Question

State impulse momentum theorem. A batsman hits a cricket ball of mass 120 g with a speed of 40 ms-1. The fielder stops the ball and the ball comes to rest in his hands in 10-3s. Calculate the average force exerted by the fielder's hands on the ball. Using the work-energy theorem , calculate the work done on the ball by this average force.

Answer 1

Question #69873, Physics / Mechanics | Relativity

State impulse momentum theorem. A batsman hits a cricket ball of mass $120\mathrm{g}$ with a speed of 40 ms⁻¹. The fielder stops the ball and the ball comes to rest in his hands in 10⁻³s. Calculate the average force exerted by the fielder's hands on the ball. Using the work-energy theorem, calculate the work done on the ball by this average force.

Solution:

Impulse momentum theorem: An impulse delivered to an object causes the object's momentum to change as follows: $F\Delta t = \Delta p = mv_{final} - mv_{initial}$

$$F = \frac{m v_{final} - m v_{initial}}{\Delta t} = 0.12 \mathrm{kg} \cdot \frac{(40 - 0) \frac{m}{s}}{10^{-3} \mathrm{s}} = 4800 \mathrm{N}$$ $$A = \Delta E = \frac{m v_{final}^2}{2} = 0.12 \mathrm{kg} \cdot \frac{40^2 \mathrm{m}^2}{2 \mathrm{s}^2} = 96 \mathrm{J}$$

Answer: Average force: 4800N

Work done: 96J

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