Question #108546

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?

Expert's answer

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

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