Calculating Coefficient of Static Friction for Crate on Inclined Plane

[craig.16]

Homework Statement

A crate resting on a rough plane is found to be on the verge of sliding when the plane is inclined at an angle of 40 degrees to the horizontal. Calculate the coefficient of static friction between the crate and plane. [

Homework Equations

f(s)<_(Mu(s))N
<_ is meant to resemble less than or equal to.

The Attempt at a Solution

All I know is the equaton i presented above, other than that I don't have a clue where to start on this one as it only provides an angle whereas the equation needs more values. If there are any other equations for static friction that this equation needs please could you post it so I can learn that and then attempt the question using the new equation.

 

[Beaker87]

The gravitational force acting on the crate is equal to mg (you don't know m, so just leave it as mg)


Try to break this force into a component parallel to the plane, and a component perpendicular to the plane.


The normal force will counteract the perpendicular component, and the frictional force will counteract the parallel component.


If you solve the problem correctly, the mass terms will cancel each other out, leaving you with a value for μ.

 

[PhanthomJay]

Craig, when the object is on the verge of sliding, then f(s) = (Mu(s))N. Draw a free body diagram of the block...identify the forces acting...choose the x-axis parallel to the plane, and the y-axis perpendicular to the plane...and apply Newton's first law in both directions, since the block is not moving in either direction. You'll need a little trig and geometry and vector component knowledge, to find the coefficient. Are you familiar with these concepts?

Edit: Per Beaker87's response...

 

[craig.16]

using mu=F/N I got a value of 0.84. Is this correct? Also the mg's did cancel out thankfully and I calculated this because my last step was mu=tan40=0.84 (2dp). I think this might be the right answer as its within the region of static friction values given in my book.

 

[PhanthomJay]

Yes, looks good!

 

[craig.16]

Good to know. Thanks for the help PhantomJay and Beaker87. Its surprising how much can be forgotten on a subject over a couple of weeks if you don't keep on top of it, even if its the little questions like this. I think it was the ridiculous 10 marks for this question that made me think it was more complicated than it actually was though.