A ball of mass m is attached to a string of length L . It is being swung in a ve

Question

A ball of mass m is attached to a string of length L. It is being swung in a vertical circle with enough speed so that the string remains taut throughout the ball's motion. Assume that the ball travels freely in this vertical circle with negligible loss of total mechanical energy. At the top and bottom of the vertical circle, the ball's speeds are vt and vb, and the corresponding tensions in the string are vector Tt and vector Tb. Vector Tt and Vector Tb have magnitudes Tt and Tb .Find Tb-Tt, the difference between the magnitude of the tension in the string at the bottom relative to that at the top of the circle.

Explanation / Answer

T_b = mg+mvb^2/R T_t = mvt^2/R-mg T_b-T_t = 2m/R(vb^2+vt^2)

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