Two different balls are rolled (without slipping) toward a common finish line. Ball 1 has an angular speed of?1=23.2 rad/s, and ball 2 has an angular speed of?2=14.8 rad/s. The first ball, which has a radius of 0.0663 m, is rolling along a conveyor belt that is moving at 1.19 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. Two balls are vertically offset and are rolling with clockwise angular speed towards a vertical finish line to the right. Ball 1 rolls with an angular speed of omega subscript 1 on a conveyor belt above ball 2. Arrows indicate that the top surface of the conveyor belt that ball 1 is on moves to the right, while the bottom surface of the conveyor belt moves to the left. Ball 2 rolls with an angular speed of omega subscript 2 on a 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 li

Question

Physics

River Cruz

27 October, 10:59

Two different balls are rolled (without slipping) toward a common finish line. Ball 1 has an angular speed of?1=23.2 rad/s, and ball 2 has an angular speed of?2=14.8 rad/s. The first ball, which has a radius of 0.0663 m, is rolling along a conveyor belt that is moving at 1.19 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. Two balls are vertically offset and are rolling with clockwise angular speed towards a vertical finish line to the right. Ball 1 rolls with an angular speed of omega subscript 1 on a conveyor belt above ball 2. Arrows indicate that the top surface of the conveyor belt that ball 1 is on moves to the right, while the bottom surface of the conveyor belt moves to the left. Ball 2 rolls with an angular speed of omega subscript 2 on a 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 li

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Answers (1)

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Malachi House · Answer 1

Ball 1 = 3.14s, ball 2 = 8.11s

Explanation:

ω₁ = 23.2rad/s

ω₂ = 14.2 rad/s

r₁ = 0.0663m

r₂ = 0.0488m

S = 8.57m

u = 1.19m/s

Assuming conveyor belt is moving towards the finish line,

W = v + u

v = ωr

ωr + u

(ω₁ * r₁) + v = (23.9 * 0.0663) + 1.19 = 2.728m/s

Angular velocity (ω) = distance moved (s) / time taken to complete 1 revolution

ω = s / t

t = s / ω

t = 8.57 / 2.728

t = 3.14s

For ball 2, the ball starts 5.54m from the finish line,

W = v + o (since there's no longer initial velocity)

ωr = v

V = 14.2 * 0.0488

V = 0.683 m/s

Velocity = distance / time

V = s / t

t = s / v

t = 5.54 / 0.683

t = 8.11s