Question

A person with mass mp=80 kg is standing at rest on a horizontal, frictionless surface holding a ball of wet clay with mass mg=10 kg . In front of the person is a large block with mass M=20 kg at rest next to a spring with stiffness k=100 N/m . The person throws the ball horizontally, it sticks to the block, and then ball and block slide and compress the spring a distance 1=0.75 m away from equilibrium before the ball-block springs back toward the person. (Assume the distance the ball is thrown is short, so that we can ignore the vertical component of its velocity.)

a) Find v P1 (the speed of the person after the ball was thrown)

b) Find Vs (the speed at which the person, ball, and block move after the ball and block bounced back off the spring and collided with the person)

c) If it takes 0.2 seconds for the person and the ball-block to get to the same velocity, find the impulse on the person due to the ball-block. AND find the force on the person due to the ball-block,

(Please be careful in your answer in part b because the person is also moving after he throws the ball. So, this will effect the final answer for their overall speed. And, please don't copy from others. They are all wrong. Thanks.

Answer 1

Solution:

Given thet:

Part(a). Since spring force is conservative force. So, by conservation of energy

By conservation of momentum,

Thus, the velocity of persion after the ball was thrown is given by

Part(b). Again, by conservation of energy, we get

Since the surface is frictionless. So, the speed of ball and block system befor the persion collide is given by

and the speed of persion collide with the ball and block system is given by

Part(c). Again by conservation of momentum, we get

Now, impulse on persion by ball and block system is given by