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 6.13 cm, is rolling along a conveyor belt which is moving at 2.19 m/s and starts out 8.87 m from the finish line. The second ball has a radius of 4.68 cm and is rolling along the stationary floor. If the second ball starts out 6.74 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

We need to first find the total speed of both balls. We need to convert the angular speed to linear speed by multiplying by the radius. The velocity of the first ball will be:

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

Hope that helps

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