At What Angle Will This Box Begin to Slide?

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1. Jan 23, 2016

x2017

1. The problem statement, all variables and given/known data

2. Relevant equations
ΣFx=max

3. The attempt at a solution

I drew a free body diagram for the box and set up the equation to solve for θ, but I'm not sure how to do it without μ

2. Jan 23, 2016

Suraj M

I don't think you need to substitute
$F_{friction}$ with $μ F_N$
They want you to use the frictional force they themselves have provided in the question.

3. Jan 23, 2016

x2017

Oh my goodness I can't believe I missed that...... Thank you!

ΣFx=max
mgx-Ffx=max
mgsinθ-Ffx=max
(100)(9.81)sinθ-490.5=(100)(0)
981sinθ=490.5
θ=sin-1(490.5/981)
θ=30°

Wow, that was an embarrassing mistake!

4. Jan 23, 2016

SammyS

Staff Emeritus
In a way, your mistake is one that is reasonable to make.

In an actual situation, the friction force does depend upon the normal force, which depends upon the angle the surface make with the horizontal.

Having the friction force be a fixed value, is not realistic.