class lecture outlines for physics 110: applied physics

Class Lecture Outlines for Physics 110: Applied Physics

Jim BogerFlathead Valley Community College

Kalispell [email protected]

November 3, 2013

Contents

1 What is Applied Physics? 11.1 General concepts of the physical world . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Laws, Hypotheses and Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Critical Thinking lives here . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Difference between Engineering and Physics . . . . . . . . . . . . . . . . . . . . . . 11.5 The list of topics we will study this semester . . . . . . . . . . . . . . . . . . . . . 11.6 Homework: None . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Tools for the study of Physics 32.1 Units of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Scientific and Engineering Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 32.3 Dimensional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.4 Accuracy & Precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.5 significant figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.6 Homework: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 Vectors 53.1 Definitions for Vectors and Scalars . . . . . . . . . . . . . . . . . . . . . . . . . . 53.2 Graphically Adding Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2.1 Add 2 vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.2.2 Add 3 vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.2.3 subtract 2 vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.3 Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.3.1 Cartesian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.3.2 Polar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.4 Mathematics of Vector Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.5 Homework: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4 Motion 74.1 Definitions for displacement velocity acceleration . . . . . . . . . . . . . . . . . . . 7

4.1.1 Motion diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.1.2 Motion terms and graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.1.3 Instant vs. average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.1.4 Connecting x,v and a graphs . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4.2 Equations of motion for constant acceleration . . . . . . . . . . . . . . . . . . . . . 84.2.1 1-D equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.2.2 Example with kinematic equations . . . . . . . . . . . . . . . . . . . . . . . 8

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iv

4.3 Homework: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

5 Example Problems using Kinematic Equations 95.1 Examples of kinematic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5.1.1 Example 1: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95.1.2 Example 2: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5.2 Projectile motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95.2.1 Description of 2D kinematics and Demos . . . . . . . . . . . . . . . . . . . 95.2.2 Example 3: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5.3 Homework: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

6 Force and Newton’s Laws of Motion 116.1 Newton’s first law: Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116.2 Newton’s second law: Changing Inertia . . . . . . . . . . . . . . . . . . . . . . . . 116.3 Gravity and Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116.4 Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116.5 Newton’s third law: Action-Reaction . . . . . . . . . . . . . . . . . . . . . . . . . 116.6 Homework: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

7 Examples Using Newton’s Laws 137.1 Examples in 1-D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

7.1.1 The Free Body Diagram FBD . . . . . . . . . . . . . . . . . . . . . . . . . 137.1.2 A simple sled example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137.1.3 The elevator example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

7.2 Examples in 2-D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137.2.1 Block on an incline plane . . . . . . . . . . . . . . . . . . . . . . . . . . . 137.2.2 Pulling a sled with a non-level rope . . . . . . . . . . . . . . . . . . . . . . 13

7.3 Examples with motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137.4 Homework: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

8 Impulse and Momentum 158.1 Impluse and Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

8.1.1 Impluse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158.1.2 Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

8.2 Homework: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

9 Collisions 179.1 Collision problems in 1-D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179.2 Collision problems in 2-D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

FVCC PHYSICS 101 Applied Physics Lectures v

9.3 Homework: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

10 Exam 1 19

10.1 Textbook Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

10.2 Textbook Chapter 2: Toolkit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

10.3 Textbook Chapter 3: Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

10.4 Textbook Chapter 4: Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

10.5 Textbook Chapter 5: Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

10.6 Textbook Chapter 6: Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

10.7 Homework: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

11 Statics 21

11.1 Equilibrium in Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

11.2 Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

11.3 Homework: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

12 Statics Examples 23

12.1 Center of Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

12.2 Example Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

12.3 Homework: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

13 Work and Energy 25

13.1 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

13.2 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

13.2.1 Potential Energy PE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

13.2.2 Kinetic Energy KE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

13.2.3 Conservation of Mechanical Energy . . . . . . . . . . . . . . . . . . . . . . 25

13.3 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

13.4 Simple Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

13.5 Homework: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

14 Rigid Body motion 27

14.1 Rotation Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

14.1.1 Rotational kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

14.1.2 Newton’s laws expressed in rotational motion . . . . . . . . . . . . . . . . . 28

14.2 Homework: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

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15 Angular Energy and Momentum 2915.1 Rotational kinetic energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2915.2 Angular Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2915.3 Homework: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

16 Circular motion 3116.1 Circular Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3116.2 Homework: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

17 Satellites 3317.1 Newton’s Universal Law of Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . 3317.2 Circular Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3317.3 Satellite Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

17.3.1 Period of a Satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3317.3.2 Ground Track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3317.3.3 LEO,MEO,GEO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3317.3.4 The Space Elevator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

18 Midterm Exam 35

19 Electrostatics 3719.1 Rules for Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3719.2 Coulomb’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

20 Ohm’s Law 39

21 Circuits 41

22 Magnetism 4322.1 Calculating the Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4322.2 Force from magnetic fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

22.2.1 Force on moving charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4322.2.2 Force on current carrying wires . . . . . . . . . . . . . . . . . . . . . . . . 43

22.3 Faraday’s law of induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4322.4 Homework: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Class Period 1

What is Applied Physics?

