A cricket ball of mass 250 g collides with a bat with velocity 10 m/s and returns with the same velocity withi

Question

A cricket ball of mass 250 g collides with a bat with velocity 10 m/s and returns with the same velocity within 0.01 second. The force acted on bat is:

Accepted Answer

1. **Convert Units:** Mass $m = 250 	ext{ g} = 0.25 	ext{ kg}$.
2. **Analyze Momentum Change:** 
   - Initial velocity $v_i = 10 	ext{ m/s}$.
   - Final velocity $v_f = -10 	ext{ m/s}$ (since it returns with the same speed in the opposite direction).
   - Change in momentum $\Delta p = m(v_f - v_i) = 0.25 	imes (-10 - 10) = 0.25 	imes (-20) = -5 	ext{ kg m/s}$.
   - Magnitude of change in momentum $|\Delta p| = 5 	ext{ kg m/s}$ [Source 68].
3. **Calculate Force:** According to Newton's Second Law, the average force is the rate of change of momentum (or Impulse divided by time).
   $$ F_{avg} = \frac{|\Delta p|}{\Delta t} $$
   $$ F_{avg} = \frac{5 	ext{ kg m/s}}{0.01 	ext{ s}} = 500 	ext{ N} $$
   [Source 66, 67].

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