# Work & Work-Energy Theorem

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## Video Clips

#### Work and Kinetic Energy

RealVideo®
7:42 minutes (0:00 - 7:42)

Definitions, with proof that work is difference in kinetic energy.

Instructor: Prof. Walter Lewin
Prior Knowledge: F=ma (6:52 of V6)

#### Work in Three Dimensions

RealVideo®
5:22 minutes (7:42 - 13:04)

Work defined by line integral; proof that work is difference in kinetic energy in 3D.

Instructor: Prof. Walter Lewin
Prior Knowledge: Work (beginning of V11)

#### Gravitational Work

RealVideo®
3:56 minutes (13:04 - 17:00)

Example of gravity acting on particle; proof that work is independent of path.

Instructor: Prof. Walter Lewin
Prior Knowledge: Work in Three Dimensions (7:42 of V11)

#### Two Basic Concepts

RealVideo®
1:44 minutes (0:00 - 1:44)

Work-Energy Theorem and conservation of mechanical energy restated.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Pendulum Oscillation Calculation II

RealVideo®
7:26 minutes (19:13 - 26:39)

Calculation of θmax by work-energy; phase angle and oscillation equation obtained.

Instructor: Prof. Walter Lewin
Prior Knowledge: Pendulum Oscillation I (12:09 of V18)

## Lecture Notes

#### Work and Energy

PDF - 1.5 MB#
Page 4 to page 6

Definition of the work-energy principle; work in one and three dimensions; variable force and work. Includes several examples.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Newton's Laws, Integration

#### Work and Energy

PDF#
Page 7 to page 15

Definition of the work-energy principle; work in one and three dimensions; variable force and work. Includes several examples.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Newton's Laws, Integration

#### Work and Force

PDF
Page 1

Work done by a force (W = F*d); conservation of energy.

Instructor: Dr. George Stephans
Prior Knowledge: Newton's Laws

#### Work-Energy Theorem

PDF
Page 1 to page 2

Relation between work done and change in energy; when to use work-energy; potential energy defined; calculating changes in potential energy.

Instructor: Dr. George Stephans
Prior Knowledge: Work and Force

#### Energy and Work

PDF
Page 1 to page 11

Energy transformations and conservation of energy; energy of system and surroundings; definition of kinetic energy, with equation (K = 1/2*m*v2); definition of work done by a constant force, with equation (Wapplied = Fx*δ x).

Prior Knowledge: Newton's Laws

#### Power

PDF
Page 20 to page 29

Definition of Work-Kinetic Energy Theorem (Kf = Ki + Wf,i); work done by non-constant force; work done along an arbitrary path; line integrals; definition of average power; definition of instantaneous power.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Energy and Work, Dot Products, Integrals

#### Experiment 5B

PDF
Page 30 to page 40

Friction experiment setup and procedure.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Friction

#### Work and Dot Product Problem Solving Strategies

PDF
Page 1 to page 4

Class problems.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Lecture 14

## Practice Problems

#### Work on Sliding Box

PDF
Problem 5

4-part problem; finding work in terms of frictional force; stopping time; work to accelerate the box.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: None

#### Work and Force

PDF
Problem 1

Work done by objects moving against forces. Solution not included.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Spring - Object on an Inclined Plane with Friction

PDF
Problem 21

Motion of an object pushed by a spring up an inclined plane.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Work on a Falling Ball

PDF
Problem 1

Work done on a falling ball. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Kinetic Energy and Friction

PDF
Problem 5

Change in kinetic energy of a puck sliding along a horizontal surface with friction. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Energy and Acceleration

PDF
Problem 6

Energy required to accelerate a car from rest to 10 mph, and from 10 mph to 20 mph. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Kinetic Energy and Force

PDF
Problem 7

Kinetic energy of a particle under the action of a variable force. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Acceleration and Work

PDF
Problem 8

Work done on an accelerating block by the force of friction. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Weightlifter

PDF
Problem 9

Work done by a weightlifter holding a barbell. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Walking and Work

PDF
Problem 10

Work done by the floor on the feet of a walking person. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Rolling and Work

PDF
Problem 11

Work done on a ball rolling in a spiral path along the inside of a hollow cylinder. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Kinetic Energy

PDF
Problem 3

Graph of kinetic energy of a falling object. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Kinetic Energy and Speed

PDF
Problem 4

Speed of a ball dropped into a jar of oil. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Qualitative Description of Work

PDF
Problem 3

Work done on a block by one person relative to that done by another person.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Work - Kinetic Energy

PDF
Problem 4

Motion of an object sliding down an inclined plane.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Work Problems

PDF#
Problem 1a to problem 1e

4 short qualitative problems on work, forces, kinetic energy, and weight.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Fly in a Jar

PDF#
Problem 1f to problem 1g

2 short qualitative problems about weighing a fly in a closed, then open, jar.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

## Exam Questions

#### Second Law and Kinetic Energy

PDF#
Problem 1

Relative motion and energy of two objects.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Suitcase on a Conveyor Belt

PDF#
Problem 9

Dynamics of a suitcase placed on a moving conveyor belt.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Exploding Projectile

PDF#
Problem 8

Finding the energy released by the explosion of a vertically launched projectile.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Descending a Slide

PDF#
Problem 10

Frictional work, speed at bottom, and transit time for sliding down.

Instructors: Dr. Peter Dourmashkin, Prof. Kate Scholberg
Prior Knowledge: None

#### Energy, Force, and Kinematics

PDF
Problem B4

Motion of a child sliding down a playground slide.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None