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15 February, 06:46

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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  1. 15 February, 06:50
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    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
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