21. A ball is attached to one end of a wire, the other end being fastened to the

Question

21. A ball is attached to one end of a wire, the other end being fastened to the ceiling. The wire is held horizontal, and the ball is released from rest (see the drawing). It swings downward and strikes a block initially at rest on a horizontal frictionless surface. Air resistance is negligible, and the collision is elastic. The masses of the ball and block are, respectively, 1.60 kg and 2.40 kg. The velocity of the ball after the collision is 0.97 m/s to the left and the velocity of the block after the collision is 3.88 m/s to the right. Find the height that the ball was released from

Explanation / Answer

here,

mass of ball , m1 = 1.6 kg

mass of box , m2 = 2.4 kg

final speed of ball , v1 = - 0.97 m/s

final speed of box , v2 = 3.88 m/s

let the speed of ball before the collison be u

using conservation of momentum

m1 * u = m1 * v1 + m2 * v2

1.6 * u = - 1.6 * 0.97 + 2.4 * 3.88

solving for u

u = 4.85 m/s

the minimum height of release , h = u^2 /(2g)

h = 4.85^2 /( 2 * 9.81)

h = 1.2 m

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