8 Pendulum Elastic Collision A pendulum of mass m = 0:37 kg and length l = 0:95

Question

8 Pendulum Elastic Collision

A pendulum of mass m = 0:37 kg and length l = 0:95 m is released from a horizontal

position. At the bottom of its swing, it collides elastically with a mass M = 0:56 kg. The

velocity of M and the maximum height of m (above the low point) are

1. 3.5 m/s in the same direction as m moved prior to the collision; 4 cm

2. 4.5 m/s in the same direction as m moved prior to the collision; 4 cm

3. 0.9 m/s in the opposite direction as m moved prior to the collision; 6 cm

4. 3.5 m/s in the same direction as m moved prior to the collision; 2 cm

Explanation / Answer

u1 = sqrt(2*g*L)= 4.31 m/s

u2 =0


a) v2 = (m-M)*u2 /(M+m) + 2*m*u1/(M+m) = (2*.37*4.31)/(0.37+0.56) = 3.429 = 3.5 m/s

b) v1 = (m-M)*u1 /(M+m) + 2*M*u2/(M+m)
v1 = ((0.37-0.56)*4.31)/(0.37+0.56) = -0.8805 m/s

h = v1^2/2g = 0.039m = 4cm

1. 3.5 m/s in the same direction as m moved prior to the collision; 4 cm

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