Question

In the figure (Figure 1) the upper ball is released from rest, collides with the stationary lower ball, and sticks to it. The strings are both 51.5 cm long. The upper ball has mass 1.70 kg and it is initially 10.0 cm higher than the lower ball, which has mass 2.80 kg . Find the frequency of the motion after the collision. Find the maximum angular displacement of the motion after the collision.

Answer 1

Solution,

From law of conservation of energy,

0.5 m2 v^2 = m2 g h

Velocity, v = sqrt (2gh) = sqrt (2 x 9.8 x 0.1) = 1.4 m/s

Using law of conservation of momentum,

m2 v = (m2 + m3) V

V = m2 v/(m2 + m3) = (1.7 x 1.4)/(1.7 + 2.8) = 0.53 m/s

Using law of conservation of energy,

hf = V^2/2g = 0.53^2/ 2 x 9.8 = 0.014 m = 1.43 cm

A)

Theta = arccos (50.07/51.5) = 13.52 degree

B)

Frequency, f = (1/2 pi) sqrt(9.8/0.515) = 0.69 Hz

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