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## Homework Statement

A block of mass m slides down a plane inclined at an angle theta with initial velocity v down the slope and with friction coefficient mu. Find T, the time in which the block comes to a rest due to friction. Use coordinates with y vertical and x horizontal.

## Homework Equations

F=ma

f=(mu)n

## The Attempt at a Solution

[tex] \vec{v} = v \cos\theta \hat{x} - v \sin\theta \hat{y} [/tex]

[tex] \\vec{\\F}_{w} = - m g \hat{y} \\ [/tex]

[tex] \vec{f} = - \mu mg \cos^{2}\theta \hat{x} + \mu m g \cos(\theta)\sin(\theta)\hat{y } \\ [/tex]

[tex] \ddot{x} = - \mu g \cos^{2}(\theta) \\ [/tex]

[tex] \dot{x} = - \mu g \cos^{2}(\theta) t + v\cos(\theta) \\ [/tex]

[tex] \ddot{y} = \mu g \cos(\theta)\sin(\theta) - g \\ [/tex]

[tex] \dot{y} = ( \mu g \cos(\theta)\sin(\theta) - g ) t - v \sin\theta \\ [/tex]

Now I should be able to set either y dot or x dot equal to zero and get T, right?

The answer I'm getting doesn't agree with the answer I got with the x-axis down the plane and the y-axis perpendicular to the plane. The answer I get in this way is

[tex] T = \frac {v_{0}}{g (\mu \cos \theta - \sin \theta)}[/tex]

I hope this works; I've never used latex before.

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