Read the first chapter in our book, an introduction to physics.

1.1 General concepts of the physical world

1.2 Laws, Hypotheses and Theories

1.3 Critical Thinking lives here

1.4 Difference between Engineering and Physics

1.5 The list of topics we will study this semester

1.6 Homework: None

1

Class Period 2

Tools for the study of Physics

Read Chapter 2. Physics is largely a quantitative study of the natural world and a few tools andtechniques are critical to stay organized. These tools may have been seen in other classes and wewill not spend a great deal of time on them. Rather, since we will use them for the rest of thesemester, you’ll get lots of practice with these tools over time.

2.1 Units of Measurement

1. Consider the concept of a naked number.

2. Special notation for dressing a number (e.g. 75 [mph])

2.2 Scientific and Engineering Notation

2.3 Dimensional Analysis

2.4 Accuracy & Precision

2.5 significant figures

1. Significant figures are a way of expressing how exact a quantity is known. The error level isimplied.

6.2→ 6.20± .05 (2.1)

2. Use Scientific notation to clarify the number of significant figures

2.6 Homework:

1. Tool Kit Problems 4: 46,49,52,54,58,64,68

2. Tool Kit Problems 5: 3,8,69,82,86,92,99,108

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4

3. Tool Kit Problems 6: 35,36,47,55,62,65,73

4. Tool Kit Problems 7: 1-10

5. Tool Kit Problems 8: 1-10

6. Tool Kit Problems 9: 1,5,31,35,43,47

7. Tool Kit Review Problem Set: 16,20,24,44

Class Period 3

Vectors

This period will cover all of chapter 3 which is a review of vectors.

3.1 Definitions for Vectors and Scalars

A vector always has at least 2 numbers to describe it. They are: Magnitude and direction.

3.2 Graphically Adding Vectors

Use the Tip-to-tail Method.

3.2.1 Add 2 vectors

3.2.2 Add 3 vectors

3.2.3 subtract 2 vectors

3.3 Coordinate Systems

3.3.1 Cartesian

or (x,y) coordinates also often called the rectangular coordinates. This is important to know.

3.3.2 Polar

or (r, θ) coordinates also often called the circular coordinates. It turns out that when dealing withcircular motion, choosing this coordinate system is helpful.

3.4 Mathematics of Vector Addition

3.5 Homework:

1. Vector Problems 3: 1,3,4,9,12,19,22,28,43,45

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6

2. Vector Problem Set: 14,17,22

3. Vector Applied Concepts: 2,4

Class Period 4

Motion

This period we are covering the material in chapter 4 of the textbook.

4.1 Definitions for displacement velocity acceleration

4.1.1 Motion diagrams

4.1.2 Motion terms and graphs

The basic equations for motion are:

x (4.1)

v =∆x

∆t=

(x2 − x1)(t2 − t1)

(4.2)

a =∆v

∆t=

(v2 − v1)(t2 − t1)

(4.3)

4.1.3 Instant vs. average

In the limit of t2 − t1 = 0, we get the tangent to the line which is the instantaneous value.

4.1.4 Connecting x,v and a graphs

Some key points:

1. The slope of the x vs. t graph is the velocity

2. The slope of the v vs. t graph is the acceleration

3. The area under the a vs. t graph is ∆v

4. The area under the v vs. t graph is ∆x

Do Knight worksheet 2.2

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4.2 Equations of motion for constant acceleration

4.2.1 1-D equations

Given that acceleration is uniform/constant, than these formulas hold true.

a(t) = constant (4.4)

v(t) = v0 + at (4.5)

x(t) = x0 + vt+1

2at2 (4.6)

