Calculate the percentage of mechanical energy lost in the inelastic collision. N

Question

Calculate the percentage of mechanical energy lost in the inelastic collision. Not sure where to start

a metal ball (avg mass of 65.75g) and plastic ball (avg mass of 9.2g) was placed into a gun and shot into a pendulum. When the ball was caught in the pendulum the average angle collected was, 52.5 degrees (metal ball) & 33.75 degrees (plastic ball). The average center of mass for the pendulum rod is, 0.265m (with metal ball in pendulum rod) and 0.253 (with plastic ball in pendulum rod). The initial velocity of the ball before the collision is: 4.569 m/s +/- 0.04772 (metal ball) & 15.32 m/s +/- 0.05415 (plastic ball).

Explanation / Answer

Since the question is not clear, I assumed that two seperate cases are considered. Case 1: Metal ball shot into the pendulum and Case 2: Plastic ball shot into the pendulum .

Height attained = L(1 - cos theta) where L is the length of the string of the pendulum and theta is the angle deflected.

For metal ball, ( Case 1)

Height attained = 0.265*(1 - cos 52.5) = 0.104 m

Energy lost = KE - PE = 0.5*0.06575*4.569^2 - 0.06575*10*0.104 = 0.618 J

For plastic ball ( Case 2)

Height attained = 0.253*(1 - cos 33.75) = 0.043 m

Energy lost = KE - PE = 0.5*0.00925*15.32^2 - 0.00925*10*0.043 = 1.082 J

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