ment Chapter 07, Problem 38 GO The wire is held horizontal, and the ball ls rele

Question

ment Chapter 07, Problem 38 GO The wire is held horizontal, and the ball ls released from rest (see the drawing). It swings downward and strikes A ball is attached to one end of a wire, the other end being fastened to the ceiling. block initially at rest on a horizontal frictionless surface. Air resistance is negligible, and the collision is elastic the wire is 1.13 m. Find the velocity (magnitude and direction) of the ball (a) Just before the collision, and (b) just after the colision . The masses of the ball and block are, respectively, 1.6 kg and 2.3 kg, and the length of (a) v- (b)v 0 TUTORIAL Version 4.24.5 Show A/ MacBook Air

Explanation / Answer

  (a) Use conservation of energy to get the pre-impact velocity:
v = (2gh) = (2 * 9.8m/s² * 1.13m) = 4.706 m/s
See drawing for direction. I'll call it "positive."

(b) Since we have an elastic head-on collision, we know (from CoE) that
the relative velocity of approach = relative velocity of separation, or
4.706 m/s = v - u
v = 4.706 + u
where v, u are the post-collision velocities of the block, ball respectively

Conserve momentum: initial p = final p
1.6kg * 4.706m/s = 1.6kg * u + 2.3kg * v substitute for v from above
7.5296 = 1.6u + 2.3(4.706 + u) = 10.8238 + 3.9u
-3.2942 = 3.9u
u = -0.844 m/s (I'll call this "negative") ball
v = 4.706 + u = 3.862 m/s ("positive") block

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