Inelastic Collision Examples: 45 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Inelastic Collision.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

A collision in which the total momentum of the system is conserved but the total kinetic energy is not — some kinetic energy is converted.

Two cars crashing and sticking together: they move as one object and kinetic energy is lost.

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How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Inelastic Collision works by defining the interacting system and comparing motion before and after the interaction.

Common stuck point: Students often know a formula related to inelastic collision but skip the recognition step: Is the interaction short, collision-like, or rotational, and have I checked whether external forces or torques can be ignored? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Is the interaction short, collision-like, or rotational, and have I checked whether external forces or torques can be ignored?

Worked Examples

Example 1

medium

0.04 \text{ kg}

bullet at

300 \text{ m/s}

embeds in a

1.96 \text{ kg}

block at rest. Find

v_f

Answer

v_{f} = 6 m/s

First step

0.04 \cdot 300 = (0.04 + 1.96) v_f = 2 v_f

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Example 2

medium

1 \text{ kg}

ball at

10 \text{ m/s}

hits a

3 \text{ kg}

ball at rest; they stick. Find

v_f

and the fraction of KE retained.

Example 3

hard

Ballistic pendulum: a

0.01 \text{ kg}

bullet embeds in a

0.99 \text{ kg}

pendulum at rest. The combined block rises

0.45 \text{ m}

(

g = 10 \text{ m/s}^2

). Find the bullet's initial speed.

Example 4

hard

0.5 \text{ kg}

projectile moving at

30 \text{ m/s}

embeds in a

4.5 \text{ kg}

block sitting on a frictionless surface attached to a spring (

k = 1000 \text{ N/m}

). Find the maximum spring compression.

Example 5

hard

m_1=2 \text{ kg}

8 \text{ m/s}

hits

m_2=3 \text{ kg}

2 \text{ m/s}

(same direction); they stick. Find

v_f

and the percent of KE lost.

Example 6

hard

Show: for a perfectly inelastic collision with masses

m

and

M

where

M

is initially at rest, the fraction of KE retained is

m/(m+M)

Example 7

challenge

0.02 \text{ kg}

bullet at

400 \text{ m/s}

embeds in a

4 \text{ kg}

wooden block hanging on a string (

g = 10 \text{ m/s}^2

). Find the maximum angle through which the block swings if the string is

1 \text{ m}

long.

Example 8

challenge

m_1 = 1 \text{ kg}

slides at

v

and hits stationary

m_2 = 1 \text{ kg}

on a frictionless surface; they stick and then compress a spring (

k=200 \text{ N/m}

) by

0.1 \text{ m}

. Find

v

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

In a perfectly inelastic collision, what happens to the two objects?

Example 2

easy

Which quantity is conserved in an inelastic collision: momentum, kinetic energy, or both?

Example 3

easy

A 2 kg ball at

3\,\text{m/s}

sticks to a 1 kg ball at rest. Find the combined velocity.

Example 4

easy

A 4 kg cart at

5\,\text{m/s}

couples to a 6 kg cart at rest. Find the common velocity.

Example 5

easy

Two equal 3 kg lumps of clay move toward each other at

4\,\text{m/s}

and

-4\,\text{m/s}

and stick. Find the final velocity.

Example 6

easy

Why is kinetic energy lost in an inelastic collision even though momentum is conserved?

Example 7

easy

A 1 kg bird lands on a 4 kg stationary float, sticking. The bird arrived at

10\,\text{m/s}

. Find their common speed.

Example 8

easy

Total momentum before a perfectly inelastic collision is

20\,\text{kg}\cdot \text{m/s}

and the combined mass is

5\,\text{kg}

. Find the final speed.

Example 9

medium

A 1000 kg car at

20\,\text{m/s}

rear-ends a 1500 kg car at rest; they lock together. Find the common velocity.

Example 10

medium

In the car collision (1000 kg at

20\,\text{m/s}

locks with 1500 kg at rest,

v_f = 8\,\text{m/s}

), how much kinetic energy is lost?

Example 11

medium

A 0.05 kg bullet at

400\,\text{m/s}

embeds in a 1.95 kg block at rest. Find the speed of the block-plus-bullet.

Example 12

medium

Two clay balls, 2 kg at

6\,\text{m/s}

and 3 kg at

-1\,\text{m/s}

, collide and stick. Find the final velocity.

Example 13

medium

A 3 kg cart at

4\,\text{m/s}

sticks to a 1 kg cart at rest. What fraction of the initial kinetic energy remains?

Example 14

medium

A 2 kg block slides at

9\,\text{m/s}

and catches a 1 kg block at

3\,\text{m/s}

(same direction); they stick. Find the final velocity.