4.2.2 Example with kinematic equations

4.3 Homework:

1. Motion Problems 1: 1,4,7,18,20,23,25,26

2. Motion Problems 2: 4,5,8,10,18,23

3. Motion Problems 3: 3,4,5,8,9,12,16,21,27

Class Period 5

Example Problems using Kinematic Equations

Practicing with 2-D kinematics

5.1 Examples of kinematic equations

5.1.1 Example 1:

Homework style problems with velocity as vectors

5.1.2 Example 2:

Homework style problems with kinematic equations

5.2 Projectile motion

5.2.1 Description of 2D kinematics and Demos

• See MIT monkey shoot video

• Do cannon ball example

5.2.2 Example 3:

2D problem using kinematic equations

5.3 Homework:

1. Motion Problems 4: 1-5,11

2. Motion Applied Concepts: 3

9

Class Period 6

Force and Newton’s Laws of Motion

In mechanics, Newton’s 3 laws are the basis. Today we cover those laws and learn to apply them

6.1 Newton’s first law: Inertia

6.2 Newton’s second law: Changing Inertia

Σ~F = m~a (6.1)

New unit: Newton, the SI unit of force:1[N ] = 1[kgm

s2]

6.3 Gravity and Weight

pounds 6= kilogramsWeight = mg (6.2)

6.4 Friction

Ff = µFN (6.3)

6.5 Newton’s third law: Action-Reaction

6.6 Homework:

1. Force Problems 2: 3,7,11,20,23,29,31

2. Force Problems 3: 2,4,9,15,17,25,30

11

Class Period 7

Examples Using Newton’s Laws

This lecture continues the discussion of the laws of motion.

7.1 Examples in 1-D

7.1.1 The Free Body Diagram FBD

7.1.2 A simple sled example

7.1.3 The elevator example

7.2 Examples in 2-D

7.2.1 Block on an incline plane

7.2.2 Pulling a sled with a non-level rope

7.3 Examples with motion

7.4 Homework:

1. Force Problems 4: 3,4,7,11,15

2. Force Problems 5: 7,9,10,12,13

3. Force, Applied Concepts: 3,4

13

Class Period 8

Impulse and Momentum

This is the chapter on the momentum. It covers impluse, which quantifies force*time and momentumwhich is a unique new term that comes directly from Newton’s laws. The principle application wewill look at is inelastic collisions.

8.1 Impluse and Momentum

8.1.1 Impluse

I = F ·∆t (8.1)

8.1.2 Momentum

p = mv (8.2)

Unit: [kg ·m/s]

8.2 Homework:

1. Momentum Problems 1: 1,5,9,11,14,18,21

2. Momentum Problems 2: 1,5,7,10

15

Class Period 9

Collisions

This is the application of momentum

9.1 Collision problems in 1-D

9.2 Collision problems in 2-D

9.3 Homework:

1. Momentum Problems 3: 3,5,6,8

17

Class Period 10

Exam 1

Review topics for Exam one

10.1 Textbook Chapter 1

No specific questions from this chapter

10.2 Textbook Chapter 2: Toolkit

sig figs, scientific notation, error analysis,

10.3 Textbook Chapter 3: Vectors

Understand the definition of a vector.Understand how to define a vector in rectangular or polar coordinates.Be able to add vectors graphically. Be able to add vectors mathematically.

10.4 Textbook Chapter 4: Motion

Understand Graphs for position, velocity and acceleration verses time.Understand mathematical definitions of velocity and acceration.

10.5 Textbook Chapter 5: Force

Be able to state Newton’s 3 laws of motion.

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20

10.6 Textbook Chapter 6: Momentum

10.7 Homework:

1. Momentum Review Problems: 2,7

2. Momentum Applied Concepts: 4

Class Period 11

Statics

Statics is the study of the forces in a structure so as to make the structure stationary. It is basedon the idea that the forces and the torques are in balance for a given body.

11.1 Equilibrium in Forces

For something to be in equilibrium, then by Newton’s second law the net force acting on the bodyhas to be zero.

Σ~F = 0 (11.1)

Examples.

11.2 Torque

τ = rF sin θ (11.2)

Since a unbalanced torque will cause an object to rotate, then we have Newton’s second law fortorque:

τ = Iα (11.3)

Here I is called the moment of inertia and works just like mass, but is a little more involved interms of calculating it. Luckily for statics, the equation we really need is when there is no angularacceleration (α = 0). For equilibrium:

Στ = 0 (11.4)

Examples

11.3 Homework:

1. Statics Problems 1: 4,7

2. Statics Problems 2: 19,21,22,23,26

21

Class Period 12

Statics Examples

Using the tools from the last lecture, do examples that were done in lab.

12.1 Center of Gravity

This section is an application of the basic laws of statics. It is left to the student to read the book onthis section, beginning on page 199. There are some homework problems assigned for this sectionso it is fair game for an exam.

12.2 Example Problems

Continue the work we began in the lab by solving problems.

