Conservation of Linear Momentum, Collisions

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Video Clips

Conservation of Momentum

RealVideo®
6:29 minutes (0:00 - 6:29)

Definitions, including p = m*v and F = dp/dt.

Instructor: Prof. Walter Lewin
Prior Knowledge: Force

Inelastic Collisions

RealVideo®
9:44 minutes (6:29 - 16:13)

Example, showing momentum conserved but kinetic energy lost; examples of KE loss.

Instructor: Prof. Walter Lewin
Prior Knowledge: Conservation of Momentum (beginning of V15)

Real-World Collisions

RealVideo®
6:39 minutes (16:13 - 22:52)

Example of inelastic car collision in 2D; explosions and gain of KE.

Instructor: Prof. Walter Lewin
Prior Knowledge: Inelastic Collisions (6:29 of V15)

Collision Demonstrations

RealVideo®
12:37 minutes (22:52 - 35:39)

Demonstrations showing blocks exploding apart on air track; p = 0 while KE increases.

Instructor: Prof. Walter Lewin
Prior Knowledge: Real World Collisions (16:13 of V15)

Elastic Collisions

RealVideo®
9:41 minutes (0:00 - 9:41)

Definition, including superelastic collisions; equations of motion for elastic collisions; limiting cases.

Instructor: Prof. Walter Lewin
Prior Knowledge: Conservation of Momentum (beginning of V15)

Elastic Collision Demonstrations

RealVideo®
13:11 minutes (9:41 - 22:52)

Elastic collisions of billiard balls and shuttles on air track; 3 demonstrations.

Instructor: Prof. Walter Lewin
Prior Knowledge: Elastic Collisions (beginning of V16)

Center of Mass Frame

RealVideo®
8:08 minutes (22:52 - 31:00)

Calculations in reference frame of CM; transforms back and forth.

Instructor: Prof. Walter Lewin
Prior Knowledge: Conservation of Momentum (beginning of V15)

Heat Loss in Collisions

RealVideo®
9:05 minutes (31:00 - 40:05)

Calculation of heat loss in inelastic collision using lab frame and CM frame; limiting cases.

Instructor: Prof. Walter Lewin
Prior Knowledge: Center of Mass Frame (22:52 of V16)

Inelastic Collision Demonstration

RealVideo®
8:46 minutes (40:05 - 48:51)

Inelastic collisions on air track with m-->m and m-->2m; detailed calculations and predictions.

Instructor: Prof. Walter Lewin
Prior Knowledge: Heat Loss in Collisions (31:00 of V16)

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)

Inelastic Collisions

RealVideo®
3:15 minutes (45:53 - 49:08)

Conservation of momentum in inelastic collisions; loss of kinetic energy to heat; internal forces.

Instructor: Prof. Walter Lewin
Prior Knowledge: Collisions (6:29 of V15)

Review of Collisions

RealVideo®
7:43 minutes (0:00 - 7:43)

Elastic and inelastic collision equations of motion; loss of kinetic energy to heat.

Instructor: Prof. Walter Lewin
Prior Knowledge: Collisions (6:29 of V15)

Lecture Notes

Momentum

PDF - 1.6 MB#
Page 1 to page 4

Definition of momentum (p = m*v); Newton's laws and momentum; law of conservation of momentum of a particle and of a system of particles, with examples; relationship between forces and momentum; elastic and inelastic collision, with examples.

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

Center of Mass Motion

PDF - 1.6 MB#
Page 1 to page 6

Center of mass of an area of constant thickness, with examples; motion of the center of mass; internal and external forces, with examples; energy of a system of particles; variable mass motion, with rocket example.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Momentum, Center of Mass

Variable Mass Example

PDF#
Page 1

Variable mass motion example problem.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 18

Impulse and Collisions

PDF#
Page 1 to page 6

Definition of impulsive force, with example; elastic and inelastic collisions, with examples in one-dimension and two-dimensions.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Momentum, Conservation of Energy

Collisions

PDF - 1.8 MB#
Page 1 to page 6

Two-dimension elastic collisions, with example; ballistic pendulum; definition and properties of collisions; collisions and kinetic energy in center of mass frame of reference.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 19

Momentum

PDF - 1.5 MB#
Page 1 to page 9

Definition of momentum (p = m*v); Newton's laws and momentum; law of conservation of momentum of a particle and of a system of particles, with examples; relationship between forces and momentum; elastic and inelastic collision, with examples.

