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 0.0663 m, is rolling along a conveyor belt which is moving at 1.44 m/s and starts out 8.57 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 6.59 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 line at the same time as the winning ball?

Explanation / Answer

SOLUTION =

first ball, radius R =0.0663 m

moving at 1.44 m/s

starts out 8.57 m

second ball R = 0.0408 m

second ball starts out 6.59 m

angular speed first =21.7  rad/s

angular speed secoond = 13.8  rad/s

the conveyor belt is moving: towards or away from the finish line?

Toward, the two speeds add and become relative speed W = V + U = WR + 1.44 = 21.7 *.0663 + 1.44=2.8787m/s.

So t = S/W = 8.57/2.87 = 2.986062 seconds to the finish line.

Away W = V - U = ? and T = S/W = ?

Ball two W = v + 0 = wr = 13.8*.0408 = ? m/s and T = D/wr = 6.59/(13.8*.0408) = 11.70431941 seconds.

This one will come in a poor second if they both start at the same time and given distances. ANS.

Ball two needs w = D/tr = 6.59/(2.98*.0408) = 54.2012 rad/s...boogaloo out. ANS.

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