Conservation of Momentum Examples in Physics

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

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

Concept Recap

In a closed system with no net external force, the total momentum of all objects remains constant before and after any interaction — momentum is conserved.

Momentum can move between objects but can't be created or destroyed.

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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: Conservation of Momentum works by defining the interacting system and comparing motion before and after the interaction.

Common stuck point: Students often know a formula related to conservation of momentum 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

5 \text{ kg}

cart moving at

4 \text{ m/s}

collides with a stationary

3 \text{ kg}

cart. They stick together. What is their final velocity?

Answer

v_f = 2.5 \text{ m/s}

First step

Total initial momentum:

p_i = m_1 v_1 + m_2 v_2 = 5 \times 4 + 3 \times 0 = 20 \text{ kg m/s}

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Example 2

hard

2 \text{ kg}

ball moving at

6 \text{ m/s}

right collides elastically with a

2 \text{ kg}

ball at rest. What are the final velocities?

Example 3

medium

2\text{ kg}

ball at

4\text{ m/s}

collides elastically with a

2\text{ kg}

ball at rest. Find their final velocities.

Example 4

medium

1\text{ kg}

ball at

4\text{ m/s}

hits a

1\text{ kg}

ball at rest and sticks. Find the energy lost in the collision.

Example 5

hard

0.02\text{ kg}

bullet at

400\text{ m/s}

embeds in a

2\text{ kg}

block hanging from a string. Find the height the block rises. Use

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

Practice Problems

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

Example 1

medium

60 \text{ kg}

astronaut floating in space throws a

5 \text{ kg}

tool at

8 \text{ m/s}

. What is the astronaut's recoil velocity?

Example 2

medium

4 \text{ kg}

firework initially at rest explodes into a

1 \text{ kg}

piece moving east at

12 \text{ m/s}

and a

3 \text{ kg}

piece moving west. What is the speed of the

3 \text{ kg}

piece?

Example 3

easy

2

kg cart at

3

m/s hits a

2

kg cart at rest and they stick. Find their common velocity.

Example 4

easy

1

kg and a

3

kg cart stick after collision; total momentum is

8

\cdot

m/s. Find the final speed.

Example 5

easy

4

kg object at

2

m/s collides with a

1

kg object at rest. What is the total momentum after?

Example 6

easy

A stationary

5

kg object explodes into two pieces. One piece carries

+12

\cdot

m/s. What is the other piece's momentum?

Example 7

easy

Two ice skaters push off from rest. One (

60

kg) moves at

2

m/s. What is the other skater's momentum?

Example 8

easy

3

kg ball at

4

m/s hits a

3

kg ball at rest and stops dead. What is the second ball's velocity?

Example 9

easy

10

kg cart at

6

m/s couples with a

20

kg cart at rest. Find their joint speed.

Example 10

easy

In a closed, frictionless system two objects collide. Is total momentum conserved?

Example 11

medium

0.05

kg bullet at

400

m/s embeds in a

2.95

kg block at rest. Find the block-bullet speed after.

Example 12

medium

2

kg object at

5

m/s collides with a

3

kg object at

-2

m/s and they stick. Find the final velocity.

Example 13

medium

1

kg ball at

6

m/s hits a

2

kg ball at rest elastically. After, the

1

kg ball moves at

-2

m/s. Find the

2

kg ball's velocity.

Example 14

medium

50

kg astronaut at rest throws a

2

kg tool at

10

m/s. Find the astronaut's recoil speed.

Example 15

medium

1500

kg car at

20

m/s rear-ends a

1000

kg car at

10

m/s (same direction); they lock together. Find their joint speed.

Example 16

medium

4

kg object at rest explodes into a

1

kg piece at

9

m/s and a

3

kg piece. Find the

3

kg piece's velocity.

Example 17

medium

2

kg ball at

3

m/s east strikes a

2

kg ball at

4

m/s north; they stick. Find the speed of the combined object.

Example 18

medium

0.5

kg ball at

4

m/s hits a

0.5

kg ball at rest. They stick. Compare kinetic energy before and after.

Example 19

medium

6

kg cart at

5

m/s collides with and sticks to a

4

kg cart at rest. Find their common velocity.

Example 20

challenge

A ballistic pendulum: a

0.02

kg bullet embeds in a

1.98

kg block, which then rises

0.2

m (

g=10

m/s

^2

). Find the bullet's initial speed.

