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## Homework Statement

A

__18.6-kg__box rests on a frictionless ramp with a

__13.7°__slope. The mover pulls on a rope attached to the box to pull it up the incline. If the rope makes an angle of

__38.8°__with the horizontal, what is the smallest force F the mover will have to exert to move the box up the ramp?

____ N

http://img93.imageshack.us/img93/7287/4figure44alt.gif [Broken]

## Homework Equations

## The Attempt at a Solution

[tex]\sum\vec{F}=ma[/tex]

[tex]\sum\vec{F}=0[/tex]

[tex]\sum\ F_{x}=0 => F_{x}-W_{x}=0[/tex]

[tex]\sum\ F_{y}=0[/tex]

I made a graph from the ramp model and found:

a=0

m=18.6 kg

θ=13.7°

σ=38.8°

B=25.1°

F=?

w=mg

[tex]F_{x}=F\cos{B}[/tex]

[tex]W_{x}=W\sin\theta[/tex]

[tex]F_{y}=F[/tex][tex]\sin[/tex][tex]B[/tex]

[tex]W_{y}=W\cos\theta[/tex]

I thought 18.6(9.81)sinθ would give me the answer but that wasn't correct.

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