action is reaction.

___ 2. F = ma.

___ 3. All objects fall with equal acceleration.

___ 4. Objects at rest stay at rest, etc.

2. The law of inertia

___ 1. is not covered in the reading assignment.

___ 2. expresses the tendency of bodies to maintain their state of motion.

___ 3. is Newton’s 3rd law.

3. “Impulse” is

___ 1. not covered in the reading assignment.

___ 2. another name for force.

___ 3. another name for acceleration.

2. Astronauts on the Moon can jump so high because

___ 1. they weigh less there than they do on Earth.

___ 2. their mass is less there than it is on Earth.

___ 3. there is no atmosphere on the Moon.

3. Is the normal force on a body always equal to its weight?

___ 1. yes

___ 2. no

Review of Chapters 2 & 4

• Displacement (position)

• Velocity

• Acceleration

A ball is tossed from an upper-story window of a building. The ball is

given an initial velocity of 8.00 m/s at an angle of 20° below the

horizontal. It strikes the ground 3.00 s later.

(a) How far horizontally from the base of the building does the ball strike the ground?

(b) Find the height from which the ball was thrown.

(c) How long does it take the ball to reach a point 10 m below the level of launching?

Contact forces

- Involve physical contact between objects.

Field forces:

-No physical contact between objects

- Forces act through empty space

gravity

electric

magnetic

Measuring forces

- Forces are often measured by determining the elongation of a calibrated spring.

- Forces are vectors!! Remember vector addition.

- To calculate net force on an object you must use vector addition.

Newton’s first law:

In the absence of external forces (no net force):

• an object at rest remains at rest

• an object in motion continues in motion with constant velocity (constant speed, straight line)

(assume no friction).

Or: When no force acts on an object, the acceleration of the object is zero.

Inertia: Object resists any attempt to change is velocity

Inertial frame of reference:

-A frame (system) that is not accelerating.

- Newton’s laws hold only true in non-accelerating (inertial) frames of reference!

Are the following inertial frames of reference:

- A cruising car?

- A braking car?

- The earth?

- Accelerating car?

- Mass of an object specifies how much inertia the object has.

- Unit of mass is kg.

- The greater the mass of an object, the less it accelerates under the action of an applied force.

- Don’t confuse mass and weight (see later).

Newton’s second law

(Very important)

The acceleration of an object is:

- directly proportional to the net force acting on it

- and inversely proportional to its mass.

amFnet

xxnet amF , yynet amF , zznet amF ,

Unit of force:

• The unit of force is the Newton (1N)

• One Newton: The force required to accelerate a 1 kg mass by 1m/s2.

• 1N = 1kg·m/s2

Two forces act on a hockey puck (mass 0.3 kg) as shown

in the figure.

(a) Determine the magnitude and direction of the net force acting on the puck

(b) Determine the magnitude and the direction of the pucks acceleration.

(c) What third force (direction and magnitude) would need to be applied to the puck so that its

acceleration is zero?

= 8.0 N

= 60°

= 5.0 N

= - 20°

• In this chapter we will learn about the relationship between the force exerted on an object

and the acceleration of the object.

• Forces

• Newton’s three laws.

Chapter 5: Force and Motion – II

Homework : (due Saturday, Sept. 18, 2010)

Chapter 6: 10AE's, 4AF's, 19, 64, 69

1. Which of these laws is not one of Newton’s laws?

___ 1. Action is reaction.

___ 2. F = ma.

___ 3. All objects fall with equal acceleration.

___ 4. Objects at rest stay at rest, etc.

2. Astronauts on the Moon can jump so high because

___ 1. they weigh less there than they do on Earth.

___ 2. their mass is less there than it is on Earth.

___ 3. there is no atmosphere on the Moon.

3. Is the normal force on a body always equal to its weight?

___ 1. yes

___ 2. no

The force of gravity and weight

• Objects are attracted to the Earth.

• This attractive force is the force of gravity Fg

• The magnitude of this force is called the weight of the object.

• The weight of an object is, thus mg (Force required to keep mass m from falling to the ground).

The weight of an object can very with location (less weight on the moon than on earth, since g is smaller).

The mass of an object does not vary.

Don’t confuse mass and weight

Consider a person standing in an elevator

that is accelerating upward. The upward

normal force N exerted by the elevator floor on the person is

1. larger than

2. identical to

3. smaller than

the downward weight W of the person.

