O /24/2014 11:00 PM A 78.5/100 /23/2014 07:55 PM Gradebook Print Calculator Peri

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O /24/2014 11:00 PM A 78.5/100 /23/2014 07:55 PM Gradebook Print Calculator Periodic Table Question 15 of 15 Map A sapling learning o different balls are rolled (without slipping) toward a common nish line. The 23.2 rad s ball, which has a radius of 6.13 cm, is rolling along a conveyor belt which is moving at 1.69 m/s and starts out 9.17 m from the finish line. The second ball has a radius of 4.28 cm and is rolling along the stationary floor. If the second ball starts out 6.14 m from the finish line, how long does each ball take to reach the finish line Number #1 17.8 rad s Number What angular speed would the losing ball have needed to cross the finish line at the same time as the winning ball? Number LU rad s Previous Give Up & View Solution Check An Next Exit Hint

Explanation / Answer

We need to convert the angular speed to linear speed by multiplying by the radius.

The velocity of the first ball will be

v1 = w1 r1 + vbelt = 23.2 (0.0613) + 1.69

v1 = 3.11 m/s

t1 = d1 / v1 = 9.17 / 3.11

t1 = 2.95 s

The velocity of the second ball will be

v2 = w2 r2 = 17.8 (0.0428)

v2 = 0.762 m/s

Now the time is t2 = d2 / v2 = 6.14 / 0.762

t2 = 8.058 s

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In order for the second ball to find in the same time as the first ball it would have to travel at:

v = d2 / t1 = 6.14 / 2.95

v = 2.08 m/s

Converting that in angular speed gives

w = v / r2 = 2.08 /0.0428

w = 48.63 rad/sec

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