1. A billiard ball moving at 5.00 m/s strikes a stationary ball ofthe same mass.

Question

1. A billiard ball moving at 5.00 m/s strikes a stationary ball ofthe same mass. After the collision, the first ball moves at 4.33m/s, at an angle of 30.0° with respect to the original line ofmotion. Assuming an elastic collision (and ignoring friction androtational motion), find the struck ball's velocity after thecollision.

A particle of mass m = 5.00 kg is released from point A and slideson the frictionless track shown in the Figure. Determine (a) theparticle's speed at points B and C and (b) the net work done by thegravitational force in moving the particle from A to C.

Explanation / Answer

1. A billiard ball moving at 5.00 m/s strikes a stationary ball ofthe same mass. After the collision, the first ball moves at 4.33m/s, at an angle of 30.0° with respect to the original line ofmotion. Assuming an elastic collision (and ignoring friction androtational motion), find the struck ball's velocity after thecollision.

     Using conservation of momentum we have

                  m u = m v cos + m v' cos

         ==> v 'cos = u - v cos = 5.00 - 4.33 * cos30 = 1.250

     and

                 0 = - m v sin + m v' sin ==> v' sin= v sin = 4.33 sin30 = 2.165

==> v' sin / v ' cos   = 2.165 / 1.250 = > tan = 1.732 ==> = 60o

                 ==> v ' = 1.250 / cos60 = 2.5m/s

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