An object is swinging from a point that is horizontal compared to the lowest point the object will reach (where the rope is vertical). If the length of the rope is 2 meters and the mass of the object is 30 kg, what is the tension in the rope at the bottom of the swing?
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  1. Drop in potential energy from horizontal to vertical orientation is
    2 meters *m* g

    This must equal 1/2 m v^2, because velocity is zero when the rope is horizontal. This means that:

    v^2 = 4 meters*g --->

    v^2/(2meters) = 2 g is the centripetal acceleration.

    Newton's second law:

    F = m a

    applied to the object gives:

    -mg + T = 2mg

    where T is the tension and we take the positive direction to be upward.

    The tension is thus T = 3 m g.

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  2. Is it vertical vs. Horizontal energy to get the Acceleration?

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  3. NVM you are relating GPE for Horizontal to KE of Horizontal.

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