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**Strangely Confusing mechanics problem!!!**

## Homework Statement

2 masses connected by a massless string which passes through a hole in a horizontal table. One mass, [tex]m_{1}[/tex], is sitting on top of the horizontal table, the other, [tex]m_{2}[/tex], hanging below the table. There IS friction between mass [tex]m_{1}[/tex] and the tabletop, coefficient of friction=[tex]\mu[/tex]. Mass [tex]m_{1}[/tex] has initial velocity [tex]v_{0}[/tex] directed perpendicular to the string.

Find the initial radius of the circular motion, the initial rate of energy dissipation, the speed after time T, and the radius after time T

## Homework Equations

Newton's Laws, centripetal acceleration, kinetic energy, etc

## The Attempt at a Solution

So, as the top mass moves it loses energy to friction and so it's velocity and radius should decrease, the tension in the rope declines as well so the lower mass descends.

The initial radius is found from a free body diagram and Newton's 2nd law. At first (at t=0) the tension balances the weight of M2 and since the tension is what provides the centripetal force I have:

[tex]T=\frac{m_{1}v_{0}^{2}}{r_{0}}=m_{2}g \Rightarrow r_{0}=\frac{m_{1}v_{0}^{2}}{m_{2}g}[/tex]

For the initial energy dissipation,

[tex]P=f\bullet v=\mu m_{1}g v_{0}[/tex]

However, for the speed and radius t seconds later I can't just multiply the power found above by the time, t, because the velocity (and hence the dissipation rate) has changed, right?. I don't know how far the mass has moved so I can't calculate the work done against friction either.

Can anyone suggest a tip?

Thanks.