A pendulum consists of a compact 0.50 kg bob attached to astring of length 1.20

Question

A pendulum consists of a compact 0.50 kg bob attached to astring of length 1.20 m. A block of mass m rests on ahorizontal frictionless surface. The pendulum is released from restat an angle of 53° with the vertical. The bob collideselastically with the block at the lowest point in its arc.Following the collision, the maximum angle of the pendulum with thevertical is 5.73°. Determine the mass m (there are twopossible values).

larger value

1 kg

smaller value

2 kg

larger value

1 kg

smaller value

2 kg

Explanation / Answer

Initial height = L (1 - cos 53) = 4.78 m = h1 Final height = L (1 - cos 5.73) = .006 m v1 = (2 g h1) = 9.67m/s    speed of bob at bottom v2 = (2 g h2) = .343m/s   recoil speed of bob In an elastic collision the relative speed of approach =relative speed of separation Thus the block can have speeds of 9.67 ± .343 = 10.0 or 9.33 m/s depending direction ofrecoil of bob Potential energy lost by bob = m g (4.78 - .006) = 23.4J M = 2 E / V2 = 46.8 / 100 = .468kg    M = 46.8 / .538 kg       the twopossible values of M Final height = L (1 - cos 5.73) = .006 m v1 = (2 g h1) = 9.67m/s    speed of bob at bottom v2 = (2 g h2) = .343m/s   recoil speed of bob In an elastic collision the relative speed of approach =relative speed of separation Thus the block can have speeds of 9.67 ± .343 = 10.0 or 9.33 m/s depending direction ofrecoil of bob Potential energy lost by bob = m g (4.78 - .006) = 23.4J M = 2 E / V2 = 46.8 / 100 = .468kg    M = 46.8 / .538 kg       the twopossible values of M

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