At What Angle Will This Box Begin to Slide?

[x2017]

Homework Statement

Homework Equations

ΣF_x=ma_x

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

 

[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.

 

[x2017]

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.

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

ΣF_x=ma_x
mg_x-F_fx=ma_x
mgsinθ-F_fx=ma_x
(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!

 

[SammyS]

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

ΣF_x=ma_x
mg_x-F_fx=ma_x
mgsinθ-F_fx=ma_x
(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!

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.