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

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 Tt and Tb. Tt and 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. Need to express the difference in tension in terms of m and g.

Explanation / Answer

given the mass of the ball is m the tension in the string at the top is Tt =(mvt2 / L ) - mg   as thecentripetal and gravitational are in the oppsite direction the tension in the string at the bottom is Tb =( mvb2 /L) + mg as the centripetal andgravitational are in the same direction    the difference is    Tb - Tt = 2mg+( mvt2 / L )+( mvb2/L)

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