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.

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

Read the full concept explanation →

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: What one object loses in momentum, another gains — the total stays constant in a closed system.

Common stuck point: Only applies when external forces are negligible (or over very short times).

Sense of Study hint: When applying conservation of momentum, first define the system and check that external forces are negligible. Then write the total momentum before the event: m_1 v_{1i} + m_2 v_{2i}. Set it equal to the total momentum after: m_1 v_{1f} + m_2 v_{2f}. Finally, solve for the unknown velocity, remembering to use signs for direction.

Worked Examples

Example 1

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A 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?

Solution

  1. 1
    Total initial momentum: p_i = m_1 v_1 + m_2 v_2 = 5 \times 4 + 3 \times 0 = 20 \text{ kg m/s}.
  2. 2
    After collision (perfectly inelastic), combined mass: m_1 + m_2 = 8 \text{ kg}.
  3. 3
    Conservation of momentum: p_f = p_i \implies (m_1 + m_2)v_f = 20 \implies v_f = \frac{20}{8} = 2.5 \text{ m/s}

Answer

v_f = 2.5 \text{ m/s}
In a perfectly inelastic collision, the objects stick together. Total momentum is conserved, but kinetic energy is not -- some is converted to heat and deformation.

Example 2

hard
A 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?

Practice Problems

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

Example 1

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A 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

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A 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?
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Background Knowledge

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

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