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8 December, 16:17

Suppose that she pushes on the sphere tangent to its surface with a steady force of F = 60 N and that the pressured water provides a frictionless support. How long will it take her to rotate the sphere one time, starting from rest?

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  1. 8 December, 16:28
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    25.06s

    Explanation:

    Remaining part of the question.

    (A large stone sphere has a mass of 8200 kg and a radius of 90 cm and floats with nearly zero friction on a thin layer of pressurized water.)

    Solution:

    F = 60N

    r = 90cm = 0.9m

    M = 8200kg

    Moment of inertia for a sphere (I) = ⅖mr²

    I = ⅖ * m * r²

    I = ⅖ * 8200 * (0.9) ²

    I = 0.4 * 8200 * 0.81

    I = 2656.8 kgm²

    Torque (T) = Iα

    but T = Fr

    Equating both equations,

    Iα = Fr

    α = Fr / I

    α = (60 * 0.9) / 2656.8

    α = 0.020rad/s²

    The time it will take her to rotate the sphere,

    Θ = w₀t + ½αt²

    Angular displacement for one revolution is 2Π rads ...

    θ = 2π rads

    2π = 0 + ½ * 0.02 * t²

    (w₀ is equal to zero since sphere is at rest)

    2π = ½ * 0.02 * t²

    6.284 = 0.01 t²

    t² = 6.284 / 0.01

    t² = 628.4

    t = √ (628.4)

    t = 25.06s
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