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Inelastic Collisions in One Dimension

Page by: OpenStax College

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College Physics

Book by: OpenStax College

We have seen that in an elastic collision, internal kinetic energy is conserved. An inelastic collision is one in which the internal kinetic energy changes (it is not conserved). This lack of conservation means that the forces between colliding objects may remove or add internal kinetic energy. Work done by internal forces may change the forms of energy within a system. For inelastic collisions, such as when colliding objects stick together, this internal work may transform some internal kinetic energy into heat transfer. Or it may convert stored energy into internal kinetic energy, such as when exploding bolts separate a satellite from its launch vehicle.

Figure 1.  An inelastic one-dimensional two-object collision. Momentum is conserved, but internal kinetic energy is not conserved. (a) Two objects of equal mass initially head directly toward one another at the same speed. (b) The objects stick together (a perfectly inelastic collision), and so their final velocity is zero. The internal kinetic energy of the system changes in any inelastic collision and is reduced to zero in this example.

Section Summary

 

 

INELASTIC COLLISION

 

     An inelastic collision is one in which the internal kinetic energy changes (it is not conserved).

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Figure shows an example of an inelastic collision. Two objects that have equal masses head toward one another at equal speeds

and then stick together. Their total internal kinetic energy is initially                                           . The two objects come to rest after sticking together, conserving momentum. But the internal kinetic energy is zero after the collision. A collision in which the objects stick together is sometimes called a perfectly inelastic collision because it reduces internal kinetic energy more than does any other type of inelastic collision. In fact, such a collision reduces internal kinetic energy to the minimum it can have while still conserving momentum.

PERFECTLY INELASTIC COLLISION

 

     A collision in which the objects stick together is sometimes called “perfectly inelastic.”

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TAKE-HOME EXPERIMENT—BOUNCING OF TENNIS BALL

 

 

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Find a racquet (a tennis, badminton, or other racquet will do). Place the racquet on the floor and stand on the handle. Drop a tennis ball on the strings from a measured height. Measure how high the ball bounces. Now ask a friend to hold the racquet firmly by the handle and drop a tennis ball from the same measured height above the racquet. Measure how high the ball bounces and observe what happens to your friend’s hand during the collision. Explain your observations and measurements.

 

The coefficient of restitution (c) is a measure of the elasticity of a collision between a ball and an object, and is defined as the ratio of the speeds after and before the collision. A perfectly elastic collision has a c of 1. For a ball bouncing off the floor (or a racquet on the floor), c can be shown to be c=(h/H)1/2 where h is the height to which the ball bounces and H is the height from which the ball is dropped. Determine c for the cases in Part 1 and for the case of a tennis ball bouncing off a concrete or wooden floor (c=0.85 for new tennis balls used on a tennis court).

1.

 

 

 

 

 

 

2.

• An inelastic collision is one in which the internal kinetic energy changes (it is not conserved).

• A collision in which the objects stick together is sometimes called perfectly inelastic because it reduces internal kinetic

  energy more than does any other type of inelastic collision.

• Sports science and technologies also use physics concepts such as momentum and rotational motion and vibrations.

 

Question 1

1. Which of the following is an example of a perfectly inelastic collision?

1. Which of the following is an example of a perfectly inelastic collision?

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b

A bullet is shot and lodges into a wooden block.

a

A hockey puck crashes into a wall and bounces backwards.

c

Two bumper cars collide and split off in different directions.

Which of the following is an example of a perfectly inelastic collision?

1

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b

A bullet is shot and lodges into a wooden block.

c

Two bumper cars collide and split off in different directions.

A hockey puck crashes into a wall and bounces backwards.

In a perfectly inelastic collision, the final velocities of the objects are the same, as when they stick together. The situation where the bullet and the wooden block collide is the only one of the three where this occurs.

Which of the following is an example of a perfectly inelastic collision?

1

Next Question

Which of the following is an example of a perfectly inelastic collision?

1

Next Question

A bullet is shot and lodges into a wooden block.

c

Two bumper cars collide and split off in different directions.

