Physics elastic collision - Billard balls?

Posted on 2014-11-21 06:06:00 in Physics by SAMUEL

Moe Mentum and Ken Ettik are playing pool. Moe hits the cue ball, sending it towards the 6 ball at 2 m/s. It strikes the stationary 6 ball off-center, moving off at a 60 degree angle from the original direction after a perfectly elastic collision. Both balls have a mass of 160 grams.

(1) Use conservation of kinetic energy to determine the angle at which the six ball moves after collision, then draw a diagram of the collision.

(2) Determine the direction of the forces of impact on the balls during collision and set up a pair of axes.

(3) Resolve the initial and final velocities into components along the axes you have chosen. What happens to the components perpendicular to the forces of impact?

(4) For the axis in the direction of the forces, calculate the velocity of the center of mass before collision.

(5) Transform the velocities along the axis in (4) to the center of mass frame.

(6) Now determine the final velocities along the axis in 5 in the CM frame and then transform them back to the pool table frame.

(7) Recombine the final velocity components to get the final velocities for the two pool balls.

(8) The six ball encounters a pencil on the table and flies off the table, bouncing off the cushion to fly upward, 60° above horizontal moving at the same speed it had on the table. What is the vertical component of the launch velocity and the maximum height it reaches?

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