- #1

FScheuer

## Homework Statement

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A block of mass m rests on an inclined plane with angle o accelerating to the right with acceleration a. The coefficient of static friction is u.

## Homework Equations

For what range of a does the block remain at rest on the plane.

## The Attempt at a Solution

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I started by drawing a free body diagram with a gravitational force, normal force, and frictional force. The horizontal component of my frictional force is in the direction of the acceleration. I believe solving for this should give me the lowest value of a where the block remains at rest. I set all of the horizontal comments equal to ma (Fncos(o) + uFncos(o) = ma), and all of the vertical components to 0 (Fnsin(o) - mg - uFnsin(o) = 0). I then set each of those equations equal to Fn, the normal force, and then set them equal to each other (ma/(cos(o)(1 + u)) = mg/(sin(o)(1 - u)). For the lowest value of a, I got a = gcot(o).

Is what I’ve done so far correct?

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