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, 1.5 kg and 2.4 kg, and the length of the wire is 1.26 m. Find the velocity (magnitude and direction) of the ball (a) just before the collision, and (b) just after the collision.

Explanation / Answer

(a) Length of wire = 1.26m Vf = v2gho =v2*9.8*1.26 = 4.97 m/sec The bottom of swing ball is moving horizontally to right which we take +x direction. The velocity of ball is Vf = 4.97 m/sec (b) Conversion of linear momentum and total kinetic energy is Vf1 = [(m1-m2)/(m1+m2)]*Vo1 ; m1 and m2 are masses of ball and block Vf1 = final velocity of ball m1 Vo1 = Velocity of ball just before collision Vf1 = [(1.5-2.3)/(1.5+2.3)]* 4.97 = -1.046315789 m/sec

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