Newton’s third law

If two objects interact, the force F12

exerted by object 1 on object 2 is equal in magnitude and opposite in direction

to the force F21

exerted by object 2 on object 1:

“For every action there is an equal and opposite

reaction.”

2112 FF

Action and reaction forces always act on different objects.

Where is the action and reaction force?

Action-reaction pairs act on DIFFERENT objects

n … normal force

When a body presses against a surface, the surface pushes on the body with a normal force n, that is perpendicular to the surface .

A locomotive pulls a series of wagons. Which is the correct analysis of the situation?

1. The train moves forward because the locomotive pulls forward slightly harder on the wagons than the

wagons pull backward on the locomotive.

2. Because action always equals reaction, the locomotive cannot pull the wagons the wagons pull backward

just as hard as the locomotive pulls forward, so there is no motion.

3. The locomotive gets the wagons to move by giving them a tug during which the force on the wagons is

momentarily greater than the force exerted by the wagons on the locomotive.

4. The locomotive’s force on the wagons is as strong as the force of the wagons on the locomotive, but the

frictional force on the locomotive

is forward and large while the backward frictional force on the wagons is small.

5. The locomotive can pull the wagons forward only if it weighs more than the wagons.

Conceptual example:

A large man and a small boy stand facing each other on frictionless ice. They put their hands together

and push against each other so that they move apart.

(a) Who moves away with the higher speed

(a) Man

(b) Boy

(c) Same

(d) Need more info

(b) Who moves farther while their hands are in contact?

• Analyzing forces

• Free body diagram

• Tension in a rope = magnitude of the force that the rope exerts on object.

Black board:

Analyzing forces:

Lamp hanging from a ceiling.

Net force on lamp is zero (not accelerating)

A traffic light weighing 125 N hangs from a cable tied to two other cables fastened to a support as shown in the

figure.

Find the tension in the three cables.

Black board example 5.4 HW 38

A worker drags a crate across a factory floor by pulling on a rope tied to the crate. The worker exerts a force of 450 N

on the rope, which is inclined at 38° to the horizontal and the floor exerts a horizontal force of 125 N that

opposes the motion. Calculate the magnitude of acceleration for the crate if

(a) Its mass is 310 kg

(b) Its weight is 310 N

(c) What is it’s speed after 5 seconds?

(Always draw a diagram).

Attwood’s machine.

Two objects of unequal mass (m1

and m2

) are hung over a pulley.

(a) Determine the magnitude of the acceleration of the two objects and the tension in the cord.

(b) Solve (a) for m1

= 2.00 kg and m2

= 4.00 kg.

Two objects of mass m1

and m2

are attached by a string over a pulley as shown in the Figure. m2

lies on an incline with

angle .

(a) Determine the magnitude of the acceleration of the two objects and the tension in the cord.

(b) m1

= 10.0 kg, m2

= 5.00 kg, = 45º

physics 113 syllabus physics 113-a fall 2010 prof. jed macosko office: olin 215, lab: olin 213...

final exam

homework problems

class midterm exams

homework notebook

late homework

force motion isept

lab sessions

exam solutions

Documents

phy 113 c general physics i 11 am – 12:15 pm tr olin 101...

phy 113 a general physics i 9-9:50 am mwf olin 101 plan...

phy 113 a general physics i 9-9:50 am mwf olin 101 plan...

phy 113 a general physics i 9-9:50 am mwf olin 101 plan...

physics 113 syllabus physics 113-a (ccn: 81104) fall 2005...

phy 113 c general physics i 11 am - 12:15 p m mwf olin...

phy 113 a general physics i 9-9:50 am mwf olin 101 plan...

olin professional development program (olin prodev) summer...

phy 113 a general physics i 9-9:50 am mwf olin 101 plan...

phy 113 a general physics i 9-9:50 am mwf olin...

phy 113 a general physics i 9-9:50 am mwf olin 101 plan...

phy 113 a general physics i 11 am-12:15 p m mwf olin 101...

physics 113 midterm 1 - wake forest...

phy 113 c general physics i 11 am – 12:15 p m mwf olin...

phy 113 a general physics i 9-9:50 am mwf olin 101 plan...

phy 113 a general physics i 9-9:50 am mwf olin 101 plan...

phy 113 c general physics i 11 am – 12:15 p m mwf olin...

phy 113 a general physics i 9-9:50 am mwf olin 101 plan...

phy 113 c general physics i 11 am – 12:15 p m mwf olin...

phy 113 a general physics i 11 am-12:15 p m mwf olin 101...