Question

A head on collision occurs between two equal mass pool balls if the cue ball is
initially traveling with a speed v and the yellow ball is at rest what statement is true about
the speed of the pool balls after the collision?

Answer 1

A. the cue ball moves backwards with a speed v and the yellow ball moves forward with
a speed v

B. the cue ball moves backwards with a speed v and the yellow ball moves forward with
a speed 2v

C. the cue ball is at rest and the yellow ball moves forward with a speed 2v

D. the cue ball is at rest and the yellow ball moves forward with a speed v

Answer 2

i'm going to go with option A on this... am i wrong? can you explain?

Answer 3

The correct answer is D.
The question assumes one knows about the physical makeup of pool balls - they are effectively non-elastic. That is, all energy (momentum) will be transferred instantaneously at the time of collision. The question implies that the head-on collision means that center of mass of the cue ball is directly in line with the center of mass of the yellow ball. It also assumes that pool balls are uniformly spherical, and that their mass is uniformly distributed within each ball, which is typically the case. A direct collision should result in the force vector of the cue ball lining up directly with the center of mass of the yellow ball, so that the yellow ball will move in the same path as the cue ball.
When contact is made, virtually all of the energy of the cue ball is passed to the yellow ball. The cue ball will then be at rest and the yellow ball (same mass) will then be traveling in the same direction at the velocity the cue was traveling. This will be true for the instant immediately after the balls collide, but as there is friction between the yellow ball and the pool table, the yellow ball will slow down as the force of the friction is turned into rotational momentum of the yellow ball.

NOTE: For those who play pool (or billiards, etc.), this is not always the result. If the cue ball had a forward or backwards spin to it (intentional or not) in addition to its linear velocity, the yellow ball would absorb only the linear momentum and the cue ball would then either roll forward or backwards, after contact, depending upon the direction of spin that it had. The contact between the balls is virtually frictionless so none of the spin would be transferred.

Answer 4

i don't play pool a lot but i have noticed that when you hit the cue ball with just the right amount of force you get the ball that was hit moving and the cue ball stopping. I was thinking option D would be a good answer but that was my train of thought at coming to that decision so i thought it to be wrong. well thanks for answering. i'm off to re-read the collisions section of my text book. lol.