A hockey puck crashes into a wall and bounces backwards.

In a perfectly inelastic collision, the final velocities of the objects are the same, as when they stick together. The situation where the bullet and the wooden block collide is the only one of the three where this occurs.

a

Which of the following is an example of a perfectly inelastic collision?

1

Next Question

b

A bullet is shot and lodges into a wooden block.

Two bumper cars collide and split off in different directions.

A hockey puck crashes into a wall and bounces backwards.

In a perfectly inelastic collision, the final velocities of the objects are the same, as when they stick together. The situation where the bullet and the wooden block collide is the only one of the three where this occurs.

a

Question 2

2. Suppose you are playing billiards and you find yourself behind the eight ball. You want....

2. Suppose you are playing billiards and you find yourself behind the eight ball. You want....

Answer

Suppose you are playing billiards and you find yourself behind the eight ball. You want to hit the cue ball at the eight ball, which is at rest, and have the cue ball bounce off at an angle of 40° to the left of the initial direction you hit the cue ball. At what angle will the eight ball recoil?

2

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b

40° to the right

a

40° to the left

c

50° to the left

d

50° to the right

Suppose you are playing billiards and you find yourself behind the eight ball. You want to hit the cue ball at the eight ball, which is at rest, and have the cue ball bounce off at an angle of 40° to the left of the initial direction you hit the cue ball. At what angle will the eight ball recoil?

2

Next Question

Suppose you are playing billiards and you find yourself behind the eight ball. You want to hit the cue ball at the eight ball, which is at rest, and have the cue ball bounce off at an angle of 40° to the left of the initial direction you hit the cue ball. At what angle will the eight ball recoil?

2

Label

b

40° to the right

40° to the left

c

50° to the left

d

50° to the right

For an elastic collision between two equal mass objects in a plane (a good approximation for billiard balls), where one body is initially at rest, the angle of separation between the final velocities is 90°. If the cue ball goes off at 40° to the left of its initial direction, the eight ball must recoil at 90° – 40° = 50° to the right.

Next Question

Suppose you are playing billiards and you find yourself behind the eight ball. You want to hit the cue ball at the eight ball, which is at rest, and have the cue ball bounce off at an angle of 40° to the left of the initial direction you hit the cue ball. At what angle will the eight ball recoil?

2

Label

a

40° to the right

40° to the left

c

50° to the left

d

50° to the right

For an elastic collision between two equal mass objects in a plane (a good approximation for billiard balls), where one body is initially at rest, the angle of separation between the final velocities is 90°. If the cue ball goes off at 40° to the left of its initial direction, the eight ball must recoil at 90° – 40° = 50° to the right.

Next Question

Suppose you are playing billiards and you find yourself behind the eight ball. You want to hit the cue ball at the eight ball, which is at rest, and have the cue ball bounce off at an angle of 40° to the left of the initial direction you hit the cue ball. At what angle will the eight ball recoil?

2

Label

a

40° to the right

40° to the left

b

50° to the left

d

50° to the right

For an elastic collision between two equal mass objects in a plane (a good approximation for billiard balls), where one body is initially at rest, the angle of separation between the final velocities is 90°. If the cue ball goes off at 40° to the left of its initial direction, the eight ball must recoil at 90° – 40° = 50° to the right.

Next Question

Suppose you are playing billiards and you find yourself behind the eight ball. You want to hit the cue ball at the eight ball, which is at rest, and have the cue ball bounce off at an angle of 40° to the left of the initial direction you hit the cue ball. At what angle will the eight ball recoil?

2

Label

a

40° to the right

40° to the left

b

50° to the left

50° to the right

For an elastic collision between two equal mass objects in a plane (a good approximation for billiard balls), where one body is initially at rest, the angle of separation between the final velocities is 90°. If the cue ball goes off at 40° to the left of its initial direction, the eight ball must recoil at 90° – 40° = 50° to the right.

d

Question 3

3. A race car driver is traveling around a loop at a speed of 110 km/h. What direction is....

3. A race car driver is traveling around a loop at a speed of 110 km/h. What direction is....

Answer

A race car driver is traveling around a loop at a speed of 110 km/h. What direction is the centripetal force of the car pointing?

