Answer to Question #108546 in Mechanics | Relativity for Chinmoy Kumar Bera

Question

A stationary ball is struck by a bat with an avg force of 60N over 10 ms. If the mass of the ball is .25 kg, what speed does it have just after the impact?

Answer 1

Solution: The second Newton's law states that the rate of change of momentum of a body is directly proportional to the force applied, and this change in momentum takes place in the direction of the applied force. $\vec F=\frac{d\vec p}{dt}$ In our task the directions of force and momentum coincides, and we can write for average magnitudes:

$F=\frac{\Delta p}{\Delta t}$ , where increment of the momentum is $\Delta p= m\cdot \Delta v$ . Since the ball is initial at rest the speed increment coincides with the final speed $v$ of the ball. We have

$F\cdot \Delta t=m \cdot v$ , and $v=\frac {F\cdot \Delta t}{m}=\frac{60N\cdot 10\cdot 10^{-3}s}{0.25 kg}=2.4 ms^{-1}$

Answer: speed of the ball just after the impact is 2.4m/s