myntgundul.. xYw chapter 10-ms-1401 × htmi?courseld 14249259&OpenVellumHMAC-7999

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myntgundul.. xYw chapter 10-ms-1401 × htmi?courseld 14249259&OpenVellumHMAC-7999b1055b12a2b41178e759; #10001 prev Ball Circling Ball Part A A ball of mass m is attached to a string of length L t is being swung in a vertical circle with enough speed the difference between the magnitude of the tension in the string at the botom relative to that Find T-T at the top of the circle so that the string remains taut throughout the balrs motion. (Figure 1) Assume that the ball travels freely in this vertical circle with negligible loss of total Express the difference in tension in terms of m and g. The quantities ri and ty should not appear in your final answer. energy. At the top and bottom of the Hints vertical circle, the ball's speeds are t and and the corresponding tensions in the string are Tt and T My Answers Give Up

Explanation / Answer

At the top:

Tt + mg = mvt^2/L

Tt = m vt^2/L - mg

At the bottom:

Tb - mg = mvb^2/L

Tb = m vb^2/L + mg

Tb - Tt = m vb^2/L + mg - m vt^2/L + mg

Tb - Tt = 2 mg + m/L (vb^2 - vt^2) (1)

from conservation of energy

1/2 m vb^2 = 1/2 m vt^2 + 2 mgL

vb^2 - vt^2 = 4 g L

putting this in (1)

Tb - Tt = 2 mg + m/L x 4 g L = 2 mg + 4 mg = 6 mg

Hence, Tb - Tt = 6 mg

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