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9 September, 07:06

The flywheel of a motor has a mass of 300.0 kg and a radius of 55 cm. If the motor can exert a torque of 2000.0 N. m on this flywheel, how much work does the motor do on the flywheel in the first 23 seconds?

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  1. 9 September, 07:16
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    Work done by torque is given as

    Word one = torque * angular displacement

    W = τ * θ

    Given that,

    τ = 2000Nm

    Mass of motor = 300kg

    Radius r = 55cm = 0.55m

    Work done by wheel in first t = 23second.

    Now we need to find the angular displacement

    We know that,

    τ = I•α

    Moment of inertia of wheel

    I = MR²

    I = 300 * 0.55²

    I = 90.75 kgm²

    Then, τ = I•α

    α = τ / I

    α = 2000/90.75

    α = 22.04rad/s²

    Then, using circular motion,

    ∆θ = wit + ½αt²

    wi = 0rad/s

    ∆θ = ½αt²

    ∆θ = ½ * 22.04 * 23²

    ∆θ = 5829.2 rad.

    Then,

    Work done?

    W = τ * θ

    W = 2000 * 5829.2

    W = 1.17 * 10 ^7 J
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