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

Center of Mass Motion

PDF - 1.6 MB#
Page 1 to page 16

Center of mass of an area of constant thickness, with examples; motion of the center of mass; internal and external forces, with examples; energy of a system of particles; variable mass motion, with rocket example.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Momentum, Center of Mass

Variable Mass Example

PDF 1.2 MB#
Page 1

Variable mass motion example problem.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 18

Impulse and Collisions

PDF 1.2 MB#
Page 2 to page 16

Definition of impulsive force, with example; elastic and inelastic collisions, with examples in one-dimension and two-dimensions.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Momentum, Conservation of Energy

Collisions

PDF - 1.1 MB#
Page 1 to page 12

Two-dimension elastic collisions, with example; ballistic pendulum; definition and properties of collisions; and collisions and kinetic energy in center of mass frame of reference.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 19

Conservation of Momentum

PDF
Page 1

Summary of work/energy; momentum defined, with equation (p = m*v); conservation of momentum.

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

Momentum and Energy

PDF
Page 1

Conservation of momentum and energy; collisions.

Instructor: Dr. George Stephans
Prior Knowledge: Momentum

Collisions

PDF
Page 1

General problem-solving strategy, techniques, and helpful hints; momentum formulas.

Instructor: Dr. George Stephans
Prior Knowledge: Momentum

Conservation of Momentum

PDF
Page 1 to page 27

Definition of momentum (p = m*v) and impulse; non-constant force and impulse; conservation of momentum; translational motion of the center of mass; modeling external forces and conservation of momentum; modeling of instantaneous collisions; momentum diagrams and equations.

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

Collision Theory

PDF#
Page 1 to page 20

Momentum and impulse equations; definition of conservation of momentum for an isolated system; momentum problem solving strategies; momentum diagram and equations; planar collision theory; elastic collisions; 2D elastic collision example problem.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Lecture 19

Experiment 7

PDF
Page 1 to page 14

Momentum and collision experiment setup and procedure.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Lecture 21

Linear Momentum Review

PDF
Page 1 to page 8

Momentum and change of momentum defined, with equations; strategies for solving momentum and impulse problems; collisions and conservation of momentum; center of mass.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Lectures 19, 21

Practice Problems

Energy and Momentum

PDF
Problem 1

Friction and acceleration; which forces must be known to solve for energy and momentum; kinetic energy and momentum in a collision. Solution not included.

Instructor: Dr. George Stephans
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

Collisions

PDF
Problem 1 to problem 2

Elastic and inelastic collisions. 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

Momentum and Mechanical Energy

PDF#
Problem 24

Inelastic collision of two bodies.

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

Exploding Projectile

PDF#
Problem 25

Elastic collision of two bodies, including projectile motion.

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

Bouncing Superballs

PDF#
Problem 26

Elastic collision of two bodies.

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

Elastic One Dimensional Collision

PDF#
Problem 27

Elastic collision of two carts on a track.

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

Conservation of Momentum

PDF#
Problem 28

Two people jumping off a railway flatcar.

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

Pendulums and Collisions

PDF#
Problem 29

Elastic and inelastic collisions between a pendulum bob and an object.

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

Momentum of Isolated Systems

PDF
Problem 1 to problem 4

Concept questions about conservation of momentum in isolated systems of one or more bodies.

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

Collisions

PDF
Problem 4 to problem 21

Concept questions about elastic and inelastic collisions between two or more bodies; some questions involve mass-spring systems.

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

Experiment 7 Pre-Lab

PDF
Problem 1

Concept questions regarding collisions of carts on a frictionless track.

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

Inelastic Collision with an Oscillating Mass

PDF
Problem 4

Motion of an oscillating mass on a spring, before and after colliding with a lump of putty.

