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 0.0738 m, is rolling along a conveyor belt which is moving at 1.94 m/s and starts out 9.17 m from the finish line. The second ball has a radius of 0.0408 m and is rolling along the stationary floor. If the second ball starts out 5.69 m from the finish line, how long does each ball take to reach the finish line? 1#___________s 2#__________s #1.) 19.7 rad/s, #2.) 17.3 rad/s

What angular speed would the losing ball have needed to cross the finish line at the same time as the winning ball? ___________rad/s

Explanation / Answer

1)

Toward, the two speeds add and become relative speed,

W = V + U = WR + 1.94 = 19.7*0.0738 + 1.94 = 3.3937 m/s.

So t = S/W = 9.17/3.3937 = 2.70 seconds to the finish line.

Away W = V - U = ? and T = S/W = ? you can do the work.

Ball two W = v + 0 = wr = 17.3*0.0448 = 0.7751 m/s

T = D/wr = 5.69/0.7751 = 7.34 seconds.

2)

Ball two needs w = D/tr = 5.69/(1.94*0.0448) = 65.47 rad/s

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