A billiard cue ball having velocity of 5.0 cm/s and a mass 0.17 kg approaches a stationary red billiard ball of
mass 0.16 kg. If the cue ball is stationary after their collision, what is the new velocity for the red ball?
To find the new velocity of the red ball after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
Momentum is calculated by multiplying an object's mass by its velocity. Let's denote the velocity of the red ball after the collision as V1 (final velocity of the red ball) and the mass of the red ball as M1 (mass of the red ball).
The total momentum before the collision (initial momentum) is given by the sum of the momenta of the two balls:
P_initial = (mass of the cue ball) * (velocity of the cue ball) + (mass of the red ball) * (velocity of the red ball)
P_initial = (0.17 kg) * (0 cm/s) + (0.16 kg) * (V1)
Since the cue ball comes to a stop after the collision, its velocity is 0 cm/s. Therefore, the equation becomes:
P_initial = (0.16 kg) * (V1)
Now, let's consider the total momentum after the collision. Since the cue ball is stationary (0 cm/s) and the red ball is moving with velocity V1, the total momentum after the collision is only due to the red ball:
P_final = (mass of the red ball) * (velocity of the red ball)
P_final = (0.16 kg) * (V1)
According to the conservation of momentum principle, P_initial (before collision) should be equal to P_final (after collision), so we can set up the equation:
P_initial = P_final
(0.16 kg) * (V1) = (0.16 kg) * (V1)
Now, we can solve for V1, the velocity of the red ball after the collision:
V1 = V1
Therefore, the new velocity for the red ball after the collision is the same as its initial velocity, which is V1. In this case, V1 remains constant and equal to the velocity of the cue ball, which is 5.0 cm/s.