A 2 kg ball moves at 3 m/s and collides with a stationary 1 kg ball. The collision is perfectly inelastic. Find the speed after the collision — Physics problems | PhysLabo
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Speed after an inelastic collision

Medium 9 grade Mechanics / Momentum
Problem statement

A ball of mass $m_1 = 2$ kg moves at $v_1 = 3$ m/s and collides head-on with a stationary ball of mass $m_2 = 1$ kg. The collision is perfectly inelastic. Find the speed of the balls after the collision.

Given
  • $m_1 = 2$ kg
  • $v_1 = 3$ m/s
  • $m_2 = 1$ kg
  • $v_2 = 0$
  • $v = ?$
Hints
Hint 1 / 2
The momentum of the system is conserved before and after the collision.
Hint 2 / 2
After a perfectly inelastic collision both balls move with a common speed — the denominator contains the sum of the masses.
Solution

In a perfectly inelastic collision the bodies stick together and move as one. The momentum of the system is the same before and after the collision:

$$m_1 v_1 = (m_1 + m_2) v$$

$$v = \frac{m_1 v_1}{m_1 + m_2} = \frac{2 \cdot 3}{2 + 1} = \frac{6}{3} = 2 \text{ m/s}$$

Answer

$v = 2$ m/s

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