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

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 53.0 cm long. The upper ball has mass 1.95 kg and it is initially 10.0 cm higher than the lower ball, which has mass 3.15 kg .

Part A

Find the frequency of the motion after the collision.

Express your answer in hertz to three significant figures.

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Part B

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

Express your answer in degrees to three significant figures.

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Explanation / Answer

(A)
f = 1/2pi * sqrt(g/L)
f = 1/(2*3.14) * sqrt(9.8/0.53)
f = 0.684 Hz

(B)
Initial Potential Energy = m*g*h
Final Kinetic Energy = 1/2 * mv^2

Using Energy Conservation -
1/2 * m*v^2 = m*g*h
v = sqrt(2*g*h)

Using conservation of momentum through the collision-
Initial Momentum = Final Momentum
1.95 * v = (3.15 + 1.95) * v1
v1 = 1.95/(3.15 + 1.95)*sqrt(2*g*h)

Now K.E changes to Final Potential Energy.
1/2 * (m1 + m2) *v1^2 = (m1 +m2)* g*h'
1/2 * v1^2 = (3.15 + 1.95)*g* L(1 - cos())
1/2 * (1.95/(3.15 + 1.95) *sqrt(2*g*h))^2 = 9.8* 0.53(1 - cos())
Solving for   -
= 13.6 o

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