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)1(4)+3(0); after 1(−2)+3(2)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 m2≫m1m_2 \gg m_1 and v2=0v_2 = 0, the light particle bounces back at speed ∣v1∣|v_1| unchanged.

Example 4

medium
A 0.2 kg0.2\,\text{kg} ball at 10 m/s10\,\text{m/s} hits a 0.6 kg0.6\,\text{kg} ball at rest elastically. Find both final velocities.

Example 5

medium
Same collision (1 kg at 4 m/s4\,\text{m/s} hits 3 kg at rest, elastic). Find the 3 kg cart's velocity using v2′=2m1m1+m2v1v_2' = \frac{2m_1}{m_1+m_2}v_1.

Example 6

easy
Define an elastic collision in one sentence.

Example 7

medium
A 0.2 kg0.2\,\text{kg} ball moving at 10 m/s10\,\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 m/s5\,\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 m/s5\,\text{m/s}, v1′=−5/3v_1' = -5/3, v2′=10/3v_2' = 10/3).

Example 10

challenge
A 1 kg ball moving at vv hits a 1 kg ball at rest elastically; they then both hit a wall. Before any wall contact, the moving ball had KE=18 JKE = 18\,\text{J}. Find vv and confirm the second ball carries 18 J18\,\text{J} after the first (equal-mass) collision.

Example 11

hard
A 1 kg1\,\text{kg} ball at 6 m/s6\,\text{m/s} collides elastically with a 2 kg2\,\text{kg} ball moving at −3 m/s-3\,\text{m/s} (head-on). Find the final velocity of the 1 kg1\,\text{kg} ball.

Example 12

medium
Verify momentum for the 2 kg/4 kg elastic collision: compute pp before and pp after using v1′=−5/3v_1' = -5/3, v2′=10/3v_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 m/s6\,\text{m/s}, ball 2 is at rest. What is ball 1's velocity after?

Example 15

challenge
A 1 kg ball at 6 m/s6\,\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 kg2\,\text{kg} moving at 3 m/s3\,\text{m/s} hits a 1 kg1\,\text{kg} stationary cart. They bounce elastically. Find both final velocities.

Example 17

medium
A 2 kg2\,\text{kg} ball at 5 m/s5\,\text{m/s} hits a 4 kg4\,\text{kg} ball at rest elastically. Find v1′v_1' using v1′=m1−m2m1+m2v1v_1' = \frac{m_1 - m_2}{m_1 + m_2}v_1.

Example 18

easy
Total kinetic energy before an elastic collision is 50 J50\,\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 m/s5\,\text{m/s}, what is the separation speed?

Example 20

medium
A 3 kg ball at 4 m/s4\,\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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