# Conservation of Energy

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## 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)

#### Mechanical Energy and Centripetal Force

RealVideo®
7:34 minutes (23:37 - 31:11)

Example of ball in rollercoaster; proof that h ≥ 2.5R for ball to make it around.

Instructor: Prof. Walter Lewin
Prior Knowledge: Conservation of Energy (17:00 of V11)

#### Wrecking Ball Demonstration

RealVideo®
3:29 minutes (45:37 - 49:06)

Conservation of mechanical energy demonstrated by swinging wrecking ball across room.

Instructor: Prof. Walter Lewin
Prior Knowledge: Conservation of Energy (17:00 of V11)

#### Simple Harmonic Motion from Energy Conservation

RealVideo®
5:08 minutes (19:35 - 24:43)

Derivation of differential equation for SHM from conservation of energy in a spring.

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

#### Ballistic Pendulum

RealVideo®
6:04 minutes (0:00 - 6:04)

Setup and calculations for system of bullet hitting pendulum to measure speed.

Instructor: Prof. Walter Lewin
Prior Knowledge: Conservation of Momentum (beginning of V15) and Pendulum (29:07 of V10)

#### Ballistic Pendulum Demonstration

RealVideo®
5:48 minutes (6:04 - 11:52)

Numerical calculations for ballistic pendulum experiment; kinetic energy loss approximated.

Instructor: Prof. Walter Lewin
Prior Knowledge: Ballistic Pendulum (beginning of V17)

#### 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

#### Block on an Inclined Plane

RealVideo®
9:12 minutes (1:44 - 10:56)

Calculation of acceleration and descent time for this system from dynamics and from conservation of energy.

Instructor: Prof. Walter Lewin
Prior Knowledge: Conservation of Mechanical Energy (17:00 of V11)

#### Pendulum Oscillation Calculation I

RealVideo®
7:04 minutes (12:09 - 19:13)

Calculation of θmax for pendulum moving upwards along arc, using conservation of energy.

Instructor: Prof. Walter Lewin
Prior Knowledge: Conservation of Mechanical Energy (17:00 of V11)

## Lecture Notes

#### Kinetic and Potential Energy

PDF - 1.5 MB#
Page 1 to page 12

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

#### 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 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

#### 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).

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Newton's Laws

#### 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

#### Work and Energy Review

PDF
Page 19 to page 38

Definitions of kinetic energy and work; work-energy relationship; work done along an arbitrary path; instantaneous power; potential energy and force; potential energy of a spring; potential energy due to gravity; conservation of mechanical energy.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Lecture 14, 16

## Practice Problems

PDF
Problem 4

3-part problem; finding normal force from wire and height the bead attains on the way back up.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: None

#### Kinetic Energy and Momentum

PDF
Problem 1 to problem 3

Changes in momentum and kinetic energy of two objects. Solution not included.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Simple Harmonic Motion

PDF
Problem 1

Momentum and kinetic energy of a baseball bat; simple harmonic motion of two mass-spring systems. Solution not included.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Circular Motion and Conservation of Mechanical Energy

PDF
Problem 23

Motion of an object along a frictionless loop-the-loop track.

Prior Knowledge: None

#### Beads Sliding Along a Ring

PDF
Problem 23

Forces acting on a suspended ring with sliding beads.

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

#### Kinetic Energy and Speed

PDF
Problem 12

Linear speed of a streetcar on a circular track. Solution not included.

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

#### Conservation of Energy

PDF
Problem 2

Velocity of a ball thrown downward in comparison to velocity of a ball dropped from rest. Solution not included.

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

#### Kinetic and Potential Energy

PDF
Problem 5

Combined kinetic and potential energy 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

#### Conservation of Energy

PDF
Problem 8

Defining a mass-spring system such that energy is conserved. Solution not included.

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

#### Conservation of Energy

PDF
Problem 9

Defining a system of a falling ball such that energy is conserved. Solution not included.

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

#### Conservation of Energy

PDF
Problem 10

Energy and work with respect to a ball lifted at constant velocity. Solution not included.

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

#### Conservation of Energy

PDF
Problem 12

Energy and work with respect to a ball lifted at constant velocity and the earth. Solution not included.

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

#### Conservation of Energy

PDF
Problem 13

Work done on a system of a cup of water and the earth. Solution not included.

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

#### Conservation of Energy

PDF
Problem 14

Work done on a system of a falling ball and the earth. Solution not included.

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

#### Conservation of Energy

PDF
Problem 17

Compression of a spring resulting from collision with a moving object. Solution not included.

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

#### Kinetic Energy of the Earth

PDF
Problem 19

Conversion of the kinetic energy of the earth-sun system to potential energy. Solution not included.

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

#### Ball and Spring

PDF
Problem 20

Work done on a ball launched vertically by a spring. Solution not included.

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

#### Cart on an Inclined Track

PDF
Problem 4

Velocity and acceleration of a cart compressing a spring on an inclined track. Solution not included.

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

#### Cart on an Inclined Track

PDF
Problem 5

Acceleration of a cart as it moves up an inclined track. Solution not included.

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

#### Experiment 6 Pre-Lab

PDF#
Problem 2

Collision of a cart with a fixed spring on a track.

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

#### Conservation of Mechanical Energy

PDF
Problem 2

Motion of a small object that slides down a large sphere and hits the ground.

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

#### Experiment 6 Analysis

PDF
Problem 5

Fitting data from Experiment 6.

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

## Exam Questions

#### Block Hanging From Two Ropes

PDF#
Problem 3

4-part problem; free-body diagram and tension while hanging; speed and tension after one rope is cut. Solutions are included after problems.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: None

#### Spring-Launched Ball

PDF#
Problem 7

Finding the spring constant of a spring from the maximum height of a ball shot by the spring.

Prior Knowledge: None

#### Conservation of Energy

PDF#
Problem 11

Motion of a small mass launched from the surface of the earth.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Spring and Loop

PDF
Problem 3

Motion of a mass propelled by a spring along a frictionless loop.

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

#### Inclined Plane, Friction, Spring

PDF
Problem 4

Motion of a mass that slides down an inclined plane and compresses a spring.

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

#### Conservation of Energy

PDF
Problem 1e

Cart rolling down an inclined plane and compressing 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