How do you get 33.79?? A certain string can withstand a maximum tension of 9.0 l

Question

How do you get 33.79??

A certain string can withstand a maximum tension of 9.0 lb without breaking. A child ties a 0.68 lb stone to one end and, holding the other end, whirls the stone in a vertical circle of radius 2.9 ft, slowly increasing the speed until the string breaks.

A certain string can withstand a maximum tension of 9.0 lb without breaking. A child ties a 0.68 lb stone to one end and, holding the other end, whirls the stone in a vertical circle of radius 2.9 ft, slowly increasing the speed until the string breaks. Where is the stone on its path when the string breaks? What is the speed of the stone as the string breaks?

Explanation / Answer

T - mg cos theta = mv^2/r

T = mg cos theta + mv^2/r

for max tension theta = 0

T = mg + mv^2/r

mv^2/r = T-mg

v^2 = (T-mg)*r/m

V = sqrt {(T-mg)r/m}

V = 33.79 ft/s

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