Uniform Circular Motion Problem. Help

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SUMMARY

The problem involves a stone tied to a string of length 1.10 m, which is whirled in both horizontal and vertical circles at a constant speed. The maximum tension in the string during vertical motion is 15.0% greater than the tension during horizontal motion. Using the equations of motion, specifically Fc = mv²/r for horizontal motion and Fc = Ft - mg for vertical motion, one can derive the relationship between speed, string length, and tension to determine the speed of the stone.

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Homework Statement


A stone tied to a string with length 1.10 m is whirled in a circle both horizontally and vertically with the same constant speed. In the vertical case the maximum tension in the string is 15.0% larger than the tension that exists when the string was horizontal. Determine the speed of the stone.

Homework Equations


a = v2/r

The Attempt at a Solution


for horizontal, my equation was Fc = mv2/r

for vertical, my equation was Fc = Ft - mg, because at the bottom of the vertical circle fg is present
mv2/r = 0.15Ft - mg

I don't know how to take this further
 
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Consider the horizontal case in more detail. There are vertical forces too. You should be able to find a relationship between the speed, the string length, and the tension.
 

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