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10 September, 12:09

A turntable A is built into a stage for use in a theatrical production. It is observed during a rehearsal that a trunk B starts to slide on the turntable 10 s after the turntable begins to rotate. Knowing that the trunk undergoes a constant tangential acceleration of 0.32 m/s2, determine the coefficient of static friction between the trunk and the turntable.

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  1. 10 September, 12:17
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    Static friction coefficient, μ = 0.41796

    Explanation:

    radius, r = 2.5 m

    constant acceleration, a = 0.32 m/s²

    time, t = 10 s

    ∴ Tangential Velocity, V = at

    ⇒ 0.32 * 10 ⇒ 3.2 m/s

    now,

    radial acceleration = V² / r

    ⇒ (3.2) ² / 2.5 ⇒ 4.096 ms⁻²

    Force required = m * radial acceleration

    μmg = m * [ (3.2) ² / 2.5]

    'm' cancels each other on both sides

    μg = (3.2) ² / 2.5

    multiply through by 'g' to make coefficient of static friction the subject

    where g = 9.8

    μ = (3.2) ² / 9.8 * 2.5

    μ = 10.24 / 24.5

    μ = 0.41796
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