Calculating angle with coefficient of static friction value!

Fireant

There's a box sitting on a plank. The coefficient of static friction is 0.33. I want to figure out at which angle the box will begin to slide if the plank is tilted.


I know the factors that come into play are FN, Fg or Fgx, and Fs.



So far I have

Fnet= FN-Fs-Fg
=FN- μs-sin∅
=cos-0.33-sin∅

This doesn't look right... can anyone help me out?

tiny-tim

Hi Fireant!
I don't understand that at all.

First, use components in the normal direction to find N.

Then you know the friction is 0.33*N, and you can use components in the slope direction to find θ.

Show us what you get.

Fireant

Hi thank you for responding!

The mass of the box is 10kg. So the normal force here would have to be mg...?

normal force=98N

Ff=μs(FN)
=0.33(98)
=32.34 N


and then
tanθ= 97.5/98
θ=44°

I got 97.5 (for the x component) from pythagorean theory...

I'm pretty lost!

tiny-tim

Hi Fireant!
No, the weight, W, is mg (98 N).

The normal force, N, is the normal component of the reaction force.

You find N by taking components in the normal direction (of N and W), and equating the sum to zero …

what do you get?

Fireant

I think i'm getting confused when you say 'the components in the normal direction'... do you mean on the y axis? Isn't that just FN? Which would be -98N ?

tiny-tim

Some people call that the y axis, some people call the vertical the y axis

That's why I say "the normal direction", so there's no confusion.
What is the normal component of W ?

Fireant

Sorry I'm at work, that's why it's taking so long to reply.

the normal component of W would be mgcostheta?

tiny-tim

Yes, so N = mgcosθ.

ok, now find the friction force, and then write the equation for components along the plank.

Fireant

so Ff=μsFN
=0.33(mgcosθ)
=0.33(98)(cosθ)
=32.34cosθ

tiny-tim

ok

now the equation along the plank

Fireant

would be...

Fnet=Fn-Ff-Fg
0=32.34cosθ-98

?

Fireant

but i'm missing

sintheta

right?

tiny-tim

yes.

Fireant

0=32.34costheta-sintheta-98

Fireant

im not sure how i would isolate theta...

tiny-tim

put = in the middle and divide

Fireant

lol i'm hopeless...! thank you so much for bearing with me

ok gonna try this out...

32.34costheta=sintheta-98

sintheta=32.34costheta+98
sintheta/32.34=costheta+98

Sorry, what am i dividing by and how?