A ball is attatched to one end of a wire, the other end being fastened to the ce

Question

A ball is attatched to one end of a wire, the other end being fastened to the ceiling. The wire is held horizontal, then released from rest. It swings downward and strikes a lock initially at rest on a horizontal frictionless surface. The collision is elastic. The masses of the ball and block are, respectively, 1.0kg and 2.0kg, and the length of the wire is 0.6 m. Find the velocity (magnitude and direction) of the ball (a) just before the collision, and (b) just after the collision. (Picture below is sideways)

Explanation / Answer

(a) Energy conservation

mgh = 1/2 m v^2

cancelling m of each side

9.8 x .6 = .5 x v^2

v = 3.42 m/s (u1 for part b)

(b) by momentum conservation and energy conservation we get velocity of block after collision

v1 = ((m1 - m2) / (m1 + m2)) u1 + ((2m2) / (m1 + m2)) u2

as u2 = 0 so

v1 = ((1 - 2) / (1 + 2)) x 3.42

v1 = - 1.14 m/s

"-" sign shows the direction is in opposite the block velocity or initial velocity.

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