Sapling Learning Map Two different balls are rolled (without slipping) toward a

Question

Sapling Learning Map Two different balls are rolled (without slipping) toward a common finish line. Their angular speeds are 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 8.57 m from the finish line. The second ball has a radius of 0.0488 m and is rolling along the stationary floor. If the second ball starts out 5.84 m from the finish line, how long does each ball take to reach the finish line? to the right. The first 24.2 rad/s #1 15.8 rad/s Number #2 What anqular speed would the losing ball have needed to cross the finish line at the same time as the winning ball? rad/s O Previous Check Answer @Nex Exil Hint

Explanation / Answer

1)

relative velocity of 1st ball woth respect to ground, v1 = w1*r1 + v

= 24.2*0.0738 + 1.94

= 3.726 m/s

time taken, t1 = d1/v1

= 8.57/3.726

= 2.30 s <<<<<<<<<----------------Answer

2)

relative velocity of 2nd ball with respect to ground, v2 = w2*r2

= 15.8*0.0488

= 0.771 m/s

time taken, t2 = d2/v2

= 5.84/0.771

= 7.57 s <<<<<<<<<----------------Answer

c)
so, t2 = t1

t2 = 2.30 s

v2 = d2/t2

= 5.84/2.3

= 2.539 m/s

v2 = r2*w2

==> w2 = v2/r2

= 2.539/0.0488

= 52.0 rad/s <<<<<<<<<----------------Answer

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