A ball of mass 50 g travels toward a catcher of a ballistic Pendulum of length 1

Question

A ball of mass 50 g travels toward a catcher of a ballistic Pendulum of length 1.0 m. The mass of the catcher is 120 g. Assume that all mass of the pendulum is in the catcher. The ball and the catcher collide and stick together. Their speed after the collision is 3.0m/s. The ball/catcher system swings together and is caught by a ratchet. The gravitational acceleration on Earth is g=9.81 m/s^2. What is the velocity of the ball before the collision? What is the change in the momentum of the ball during the collision? How much energy is lost in the collision? At what height is the ball/catcher system caught by the ratchet?

Explanation / Answer

a)
Use conservation of momentum:
initial momentum of ball = final momentum of ball catcher system
m*v1i = (m+M)*vf
0.05*v1i = (0.05 + 0.120)*3
v1i = 10.2 m/s
Answer: 10.2 m/s

b)
change in momentum of ball = m*(v1i-v1f)
= 0.05*(10.2-3)
= 0.36 Kgm/s
Answer: 0.36 Kgm/s

c)
Energy lost = initial energy - final energy
=0.5* m*v1i^2 - 0.5*(m+M)*vf^2
=0.5* 0.05*10.2^2 - 0.5*(0.05 + 0.120)*3^2
=2.601 - 0.765
= 1.836 J
Answer: 1.836 J

d)
Use conservation of energy:
0.5*(m+M)*vf^2 = (m+M)*g*h
0.5*vf^2 = g*h
0.5*3^2 = 9.81*h
h= 0.46 m
Answer: 0.46 m

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