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 48.5cm long. The upper ball has mass is 1.90kg and it is initially 10.0 cm higher than the lower ball, which has mass 3.05kg

Part A

Find the frequency of the motion after the collision.

Part B

Find the maximum angular displacement of the motion after the collision.

Answer 1

A)

Here , as l = 0.485 m

the frequency fo the motion

f = sqrt(g/l)/2pi

f = sqrt(9.8/.485)/6.282

f = 0.716 Hz

the frequency of the motion after the collision is 0.716 Hz

B)

for the upper ball ,

speed before collision , u = sqrt(2*9.8*.10)

u = 1.4 m/s

Now, using conservation of momentum

1.4 * 1.90 = (1.90 + 3.05)*v

v = 0.537 m/s

let the maximum angle from vertical is theta

Now, using conservation of energy,

mg*l*(1 - cos(theta)) = 0.5*mv^2

9.8 * 0.485 *(1 - cos(theta)) = 0.5 * 0.537^2

cos(theta) = 0.9696

theta = 14.2 degree = 0.247 radians

the maximum angular displacement is 0.247 radians