12.3 Homework:

1. Statics Problems 3: 1,2,5,6,8,12,13,16,17,22

2. Statics Problems 4: 9,13,15,17

3. Statics Problems 5: 1,4,7,9,10,14

4. Statics Review Problems: 14,16,23,27

23

Class Period 13

Work and Energy

Energy is another fundamental quantity in physics. It is defined as the amount of work it can do onan object. So we start with the mathematical definition of work. Since energy cannot be created ordestroyed, then we get to the main application of energy which is solving problems with the conceptof the conservation of energy.

13.1 Work

W = F · d (13.1)

W = Fd cos θ (13.2)

13.2 Energy

Wnet = ∆KE (13.3)

W = −∆PE (13.4)

13.2.1 Potential Energy PE

PE = mgh (13.5)

13.2.2 Kinetic Energy KE

KE =1

2mv2 (13.6)

13.2.3 Conservation of Mechanical Energy

When there are not non-conservative forces acting on a system (i.e. friction) then mechanical energyis conserved.

KEi + PEi = KEf + PEf (13.7)

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26

13.3 Power

P =W

∆t(13.8)

13.4 Simple Machines

Pulleys, gears, lever arms, ramps and jacks are all simple machines and conservation of energy is theprinciple behind them. In short, if you need to do work on a box by lifting it, you can lift it with alarge force and short distance or small force and large distance.

F1 · d1 = F2 · d2 (13.9)

13.5 Homework:

1. Work Problems 1: 1,4,9,13,15

2. Work Problems 2: 5,8,14,15,19,20

3. Work Problems 3: 3,8,9,15,16,17

4. Work Problems 4: 3,5,6,9,10

Class Period 14

Rigid Body motion

Rotations represent a significant expansion of Newton’s three laws to rigid bodies. All of the conceptscovered so far have an equivalent expression in rotational motion. Most important is that the motionof an extended rigid body can be broken into two parts: motion of the center of mass, and rotationalmotion about the center of mass. Up to this point, we have concentrated on the motion of thecenter of mass. Now we study the rotational motion.

14.1 Rotation Quantities

Here are the basic equations for rotational motion.

π =C

D(14.1)

θ...measured in radians (14.2)

ω =∆θ

∆t(14.3)

α =∆ω

∆t(14.4)

(14.5)

14.1.1 Rotational kinematics

When angular acceleration is constant (α = constant) then we have a set of equations that matchlinear motion kinematic equations.

θ(t) = θ0 + ωt+1

2αt2 (14.6)

ω(t) = ω0 + αt (14.7)

α(t) = constant (14.8)

Use these equations in an example.

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28

14.1.2 Newton’s laws expressed in rotational motion

In statics torque was set to zero. Now we see that it is really related to angular acceleration andthe constant of proportionality is called the moment of inertia, I.

τ = Iα (14.9)

~τ = ~r × ~F (14.10)

Some moments of Inertia:

• Solid disk spinning about its axis: I = 12MR2

• Solid ball spinning about its diameter: I = 25MR2

• A wheel with its mass concentrated at the rim: I = MR2

Work on the Atwood machine example. This is a longer example and may need the next classperiod.

14.2 Homework:

1. Rotational Problems 1: 1,4,9,18,20,21,23

Class Period 15

Angular Energy and Momentum

Today we cover 2 very interesting implications of rotational motion: The first is rotational kineticenergy and the second is angular momentum

15.1 Rotational kinetic energy

Here are the basic equations for rotational motion.

KE =1

2Iω2 (15.1)

15.2 Angular Momentum

~L = ~r × ~p (15.2)

~L = I~ω (15.3)

Angular momentum is related to Torque precisely as linear momentum is related to Force. Tochange the linear momentum of an object we have to apply an external force. To change theangular momentum of an object we have to apply torque.DEMO: The gyroscopic wheel.

15.3 Homework:

1. Rotational Problems 1: 1,4,9,18,20,21,23

2. Special Problem 1: A motor-driven grinding wheel starts from rest and receives a constantcounterclockwise angular acceleration of 3.00[ rad

s2] for 12.0[s]. Determine its angular velocity

at the end of this period and the angle through which it has turned.

3. Special Problem 2: A one gallon bucket is lowered into a water well that is 30 [ft] deep. Therope attached to the bucket coils around a solid drum of mass 2[slugs] and the diameter is 8[in]. The handle to crank the bucket up and down is attached to a bicycle wheel and has amass of 0.4 [slugs] and diameter 27 [in]. Assume all of the mass of the wheel/handle is at therim of the wheel. If you crank a full bucket with weight 9 [lb] to the top, then let go of thewheel, what is the velocity of the handle on the wheel when the bucket reaches the water.

