Section 4.7: Momentum Problem-Solving

When solving momentum problems, it is important to apply a clear, step-by-step strategy. Momentum conservation applies only when no net external force acts on the system. Depending on the collision or explosion type, kinetic energy may or may not be conserved.

General Strategy:

  1. Draw a diagram showing all objects before and after interaction.
  2. Define the system and choose a positive direction (usually right or upward).
  3. Write the momentum conservation equation:
    \[ p_{i,\text{total}} = p_{f,\text{total}} \]
  4. Substitute known values for masses and velocities.
  5. Solve for the unknown(s).
  6. Check the direction of velocities and interpret results physically.

Example

A 1200 kg car moving east at 20 m/s collides with a 1000 kg car moving west at 15 m/s. If the cars lock together after the collision, find their final velocity.

Initial momentum: \((1200)(20) + (1000)(-15) = 24000 - 15000 = 9000 \, \text{kg·m/s}\) Final mass: \(1200 + 1000 = 2200 \, \text{kg}\) Final velocity: \(v = \dfrac{9000}{2200} \approx 4.09 \, \text{m/s east}\) The cars move together east at about 4.1 m/s.

Practice Problems

  1. A 0.15 kg baseball moving at 25 m/s is caught by a glove that brings it to rest in 0.2 s. Find the impulse on the ball and the average force exerted by the glove.
  2. A 2000 kg truck moving at 12 m/s rear-ends a 1000 kg car moving at 6 m/s in the same direction. They stick together. Find their final velocity.
  3. A 2 kg object moving east at 10 m/s collides elastically with a 4 kg object at rest. Find the velocities after collision.
  4. A 50 g bullet moving at 400 m/s embeds into a 2 kg block at rest. Find the velocity of the block and bullet system immediately after impact.
  5. A 1000 kg car moving at 15 m/s east collides head-on with a 1200 kg car moving at 10 m/s west. If they stick together, find the velocity of the wreckage.
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