Conservation of Momentum Physics Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
A 4 kg4 \text{ kg} firework initially at rest explodes into a 1 kg1 \text{ kg} piece moving east at 12 m/s12 \text{ m/s} and a 3 kg3 \text{ kg} piece moving west. What is the speed of the 3 kg3 \text{ kg} piece?

Solution

  1. 1
    Initial momentum is zero because the firework starts at rest.
  2. 2
    Let east be positive. Then 0=(1)(12)+3v0 = (1)(12) + 3v
  3. 3
    Solve: 3v=−12⇒v=−4 m/s3v = -12 \Rightarrow v = -4 \text{ m/s}

Answer

4 m/s west4 \text{ m/s west}
When no external force acts on the system, total momentum stays constant. If one fragment moves east, the other must carry equal momentum west.

About Conservation of Momentum

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

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More Conservation of Momentum Examples

Example 1 medium

A [formula] cart moving at [formula] collides with a stationary [formula] cart. They stick together.

Example 2 hard

A [formula] ball moving at [formula] right collides elastically with a [formula] ball at rest. What

Example 3 medium

A [formula] astronaut floating in space throws a [formula] tool at [formula]. What is the astronaut'

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