1. A billiard ball of mass m = 0.25 kg strikes the cushion of a billiard table a
ID: 1350785 • Letter: 1
Question
1.
A billiard ball of mass m = 0.25 kg strikes the cushion of a billiard table at ?1 = 42° and a speed v1 = 26 m/s. It bounces off at an angle of ?2 = 710 and a velocity of v2 = 11 m/s. What is the magnitude of its change in momentum (in kg·m/s)?
2. In a game of billiards, the cue ball is traveling eastward when it strikes a second ball that is initially at rest. After the collision, the cue ball moves at 4.01 m/s, 25.0° south of east, and the second ball's speed is 3.51 m/s. At what angle (north of east) does the second ball travel? Assume each ball has a mass of 162 g.
What was the speed of the cue ball prior to the collision?
Explanation / Answer
1.
Initial momentum, pi = mvi = 0.25 [26 (sin42o i + cos42o j)] = 4.35 i + 4.83 j
Final momentum, pf = mvf = 0.25 [11 (sin71o i - cos71o j)] = 2.6 i - 0.895 j
Change in momentum = pf - pi = -1.75 i - 5.725 j
Magnitude of change in momentum, |pf - pi| = [(-1.75)2 + (-5.725)2]1/2 = 5.986 kg-m/s
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