Pool Table Facts
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physics 20 N?
an overhead view of the path taken by a 0.167 kg cue ball as it bounces from a rail of a pool table. The ball’s initial speed is 2.95 m/s, and the angle θ1 is 56.1°. The bounce reverses the y component of the ball’s velocity but does not alter the x component. What are (a) angle θ2 and (b) the change in the ball’s linear momentum in unit-vector notation? (The fact that the ball rolls is irrelevant to the problem.)
(a)
The ratio of the velocities gives the tangent of the angle theta1 or theta2, assuming these are measured from the rail.
As the x component of velocity is unchanged and the y component is reversed, theta2 is equal to theta1, but measured in the opposite direction from the rail.
(b)
If i is parallel to the rail and j perpendicular to it and the ball initially comes from the right, the initial momentum is:
- [0.167 * 2.95 sin(theta1)]i- [0.167 * 2.95 cos(theta1)] j
The momentum after collision is:
[0.167 * 2.95 sin(theta1)]i- [0.167 * 2.95 cos(theta1)] j
The change is therefore:
[2 * 0.167 * 2.95 sin(theta1)] i
= [0.985 sin(theta1)] i.
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