Two different balls are rolled (without slipping) toward a common finish line. T

Question

Two different balls are rolled (without slipping) toward a common finish line. Their angular speeds are shown to the right. The first ball, which has a radius of 0.0563 m, is rolling along a conveyor belt which is moving at 1.19 m/s and starts out 9.32 m from the finish line. The second ball has a radius of 0.0508 m and is rolling along the stationary floor. If the second ball starts out 5.99 m from the finish line, how long does each ball take to reach the finish line?

Two different balls are rolled (without slipping) toward a common finish line. Their angular speeds are shown to the right. The first ball, which has a radius of 0.0563 m, is rolling along a conveyor belt which is moving at 1.19 m/s and starts out 9.32 m from the finish line. The second ball has a radius of 0.0508 m and is rolling along the stationary floor. If the second ball starts out 5.99 m from the finish line, how long does each ball take to reach the finish line? What angular speed would the losing ball have needed to cross the finish at the same time as the winning ball?

Explanation / Answer

so for ball 1:

vtoal = v belt + v ball = 1.19 + 19.2*0.0563

t = d/vtotal = 9.32/(1.19 + 19.2*0.0563) = 4.10 s

for ball 2;

t = 5.99/(13.3*0.0508)= 8.87 s

2)

for ball 2 to win we want t = 4.1 s

so 4.1 = 5.99/(w*0.0508)

w=28.8 rad/s

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