5. During a game of pool you hit the cue ball such that it strikes another ball

Question

5. During a game of pool you hit the cue ball such that it strikes another ball sitting at rest. Note that since there is a loud noise generated by the collision, there is some KE lost and as such it isn’t a perfectly elastic collision. The cue ball grazes the striped ball so that the two fly off in opposing directions as shown below. The cue ball and the striped ball both have masses of 0.195 kg and the cue ball is initially given a speed of 1.4 m/s. If the cue ball recoils with an angle of 1=40 degrees and the target ball recoils with an angle of 50 degrees, find the following: a. total momentum of the system before the collision, bot x and y directions. b. total momentum of the system after the collision (an equation), both x and y directions. c. the final speeds of each ball after the collision.

Explanation / Answer

during the impact the will be momentum conserve because there is no external forse acting on the system

so A) assuming initial velocity is in x direction

initial momentum = mu1 = 0.195 * 1.4 = 0.273 kg m/s

B)

because there is no initial monmentum in y direction so there will be no final momentum in y direction

so y component of both balls = same so that they cancelld

mv1 sin(40) = mv2 sin(50)

v1/v2 = sin(50) / sin(40) = 1.19

and final momentum in x diretion = initial momentum = 0.273 kg m/s

C)

final momentum in x diretion = initial momentum = 0.273 kg m/s

mv1 cos(40) + mv2 cos(50) = 0.273

1.19*v2 *0.766 + v2 * 0.643 = 1.4

v2 = 0.9 m/s

v1 = 1.19 v2 = 1.07 m/s

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