A pendulum consists of a compact 0.70 kg bob attached to a string of length 1.10

Question

A pendulum consists of a compact 0.70 kg bob attached to a string of length 1.10 m. A block of mass m rests on a horizontal frictionless surface. The pendulum is released from rest at an angle of 53? with the vertical. The bob collides elastically with the block at the lowest point in its arc. Following the collision, the maximum angle of the pendulum with the vertical is 5.73?. Determine the mass m (there are two possible values).

larger value kg smaller value kg A pendulum consists of a compact 0.70 kg bob attached to a string of length 1.10 m. A block of mass m rests on a horizontal frictionless surface. The pendulum is released from rest at an angle of 53½ with the vertical. The bob collides elastically with the block at the lowest point in its arc. Following the collision, the maximum angle of the pendulum with the vertical is 5.73½. Determine the mass m (there are two possible values). larger value kg smaller value kg

Explanation / Answer

speed of pendulum before collision
u

0.5*m*u*u = m*9.8* 1.1*(1-cos53)
u = 2.93 m/s

aftr collision speed b V

0.5*m*v*v = m*9.8*(1-cos5.73)

V = 0.312 m/s

conservation of momentum

-0.7 *2.93 + m*0 = 0.7*0.312   + m*v2

m*v2 = - 2.269 m/s

1 = 2.93/(0.312-v2)
V2 = -2.618 m/s

m = 0.8669 kg

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