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

Two Dimensional Elastic Collision

PDF#
Problem 2

Motion of two objects that collide elastically.

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

Experiment 7 Analysis

PDF#
Problem 3

Analysis of data collected in Experiment 7.

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

Ballistic Pendulum

PDF#
Problem 4

Measuring the speed of a bullet by shooting a block suspended by two cables.

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

Experiment 9 Analysis

PDF#
Problem 2

Analysis of data collected in Experiment 9.

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

Sliding on Ice

PDF
Problem 3

9-part momentum problem: finding speed and kinetic energy for two people sliding a block.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

Puck Collision

PDF#
Problem 4

For two elastically colliding pucks, calculating velocity and kinetic energy before and after collision.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

Surprising Bounce

PDF#
Problem 5

Calculating height of tennis ball bouncing off dropped basketball.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

Collisions in Center of Mass Frame

PDF#
Problem 6

Momentum, kinetic energy, and velocity of center of mass for exploding particle.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

Slingshot Encounter

PDF#
Problem 2

Gain in mechanical energy from looping around a planet; finding new velocity and energy.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

Exam Questions

Skewed Collision

PDF#
Problem 1

4-part problem; two balls collide at angle; finding momentum, speed before and after, and velocity of center of mass. Solutions are included after problems.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: None

2D Collision

PDF#
Problem 1

Finding resultant velocity and kinetic energy for 2D collision; elastic vs. inelastic collision. Solutions are included after problems.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: None

Glancing Collision

PDF#
Problem 4

Straight rod brushes against fixed object; finding ω, kinetic energy, speeds of both ends after collision. Solutions are included after problems.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: None

Elastic Collision

PDF#
Problem 3

Collision of two hockey pucks.

Instructor: Dr. George Stephans
Prior Knowledge: None

Collisions

PDF#
Problem 5

Short answer questions about elastic and inelastic collisions.

Instructor: Dr. George Stephans
Prior Knowledge: None

Linear Collision

PDF#
Problem 6

Motion of two steel balls following a linear collision.

Instructor: Dr. George Stephans
Prior Knowledge: None

Collision of a Ball and a Block

PDF#
Problem 9

Motion of a moving ball colliding with a stationary block.

Instructor: Dr. George Stephans
Prior Knowledge: None

Collision with Mass on a Spring

PDF#
Problem 10

Inelastic collision of a clay ball with a block connected to a spring.

Instructor: Dr. George Stephans
Prior Knowledge: None

Momentum in Explosion(8.01X, Fall 2002)

PDF#
Problem 6

Final speed and lost kinetic energy in explosion into two pieces.

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

Elastic Collision(8.01X, Fall 2002)

PDF#
Problem 7

Calculating final and initial speed of one object in collision, as well as the mass ratio.

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

Inelastic Collision with a Spring(8.01X, Fall 2002)

PDF#
Problem 6

For inelastic collision, finding initial and final velocities and pendulum attributes.

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

Impulse for a Bouncing Ball(8.01X, Fall 2002)

PDF#
Problem 12

6-part problem; p of ball before and after hitting floor; average force and impulse; change in kinetic energy.

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

Center of Mass Reference Frame

PDF
Problem 1a

Elastic collision of two rolling carts with respect to reference frame moving with the center of mass.

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

Collisions

PDF
Problem 1b

Collision of a moving body with a stationary body attached to a spring.

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

Exploding Puck

PDF
Problem 2

Conservation of momentum of an exploding puck.

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

Conservation of Energy and Momentum

PDF
Problem B2

Collision of a body with another body connected to a spring.

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

Block and Spring

PDF
Problem 1c

Inelastic collision involving an oscillating mass attached to a spring.

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

Elastic Collision

PDF
Problem 2a to problem 2b

Calculating speed of both objects after an elastic collision between a bullet and a pendulum.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

Inelastic Collision with Pendulum

PDF
Problem 2c to problem 2d

Calculating θmax for pendulum after an inelastic collision between a bullet and a pendulum.

Instructor: Prof. Walter Lewin
Prior Knowledge: None