In this worksheet, we will practice solving problems on the impact of two particles using conservation of linear momentum and Newton's law of restitution.
Q1:
A sphere of mass 720 g fell vertically from a height of 2.5 m into a liquid. As a result of the impact, its speed slowed until it was descending through the liquid uniformly covering 7 m every 4 seconds. Determine the magnitude of the impulse of the liquid on the sphere, given that the acceleration due to gravity is .
Q2:
A smooth stone of mass 4 kg fell for 3 seconds before it entered a liquid. After the impact, the stone descended through the liquid uniformly, covering 3.5 m every 2.5 seconds. Given that the duration of the impact between the stone and the liquid was of a second, determine the magnitude of the impact force. Take .
Q3:
A man was standing inside an electric lift which was descending at 85 cm/s. He dropped a smooth ball of mass 58 g from a height of 40 cm above the lift’s floor. Given that the ball did not rebound after its impact with the floor, find the impulse the floor exerted on the ball as a result of the impact. Consider the acceleration due to gravity to be 9.8 m/s2.
Q4:
A body of mass 70 g fell from a height of 90 cm above a pond and plunged into the water. After penetrating the surface, it travelled 120 cm in 4 seconds while decelerating at 1.8 m/s2. Find the magnitude of the impulse of the water on the body. Consider the acceleration due to gravity to be 9.8 m/s2.