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

Question

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, 1.8 kg and 2.4 kg, and the length of the wire is 1.14 m. Find the velocity (magnitude and direction) of the ball (a) just before the collision, and (b) just after the collision.

Explanation / Answer

Given that

The length of the wire is (L) =1.14m

The final velocity is given by

vf =Sqrt(2gho) =Sqrt(2*9.81*1.14) =4.729m/s

At the bottom of the swing the ball is moving horizontally and to the right ,which we take +x -direction. Thus the velocity of the ball is vf =+4.729m/s

b)

The conservation of linear momentum and the conservation of the total kinetic energy is the velocity of the ball just before the collision is given by

vf1 =(m1-m2)/(m1+m2)vf =[(1.8-2.4)/(1.8+2.4)]*(4.729m/s) =-0.675m/s

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