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## Homework Statement

Crate of mass

*m*is pushed horizontally with force

*F*up an inclined plane of θ from ground. The plane has a friction coefficient of μ.

a) draw free body diagram of crate

b) derive expression for normal force

c) derive expression for acceleration

*** Use ONLY

*m, g, F, μ, θ *****

## Homework Equations

ΣF = ma

|a| = √(a

_{x}

^{2}+a

_{y}

^{2})

## The Attempt at a Solution

Included is a picture of the problem with my free body diagram.

I set the normal as the y axis so that when solving ΣFy=ma

_{y}I can set a

_{y}=0.

ΣF

_{x}=ma

_{x}=-μN+Fcosθ-mgsinθ

ΣF

_{y}=ma

_{y}=N-Fsinθ-mgcosθ

a

_{y}=0 so N = Fsinθ+mgcosθ (part b)

Since a

_{y}=0, a=√a

_{x}

^{2}= a

_{x}. Substituting N into a

_{x}:

ma

_{x}=-μ(Fsinθ+mgcosθ)+Fcosθ-mgsinθ

is this correct?