(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A woman attempts to push a box of books that has mass 36.5 kg up a ramp inclined at an angle 27.5 degrees above the horizontal. The coefficients of friction between the ramp and the box are mu_s and mu_k. The force F applied by the woman is horizontal.

Assume that mu_s is 0.860 and that mu_k is 0.320. What magnitude of force must the woman apply to keep the box moving up the ramp at constant speed?

2. Relevant equations

acceleration = 0

w = 36.5(9.8) = 357.7

μ_{s}= f_{s}/n

μ_{k}= f_{k}/n

n - 357.7cos(27.5) - Fsin(27.5) = 0

n=Fsin(27.5)+357.7cos(27.5)

Fcos(27.5) - 357.7sin(27.5) - fs = 0

(fs = μs*n)

3. The attempt at a solution

I know μ_{s}= [Fcos(27.5) - 357.7sin(27.5)] / [357.7cos(27.5) + Fsin(27.5)]

I tried solving for F and i got 219.8 but that is wrong and i think it may have to do with something about not factoring in the μ_{k}.

Any suggestions?

Thank you

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# Homework Help: Pushing books - force, kinetic and static friction

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