# Forces & Potential Energy

This section contains documents created from scanned original files and other
documents that could not be made accessible to screen reader software. A "#"
symbol is used to denote such documents.

## Video Clips

#### Conservation of Mechanical Energy

RealVideo®
6:37 minutes (17:00 - 23:37)

Potential energy defined; proof of conservation of mechanical energy.

Instructor: Prof. Walter Lewin
Prior Knowledge: Gravitational Work (13:04 of V11)

#### Universal Gravitation

RealVideo®
5:57 minutes (31:11 - 37:08)

Work when g varies; statement of law of universal gravitation; calculation of g.

Instructor: Prof. Walter Lewin
Prior Knowledge: Gravitational Work (13:04 of V11)

#### Stable and Unstable Equilibrium

RealVideo®
4:39 minutes (14:56 - 19:35)

Types of equilibrium; stable, with restoring force; unstable, with negative U".

Instructor: Prof. Walter Lewin
Prior Knowledge: Force and Potential Energy (7:00 of V13)

## Lecture Notes

#### Friction

PDF - 1.6 MB#
Page 1 to page 6

Definitions of kinetic friction and static friction, as well as drag force and the terminal speed of falling bodies in air. Includes a number of friction example problems.

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

#### Kinetic and Potential Energy

PDF - 1.5 MB#
Page 1 to page 6

Kinetic energy of a particle; gravitational potential energy; the law of conservation of mechanical energy. Includes several examples.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 12, Integration

#### Conservation of Energy

PDF - 1.3 MB#
Page 1 to page 5

Definition of the law of conservation of energy, with examples; definition of conservative forces and the potential energy of conservative forces.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 13, Integration

#### Potential Energy

PDF - 1.5 MB#
Page 1 to page 6

Spring potential energy and gravitational potential energy, with several examples; superposition of conservative forces; definition of non-conservative forces; conversion between forces and resultant potential energies.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 14, Integration, Partial Derivatives

#### Friction

PDF#
Page 1 to page 14

Definitions of kinetic friction and static friction, as well as drag force and the terminal speed of falling bodies in air. Includes a number of friction example problems.

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

#### Kinetic and Potential Energy

PDF#
Page 1 to page 15

Kinetic energy of a particle; gravitational potential energy; the law of conservation of mechanical energy. Includes several examples.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 12, Integration

#### Conservation of Energy

PDF#
Page 1 to page 12

Definition of the law of conservation of energy, with examples; definition of conservative forces and their potential energy.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 13, Integration

#### Potential Energy

PDF#
Page 1 to page 12

Spring potential energy and gravitational potential energy, with several examples; superposition of conservative forces; definition of non-conservative forces; conversion between forces and resultant potential energies.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 14, Integration, Partial Derivatives

#### 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

#### Potential Energy

PDF
Page 1 to page 2

Calculating potential energy; using potential energy to calculate force; potential energy vs. position diagrams.

Instructor: Dr. George Stephans
Prior Knowledge: Work-Energy

#### Potential Energy of Springs

PDF
Page 1 to page 2

Equation for the potential energy of a spring; potential energy of a vertical spring plus gravity.

Instructor: Dr. George Stephans
Prior Knowledge: Potential Energy

#### 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

#### Potential Energy

PDF
Page 1 to page 24

Definition of conservative force; change in potential energy and conservation of mechanical energy; energy curves; potential energy for gravity and springs; energy changes for conservative and non-conservative forces.

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

## Practice Problems

#### Potential Energy

PDF
Problem 1

Potential energy of systems as a function of position. Solution not included.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Potential Energy

PDF
Problem 1

Finding velocity from a potential energy diagram; potential energy of a spring. Solution not included.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Calculating Work Integrals

PDF
Problem 20a

Work done by gravity near the surface of the earth.

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

#### Calculating Work Integrals

PDF
Problem 20b

Work done by the spring force.

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

#### Calculating Work Integrals

PDF
Problem 20c

Work done by the inverse square gravitational force.

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

#### Journey to the Center of the Earth

PDF
Problem 22

Finding the time it takes for an object to traverse a hole through the earth.

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

#### Oscillation and Potential Energy

PDF
Problem 1

Potential energy of a spring as a function of a connected oscillating cart. Solution not included.

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

#### Potential Energy Graph

PDF
Problem 6

Determining maximum velocity of a particle from a graph of potential energy vs. position. Solution not included.

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

#### Path Dependence of Force

PDF
Problem 7

Average force exerted to ride a bicycle up a hill by two different paths. Solution not included.

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

#### Energy of a Spring

PDF
Problem 18

Energy stored in a spring at maximum compression. Solution not included.

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

## Exam Questions

#### Rocket Flight

PDF#
Problem 13

Comparing the work done by two different rockets.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Force and Potential Energy

PDF
Problem 1d

Force exerted to ride a bicycle up a hill.

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

#### Spring - Launched Projectile

PDF
Problem 2

Motion of a marble launched from a table by a spring.

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

#### Spring on an Inclined Plane

PDF#
Problem 1

5-part problem involving Hooke's Law, friction, and conservation of energy.

Instructor: Prof. Walter Lewin
Prior Knowledge: None