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30

Figure 15.1

4. Special Problem 3: A string is wrapped around a uniform cylinder is released from rest withthe string vertical and its top end tied to a fixed bar. Show that (a) the tension in the stringis one-third the weight of the cylinder, (b) the magnitude of the acceleration of the center

of gravity is 2g3

, and (c) the speed of the center of gravity is√

4gh3

after the cylinder has

descended through distance h. The moment of inertia I = 12MR2.

Class Period 16

Circular motion

Circular motion isn’t just another motion to analyze. It is quite literally the motion that makes lifein the universe possible. Without it we would be sucked into massive stars and be crushed, thanksto the one-way force of gravity.

16.1 Circular Motion

An acceleration is a vector that can change the velocity vector. The velocity vector can be increased,decreased or simply change direction. Circular motion is the case where the acceleration vector ischanging the velocity vector’s direction.

|Fc| =mv2

r(16.1)

|Fc| = mrω2 (16.2)

~Fc = −mrω2r (16.3)

The magnitude is given but the sign must be pointing to the center of the rotation. We know thisbecause the motion is completely understood.

16.2 Homework:

1. Rotational Problems 6: 7,9

2. Rotational Problems 7: 7,9

3. Gravitation Problems 1: 1-5,10

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Class Period 17

Satellites

No motion is more fundamental as circular motion. It is the motion that is a match for the relentlessgravity that stalks the universe.

17.1 Newton’s Universal Law of Gravity

~Fg = Gm1m2

r212r (17.1)

G = 6.67× 10−11

[Nm2

kg2

](17.2)

17.2 Circular Motion

Fc = mv2

r(17.3)

17.3 Satellite Motion

17.3.1 Period of a Satellite

17.3.2 Ground Track

17.3.3 LEO,MEO,GEO

see the website ”Heavens Above”

17.3.4 The Space Elevator

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Class Period 18

Midterm Exam

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Class Period 19

Electrostatics

A quick tour of electrostatics

19.1 Rules for Charge

• Charge is quantized

• Like charges repel

• Opposite charges attract

• charge is a fundamental part of the atom

19.2 Coulomb’s law

This law is just like gravity, but much stronger.

~F12(r) =kq1q2r212

r (19.1)

The k = 9× 109 is the electrostatic constant

19.3 The Electric Field

Fields are real. They are an alteration of space. Specifically, fields affect charged particles. It is theelectric field effect.

~E =~F

q(19.2)

• Electric field lines

• Demo Phet field hockey

•

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19.4 The electric dipole

19.5 Charge Distributions and fields

Class Period 20

Ohm’s Law

Ohm’s law is central to circuits

20.1 Ohm’s Law

Starting from E fields, derive V=IR

20.1.1 Resistivity and conductivity

20.1.2 Calculating R

R =ρL

A(20.1)

20.1.3 Resistivity dependance on temperature

20.1.4 Ohmic and non-Ohmic devices

20.2 Power

P = V I (20.2)

P =V 2

R(20.3)

P = I2R (20.4)

20.3 The complete circuit

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Class Period 21

Circuits

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Class Period 22

Magnetism

The book is rather light in their treatment of Magnetism. So I have added some addition problemsin here.

22.1 Calculating the Magnetic Field

22.2 Force from magnetic fields

22.2.1 Force on moving charges

22.2.2 Force on current carrying wires

22.3 Faraday’s law of induction

22.4 Homework:

1. Magnetism Problems 2: 1,3,7,8,11,13

2. An electron is a accelerated through 2, 400[V ] from rest and enters a region where their is auniform magnetic field of 1.70[T ]. Calculate the minimum and maximum force possible onthis electron.

3. An α−particle, is traveling at 3.00 × 106[m/s] perpendicular to a magnetic field of 3.6[T ].What is its radius of motion?

4. Two parallel wires each carrying 4.00[A] in the same direction are 15[cm] apart. Calculate themagnitude of the force between them. Are they attracting or repelling each other?

5. A cathode ray tube is shown in the figure. Electrons are guided through the plates shown bycrossed electric and magnetic fields shown. Calculate a formula for the condition where theelectrons are undeflected.

6. A single loop of wire has resistance of 2.0[Ω] and a radius of 5.0[cm]. If it is placed in amagnetic field that is changing at 1.2 × 10−1[T/s] and the surface normal of the loop isparallel to the vector B field, what is the current in the loop?

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44

Figure 22.1

7. A single loop of wire has resistance of 2.0[Ω] and a radius of 5.0[cm]. If it is placed in amagnetic field that is changing at 1.2 × 10−1[T/s] and the surface normal of the loop is at30[deg] to the vector B field, what is the current in the loop?

class lecture outlines for physics 110: applied physics

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