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 6.88 cm, is rolling along a conveyor belt which is moving at 1.19 m/s and starts out 8.57 m from the finish line. The second ball has a radius of 4.48 cm 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 ________ #2 ________ 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

v1=1r1+vbelt=20.2(.0613)+2.19

v1=3.42826 m/s

Now to find the time:

t1=d1/v1=8.87/3.4286

t1=2.587 seconds

The velocity of the second ball will be

v2=2r2=17.3(.0468)

v2=.80964

Now the time is:

t2=d2/v2=6.74/.80964

t2=8.325 seconds

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=6.74/2.587

v=2.605 m/s

Converting that in angular speed gives;

=v/r2=2.605/.0468

=55.67 rad/sec

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