A wooden ball of mass M = 0.500 kg is suspended from a wire of length L = 1.50 m

Question

A wooden ball of mass M = 0.500 kg is suspended from a wire of length L = 1.50 m. A small piece of putty (mass m = 0.100 kg) is traveling at 10.0 m/s when it hits the wooden ball and sticks to it. Calculate the maximum angle theta reached by the putty and ball as they swing upward. Clearly identify any conservation laws you are using, and explain your reasoning. Suppose that instead of a piece of putty, a steel ball (same mass 0.100 kg, same speed 10.0 m/s) strikes the wooden ball and rebounds at 5.00 m/s. Calculate the maximum angle reached in this case.

Explanation / Answer

1)initially by conservation of momentum v2=0.1 * 10/(0.1 +0.5)=1.67 m/s

By Law of conservation of energy

1/2 m v^2 =m g h

h=v^2/2g = 0.139m

so maximum angle = cos-1(1.5-0.139/1.5)=24.87 deg

2)by again law of conservation of momentum m1*v1=m2*v2-m1*v3

v2=0.1*10+0.1*5/0.5=3m/s

By Law of conservation of energy

1/2 m v^2 =m g h

h=v^2/2g = 0.45

so maximum angle =cos-1(1.5-0.45/1.5)=45.57 deg

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