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A 0.100 kg pendulum ball is released as shown in the figure below. At the bottom

ID: 1358675 • Letter: A

Question

A 0.100 kg pendulum ball is released as shown in the figure below. At the bottom of the swing, the ball hits a small 0.300 kg object initially at rest.

a. Find the speed the ball has just before it hits the object, if the length of the pendulum string is 1.500 m. (Figure a)

b. Consider that the collision is elastic and calculate the speed of the ball and the object just after the collision. (Figure b)

c. Now consider that the collision is totally inelastic, and the ball sticks to the object. How high is the CM of the ball+object going to rise after the collision, before it momentarily stops again? (Figure c)

d. Calculate the tension of the pendulum string just before and just after the inelastic collision in part (c).

Explanation / Answer

the speed the ball has just before it hits the object is

u1 = root 2gL = root 2 ( 9.8) ( 1.5 m) = 5.42 m/s

(b)

vb = ( m1- m2/ m1+ m2) u1

= (0.1-0.3)/0.1+0.3) 5.42 m/s

=-2.71 m/s

vo =( 2 m1/ m1+ m2 ) u1= 2 ( 0.1)/ 0.1 + 0.3) 5.42 m/s = 2.71 m/s

(3)

mb u1 + mo u2 = ( mb+ mo) v

0.1 ( 5.42) + 0.3 ( 0) = ( 0.1 + 0.3) v

v = 1.355 m/s

(4)

just before

T = (mb) g cos theta

just after

T = ( mb+ mo) cos theta