Example 21

challenge

3

kg object at

4

m/s collides elastically with a

1

kg object at rest. Find the

1

kg object's velocity after (elastic, 1D).

Example 22

challenge

2

kg cart at

3

m/s and a

1

kg cart at

-3

m/s collide and stick on a frictionless track, then the combined cart compresses a spring. Find the joint speed before hitting the spring.

Example 23

easy

3\text{ kg}

cart at

4\text{ m/s}

collides with a

5\text{ kg}

cart at rest. They stick. Find their common speed.

Example 24

easy

0.04\text{ kg}

bullet at

300\text{ m/s}

embeds in a

4\text{ kg}

block at rest. Find their joint speed.

Example 25

easy

A stationary

10\text{ kg}

object explodes into a

4\text{ kg}

piece going east at

6\text{ m/s}

and a

6\text{ kg}

piece. Find the

6\text{ kg}

piece's velocity.

Example 26

easy

1\text{ kg}

object at

5\text{ m/s}

collides with a

1\text{ kg}

object at

-3\text{ m/s}

and they stick. Find their final velocity.

Example 27

easy

70\text{ kg}

person on frictionless ice throws a

5\text{ kg}

ball at

4\text{ m/s}

east. Find the person's velocity.

Example 28

medium

3\text{ kg}

cart at

6\text{ m/s}

and a

2\text{ kg}

cart at

-2\text{ m/s}

collide and stick. Find their joint speed.

Example 29

medium

1\text{ kg}

ball at

6\text{ m/s}

hits a

3\text{ kg}

ball at rest elastically. Find the

3\text{ kg}

ball's velocity.

Example 30

medium

1\text{ kg}

ball at

6\text{ m/s}

hits a

3\text{ kg}

ball at rest elastically. Find the

1\text{ kg}

ball's velocity after.

Example 31

medium

4\text{ kg}

object at rest explodes into a

1\text{ kg}

piece going

+8\text{ m/s}

and a

3\text{ kg}

piece. Find the

3\text{ kg}

piece's velocity.

Example 32

medium

2000\text{ kg}

truck at

20\text{ m/s}

collides head-on with a

1000\text{ kg}

car at

30\text{ m/s}

(opposite direction). They lock together. Find their joint velocity (truck's direction +).

Example 33

medium

0.5\text{ kg}

ball moving east at

3\text{ m/s}

collides with a

0.5\text{ kg}

ball moving north at

4\text{ m/s}

and they stick. Find the speed of the combined object.

Example 34

medium

0.15\text{ kg}

baseball at

40\text{ m/s}

is hit and rebounds at

50\text{ m/s}

in the opposite direction. Find the magnitude of the impulse on the ball.

Example 35

medium

60\text{ kg}

skater at

4\text{ m/s}

catches a

4\text{ kg}

bag thrown at

-6\text{ m/s}

. Find the skater-bag system's velocity after.

Example 36

hard

Two ice skaters push off from rest. Skater A (

45\text{ kg}

) drifts east at

2\text{ m/s}

. Skater B (

60\text{ kg}

) drifts ___?

Example 37

hard

2\text{ kg}

ball at

5\text{ m/s}

hits a

3\text{ kg}

ball at

-2\text{ m/s}

elastically. Find the velocity of the

2\text{ kg}

ball after.

Example 38

hard

2\text{ kg}

ball at

5\text{ m/s}

hits a

3\text{ kg}

ball at

-2\text{ m/s}

elastically. Find the velocity of the

3\text{ kg}

ball after.

Example 39

hard

1500\text{ kg}

rocket ejects

0.5\text{ kg}

of gas per second at

1000\text{ m/s}

relative to the rocket. Find the thrust force.

Example 40

hard

0.05\text{ kg}

bullet is fired horizontally from a

4\text{ kg}

rifle, leaving at

400\text{ m/s}

relative to the ground. Find the rifle's recoil speed.

Example 41

challenge

5\text{ kg}

object at rest explodes into three equal

\tfrac{5}{3}\text{ kg}

fragments. Two fly off perpendicularly at

6\text{ m/s}

each. Find the speed and direction of the third fragment.

Example 42

challenge

1\text{ kg}

ball moving east at

4\text{ m/s}

collides elastically with a

1\text{ kg}

ball at rest. After the collision, the incident ball moves at

30^\circ

above east. Find the speed of each ball after the collision.

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Related Concepts

Momentum Impulse Elastic Collision Inelastic Collision

Background Knowledge

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

momentumimpulse