- #1

jumbogala

- 423

- 4

## Homework Statement

A brick is projected up an inclined plane with an initial speed v

_{0}.

If the inclination of the plane is 30 degrees and the coefficient of sliding friction μ = 0.1, find the total time for the block to return to its original position.

## Homework Equations

## The Attempt at a Solution

Consider the x-axis to be along the inclined plane. Then there are two forces acting along the x axis: the x component of gravity, and the friction.

X component of gravity: mgsin(30)

fricition: mgcos(30)μ, since mgcos(30) is the normal force on the brick

Then ma = -mgsin(30) - mgcos(30)μ or a = -gsin(30) - gcos(30)μ

a = dv/dt, so:

dv = (-gsin(30) - gcos(30)μ) dt

Integrating both sides gives

v = -gsin(30)t - gcos(30)μt + C, where C is a constant of integration

The initial conditions are at t = 0, v = v

_{0}so C = V

_{0}

Then v = -4.905t - 0.85t + V

_{0}= -5.755t + V

_{0}

Going up the incline, I set v = 0 and find that t = V

_{0}/ 5.755

**I'm not sure if I can just double the above, because on the way up the incline gravity and friction are in the same direction. On the way down, they are in opposite directions.**

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