- #1

Karol

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## Homework Statement

A stone tied to a rope rotates in a vertical circle. prove that the tension in the rope at the lowest point is 6 times the stone's weight bigger than at the highest point.

## Homework Equations

Potential energy: [itex]E_P=mgh[/itex]

Kinetic energy: [itex]E_K=\frac{1}{2}mV^2[/itex]

Radial force: [itex]F_R=m\frac{V^2}{R}[/itex]

## The Attempt at a Solution

V

_{0}is the velocity at the top and V

_{2}is at the bottom and R is the radius.

[tex]\frac{1}{2}mV_0^2=\frac{1}{2}mV_2^2-2Rmg \rightarrow V_2^2=V_0^2+4gR[/tex]

The ratio of radial forces at the bottom and at the top:

[tex]\frac{F_B}{F_T}=\frac{\frac{V_B^2}{R}}{\frac{V_T^2}{R}}=\frac{V_B^2}{V_T^2}=\frac{V_0^2+4gR}{V_0^2}=1+\frac{4gR}{V_0^2}[/tex]

First it includes V

_{0}and R, it's not fixed, and secondly it doesn't even come close to the form.

Of course i have to deduce, at the upper point, the weight of the stone from the radial force and add it at the lowest point, but my solution doesn't even come close.

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