Practice Elastic Collision in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A collision in which both the total momentum and the total kinetic energy of the system are fully conserved after impact.

Billiard balls bouncing off each other: the total energy stays the same, nothing is lost to heat or deformation.

Showing a random 20 of 50 problems.

Example 1

medium

Verify momentum for the 1 kg/3 kg elastic collision: before

1(4)+3(0)

; after

1(-2)+3(2)

. Are they equal?

Example 2

easy

True or false: in an elastic collision, individual KEs of each object are conserved.

Example 3

hard

Show: in an elastic 1D collision with

m_2 \gg m_1

and

v_2 = 0

, the light particle bounces back at speed

|v_1|

unchanged.

Example 4

medium

0.2\,\text{kg}

ball at

10\,\text{m/s}

hits a

0.6\,\text{kg}

ball at rest elastically. Find both final velocities.

Example 5

medium

Same collision (1 kg at

4\,\text{m/s}

hits 3 kg at rest, elastic). Find the 3 kg cart's velocity using

v_2' = \frac{2m_1}{m_1+m_2}v_1

Example 6

easy

Define an elastic collision in one sentence.

Example 7

medium

0.2\,\text{kg}

ball moving at

10\,\text{m/s}

bounces elastically straight back off a wall. Find the impulse delivered to the ball.

Example 8

medium

A 2 kg ball at

5\,\text{m/s}

collides elastically head-on with a 2 kg ball at rest. Find both final velocities (equal masses).

Example 9

medium

Verify KE for the 2 kg/4 kg elastic collision (incoming 2 kg at

5\,\text{m/s}

v_1' = -5/3

v_2' = 10/3

Example 10

challenge

A 1 kg ball moving at

v

hits a 1 kg ball at rest elastically; they then both hit a wall. Before any wall contact, the moving ball had

KE = 18\,\text{J}

. Find

v

and confirm the second ball carries

18\,\text{J}

after the first (equal-mass) collision.

Example 11

hard

1\,\text{kg}

ball at

6\,\text{m/s}

collides elastically with a

2\,\text{kg}

ball moving at

-3\,\text{m/s}

(head-on). Find the final velocity of the

1\,\text{kg}

ball.

Example 12

medium

Verify momentum for the 2 kg/4 kg elastic collision: compute

p

before and

p

after using

v_1' = -5/3

v_2' = 10/3

Example 13

easy

The unit of momentum in SI is ___.

Example 14

easy

Two billiard balls of equal mass collide elastically head-on. Ball 1 moves at

6\,\text{m/s}

, ball 2 is at rest. What is ball 1's velocity after?

Example 15

challenge

A 1 kg ball at

6\,\text{m/s}

collides elastically head-on with a 2 kg ball at rest. Find both final velocities.

Example 16

hard

A spring-loaded cart of mass

2\,\text{kg}

moving at

3\,\text{m/s}

hits a

1\,\text{kg}

stationary cart. They bounce elastically. Find both final velocities.

Example 17

medium

2\,\text{kg}

ball at

5\,\text{m/s}

hits a

4\,\text{kg}

ball at rest elastically. Find

v_1'

using

v_1' = \frac{m_1 - m_2}{m_1 + m_2}v_1

Example 18

easy

Total kinetic energy before an elastic collision is

50\,\text{J}

. What is it after?

Example 19

easy

For a head-on elastic collision, the relative velocity of approach equals the relative velocity of separation. If approach speed is

5\,\text{m/s}

, what is the separation speed?

Example 20

medium

A 3 kg ball at

4\,\text{m/s}

and a 1 kg ball at rest collide elastically. Using the relative-velocity rule, find the separation speed.

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Related Concepts

Conservation of Momentum Kinetic Energy Inelastic Collision