Example 15

medium

A 5 kg object at

4\,\text{m/s}

collides and sticks with an object, ending at

2\,\text{m/s}

. Find the mass of the second object (initially at rest).

Example 16

medium

A 2 kg cart at

6\,\text{m/s}

sticks to a 4 kg cart at rest. Find the common velocity.

Example 17

medium

A 0.1 kg ball of clay at

12\,\text{m/s}

sticks to a 0.3 kg ball at rest. Find the common speed.

Example 18

challenge

Ballistic pendulum: a 0.02 kg bullet embeds in a 1.98 kg block hanging at rest. The block rises

0.2\,\text{m}

(

g = 10\,\text{m/s}^2

). Find the bullet's initial speed.

Example 19

challenge

A 2 kg block at

8\,\text{m/s}

sticks to a 2 kg block at rest; the combined block then slides onto a rough patch with

\mu_k = 0.4

(

g = 10\,\text{m/s}^2

). How far does it slide before stopping?

Example 20

challenge

A 3 kg cart at

4\,\text{m/s}

collides and sticks with a 1 kg cart moving toward it at

4\,\text{m/s}

. Find the final velocity and the percentage of kinetic energy lost.

Example 21

easy

2 \text{ kg}

block at

6 \text{ m/s}

sticks to a

4 \text{ kg}

block at rest. Find

v_f

Example 22

easy

1.5 \text{ kg}

ball at

8 \text{ m/s}

sticks to a

0.5 \text{ kg}

ball at rest. Find

v_f

Example 23

easy

5 \text{ kg}

cart at

4 \text{ m/s}

collides with and sticks to a

5 \text{ kg}

cart at rest. Find

v_f

Example 24

easy

Two

2 \text{ kg}

lumps move at

+3 \text{ m/s}

and

-1 \text{ m/s}

and stick. Find

v_f

Example 25

easy

0.4 \text{ kg}

glob of clay at

5 \text{ m/s}

hits and sticks to a

0.1 \text{ kg}

glob at rest. Find

v_f

Example 26

medium

For the bullet-block above (

0.04

kg at

300

m/s,

1.96

kg at rest,

v_f = 6 \text{ m/s}

), find the fraction of KE lost.

Example 27

medium

1200 \text{ kg}

car at

15 \text{ m/s}

rear-ends a

1800 \text{ kg}

truck at rest; they lock. Find

v_f

Example 28

medium

For the car-truck collision above (

v_f = 6 \text{ m/s}

, total mass

3000

kg), how much KE is lost?

Example 29

medium

3 \text{ kg}

cart at

5 \text{ m/s}

collides head-on with a

2 \text{ kg}

cart at

-3 \text{ m/s}

and they stick. Find

v_f

Example 30

medium

6 \text{ kg}

object initially moving at

5 \text{ m/s}

collides with and sticks to a stationary object; the combined system ends at

3 \text{ m/s}

. Find the unknown mass.

Example 31

medium

0.2 \text{ kg}

snowball at

20 \text{ m/s}

sticks to a

1.8 \text{ kg}

stationary target. Find

v_f

Example 32

medium

Two ice skaters,

60 \text{ kg}

2 \text{ m/s}

and

80 \text{ kg}

at rest, grab and skate together. Find

v_f

Example 33

medium

2 \text{ kg}

4 \text{ m/s}

hits and sticks to

3 \text{ kg}

moving the same direction at

1 \text{ m/s}

. Find

v_f

Example 34

hard

4 \text{ kg}

block at

6 \text{ m/s}

sticks to a

2 \text{ kg}

block at rest; the combined mass slides onto a

\mu_k = 0.5

patch (

g = 10 \text{ m/s}^2

). How far does it slide?

Example 35

hard

Two equal

m=2 \text{ kg}

blocks at

5 \text{ m/s}

collide head-on (one at

+5

, one at

-5

) and stick. Find

v_f

and the fraction of KE lost.

Example 36

hard

0.5 \text{ kg}

dart at

20 \text{ m/s}

sticks to a

2 \text{ kg}

block on a frictionless incline. They slide up the incline. Find the height gained (

g = 10 \text{ m/s}^2

Example 37

hard

80 \text{ kg}

player runs at

5 \text{ m/s}

east and tackles a

100 \text{ kg}

player moving at

3 \text{ m/s}

north. They stick. Find the magnitude of

v_f

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Related Concepts

Conservation of Momentum Kinetic Energy Elastic Collision

Background Knowledge

These ideas may be useful before you work through the harder examples.

conservation of momentumkinetic energy