3

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b

Towards the center of the loop

a

Outside of the loop

c

Straight downwards

d

More information is needed

A race car driver is traveling around a loop at a speed of 110 km/h. What direction is the centripetal force of the car pointing?

3

Label

Centripetal force is a "center seeking" force.

It always points toward the center of rotation.

Done

A race car driver is traveling around a loop at a speed of 110 km/h. What direction is the centripetal force of the car pointing?

3

b

Towards the center of the loop

Outside of the loop

c

Straight downwards

d

More information is needed

Label

Done

A race car driver is traveling around a loop at a speed of 110 km/h. What direction is the centripetal force of the car pointing?

3

Centripetal force is a "center seeking" force.

It always points toward the center of rotation.

Towards the center of the loop

Outside of the loop

c

Straight downwards

d

More information is needed

a

Label

Done

A race car driver is traveling around a loop at a speed of 110 km/h. What direction is the centripetal force of the car pointing?

3

Centripetal force is a "center seeking" force.

It always points toward the center of rotation.

b

Towards the center of the loop

Outside of the loop

Straight downwards

d

More information is needed

a

Label

Done

A race car driver is traveling around a loop at a speed of 110 km/h. What direction is the centripetal force of the car pointing?

3

Centripetal force is a "center seeking" force.

It always points toward the center of rotation.

b

Towards the center of the loop

Outside of the loop

c

Straight downwards

More information is needed

a

CONCEPT COACH

My Progress

My Progress

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Introduction: The Nature of Science and Physics

Physics: An Introduction

Physical Quantities and Units

Accuracy, Precision, and Significant Figures

Approximation

1

1.1

1.2

1.3

1.4

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Kinematics

Displacement

Vectors, Scalars, and Coordinate Systems

Time, Velocity, and Speed

Acceleration

Motion Equations for Constant Acceleration in One Dimension

Problem-Solving Basics for One-Dimensional Kinematics

Falling Objects

Graphical Analysis of One-Dimensional Motion

2

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

Two-Dimensional Kinematics

Kinematics in Two Dimensions: An Introduction

Vector Addition and Subtraction: Graphical Methods

Vector Addition and Subtraction: Analytical Methods

Projectile Motion

Addition of Velocities

3

3.1

3.2

3.3

3.4

3.5

Dynamics: Force and Newton's Laws of Motion

Development of Force Concept

Newton’s First Law of Motion: Inertia

Newton’s Second Law of Motion: Concept of a System

Newton’s Third Law of Motion: Symmetry in Forces

Normal, Tension, and Other Examples of Forces

Problem-Solving Strategies

Further Applications of Newton’s Laws of Motion

Extended Topic: The Four Basic Forces—An Introduction

4

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

Further Applications of Newton's Laws: Friction, Drag, and Elasticity

Friction

Drag Forces

Elasticity: Stress and Strain

5

5.1

5.2

5.3

Uniform Circular Motion and Gravitation

Rotation Angle and Angular Velocity

Centripetal Acceleration

Centripetal Force

Fictitious Forces and Non-inertial Frames: The Coriolis Force

Newton’s Universal Law of Gravitation

Satellites and Kepler’s Laws: An Argument for Simplicity

6

6.1

6.2

6.3

6.4

6.5

6.6

Work, Energy, and Energy Resources

Work: The Scientific Definition

Kinetic Energy and the Work-Energy Theorem

Gravitational Potential Energy

Conservative Forces and Potential Energy

Nonconservative Forces

Conservation of Energy

Power

Work, Energy, and Power in Humans

World Energy Use

7

7.1

7.2

7.3

7.4

7.5

7.6

7.7

7.8

7.9

Linear Momentum and Collisions

Linear Momentum and Force

Impulse

Conservation of Momentum

Elastic Collisions in One Dimension

Inelastic Collisions in One Dimension

Collisions of Point Masses in Two Dimensions

8

8.1

8.2

8.3

8.4

8.5

8.6

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