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23 May, 05:20

Suppose that she pushes on the sphere tangent to its surface with a steady force of F = 75 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. 23 May, 08:51
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    The time taken to rotate the sphere one time is, t = 22 s

    Explanation:

    Given data,

    The mass of the sphere, m = 8200 kg

    The radius of the sphere, r = 90 cm

    =.9 m

    The force applied by the girl, F = 75 N

    The moment of inertia of the sphere is,

    I = 2/5 mr²

    = (2/5) 8200 x (.9) ²

    = 2657 kg·m²

    The torque,

    τ = I α

    75 x 0.9 = 2657 x α

    α = 0.0254 rad/s²

    The angular displacement,

    θ = ½αt²

    2π = ½ x 0.0254 rad/s² x t²

    t = 22 s

    Hence, the time taken to rotate the sphere one time is, t = 22 s
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