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 0.0738 m, is rolling along a conveyor belt which is moving at 1.69 m/s and starts out 8.87 m from the finish line. The second ball has a radius of 0.0428 m 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?

B) What angular speed would the losing ball have needed to cross the finish line at the same time as the winning ball?

Explanation / Answer

1) for first conveyer, it is having angular velocity w =23.7 rad/s

we know that w=v/r

where v=linear velocity and r = radius

given r=0.0738 m

so here v= rw = 0.0738*23.7= 1.75 m/s

but given that the conveyer is moving at a speed of 1.69 m/s

so the total velocity with which the ball is moving is 1.75+ 1.69 =3.41 m/s

and time taken to cover the distance 8.87 m

t=s/v= 8.87/3.41= 2.6sec
------------------------------------------------

2) for second ball v=rw

v = 0.0428 * 13.3 = 0.57

v=0.57m/s

time taken is t=s/v

s= 6.74 m

so t= 6.74/0.57= 11.82 sec

inorder to cover the distnce of 6.74 m in time taken by first ball the speed shoul be high

so v=s/t here t= 2.6 s

v = 6.74/2.6 = 2.6 m/s

so w= 2.6/0.0428= 60.7 rad/s------<<<<<<Answer

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