Conservation of Momentum Physics Example 1

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

Example 1

medium
A 5 kg5 \text{ kg} cart moving at 4 m/s4 \text{ m/s} collides with a stationary 3 kg3 \text{ kg} cart. They stick together. What is their final velocity?

Solution

  1. 1
    Total initial momentum: pi=m1v1+m2v2=5×4+3×0=20 kg m/sp_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: m1+m2=8 kgm_1 + m_2 = 8 \text{ kg}.
  3. 3
    Conservation of momentum: pf=pi  ⟹  (m1+m2)vf=20  ⟹  vf=208=2.5 m/sp_f = p_i \implies (m_1 + m_2)v_f = 20 \implies v_f = \frac{20}{8} = 2.5 \text{ m/s}

Answer

vf=2.5 m/sv_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.

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 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'

Example 4 medium

A [formula] firework initially at rest explodes into a [formula] piece moving east at [formula] and

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