# Conservation of Linear Momentum, Collisions

## Conservation of Momentum

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

• Watch {}video clip from Lecture 15 (0:00 - 6:29)

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

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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.

Two people jumping off a railway flatcar.

## Inelastic Collisions

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

• Watch {}video clip from Lecture 15 (6:29 - 16:13)

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

• Watch {}video clip from Lecture 18 (45:53 - 49:08)

## Real-World Collisions

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

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• Watch {}video clip from Lecture 15 (16:13 - 22:52)

## Collision Demonstrations

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

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• Watch {}video clip from Lecture 15 (22:52 - 35:39)

## Elastic Collisions

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

• Watch {}video clip from Lecture 16 (0:00 - 9:41)

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

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Collision of two hockey pucks.

## Elastic Collision Demonstrations

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

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• Watch {}video clip from Lecture 16 (9:41 - 22:52)

## Center of Mass Frame

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

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• Watch {}video clip from Lecture 16 (22:52 - 31:00)

## Heat Loss in Collisions

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

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• Watch {}video clip from Lecture 16 (31:00 - 40:05)

## Inelastic Collision Demonstration

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

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• Watch {}video clip from Lecture 16 (40:05 - 48:51)

## Ballistic Pendulum

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

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• Watch {}video clip from Lecture 17 (0:00 - 6:04)

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

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## Ballistic Pendulum Demonstration

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

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• Watch {}video clip from Lecture 17 (6:04 - 11:52)

## Review of Collisions

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

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• Watch {}video clip from Lecture 29 (0:00 - 7:43)

## Momentum

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.

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## Center of Mass Motion

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.

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## Variable Mass Example

Variable mass motion example problem.

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## Impulse and Collisions

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

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## Collisions

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

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

Elastic and inelastic collisions. Solution not included.

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

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

## Momentum and Energy

Conservation of momentum and energy; collisions.

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## Collision Theory

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.

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## Experiment 7

Momentum and collision experiment setup and procedure.

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## Linear Momentum Review

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

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## Energy and Momentum

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

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## Kinetic Energy and Momentum

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

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## Simple Harmonic Motion

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

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## Momentum and Mechanical Energy

Inelastic collision of two bodies.

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## Exploding Projectile

Elastic collision of two bodies, including projectile motion.

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## Bouncing Superballs

Elastic collision of two bodies.

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## Elastic One Dimensional Collision

Elastic collision of two carts on a track.

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## Pendulums and Collisions

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

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## Momentum of Isolated Systems

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

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## Experiment 7 Pre-Lab

Concept questions regarding collisions of carts on a frictionless track.

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## Inelastic Collision with an Oscillating Mass

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

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## Two Dimensional Elastic Collision

Motion of two objects that collide elastically.

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## Experiment 7 Analysis

Analysis of data collected in Experiment 7.

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## Experiment 9 Analysis

Analysis of data collected in Experiment 9.

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## Sliding on Ice

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

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## Puck Collision

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

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## Surprising Bounce

Calculating height of tennis ball bouncing off dropped basketball.

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## Collisions in Center of Mass Frame

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

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## Slingshot Encounter

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

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## Skewed Collision

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.

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## 2D Collision

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

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## Glancing Collision

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

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## Linear Collision

Motion of two steel balls following a linear collision.

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## Collision of a Ball and a Block

Motion of a moving ball colliding with a stationary block.

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## Collision with Mass on a Spring

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

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## Momentum in Explosion (8.01X, Fall 2002)

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

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## Elastic Collision (8.01X, Fall 2002)

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

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

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

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

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

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## Center of Mass Reference Frame

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

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## Exploding Puck

Conservation of momentum of an exploding puck.

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## Conservation of Energy and Momentum

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

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## Block and Spring

Inelastic collision involving an oscillating mass attached to a spring.

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## Inelastic Collision with Pendulum

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

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## Billiard Ball Collision

5-part collision problem; finding p before and after, as well as resultant velocities and kinetic energy.

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