A solid uniform 45.0 kg ball of diameter 32.0 cm is supported against a vertical frictionless wall using a thin 30 cm wire of negligible mass. (a) make a free body diagram for the ball and use it to find the tension in the wire and (b) how hard does the ball push against the wall?
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It looks as though the 30 cm length coverst the length of the wire from the wall to the surface of the sphere. When I worked it out I added the length of the radius to it.

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  1. Where is the wire attached to the ball? If the wall contact point is frictionless, the wire attached to the ball must, if extended, pass thtough the center of the ball; otherwise the string will apply an unbalanced torque about the center.

    The angle the string makes with the wall is given by
    sin A = R/(R + 30) = 32/62
    A = 31.1 degrees

    Now apply a moment balance about the string contact point at the wall. The string tension applies no moment there since it passes through the point. If F is the contact force at the wall,
    M g *32 = F * (30 + 32)cos 31.1

    F = 45*9.8/[0.62 cos 31.1)= 830 N

    You can get the string tension T from a hotizontal force balance.

    F = T sin 31.1

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