In the figure, (Figure 1) the upper ball is released from rest, collides with th

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 54.0  cm long. The upper ball has a mass of 1.90  kg and it is initially 10.0  cmhigher than the lower ball, which has a mass of 3.40  kg .

Part A

Find the magnitude of the momentum of the 1.90-kg ball just before it collides with the 3.40-kg ball.

Part B

Find the speed of the two balls (now stuck together) at the instant immediately after the collision.

Part C

Find the frequency of the pendulum motion after the collision.

Explanation / Answer

Let

m1 = 1.9 kg

m2 = 3.4 kg

A) Let u is the speed of m1 before hitting the second ball.

Apply conservation of energy

m1*g*h = (1/2)*m1*u^2

==> u^2 = 2*g*h

u = sqrt(2*g*h)

= sqrt(2*9.8*0.1)

= 1.4 m/s

momentum of m1, P1 = m1*u

= 1.9*1.4

= 2.66 kg.m/s

B) Let V is the speed of two balls after the collsion.

Apply conservation of momentum

m1*u = (m1+m2)*v

v = m1*u/(m1+m2)

= 1.9*1.4/(1.9 + 3.4)

= 0.5 m/s

C) Frequency of Oscillation does not depend on mass of the balls.

frequency of Oscillation,
f = sqrt(g/L)/(2*pi)

= sqrt(9.8/0.54)/(2*pi)

= 0.678 Hz

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