Static friction of a block on an incline?

[Tim Wellens]

Homework Statement

We are dealing with a block on an incline that you can alter the angle with.

The inclination angle was increased until we reached a certain angle(critical angle) that the block just begins to slide at. Use this critical angle and your previous answers for the normal force and frictional force at rest to write an equation for the coefficient of static friction. Equation should be in terms of the angle when the block begins to slide and if needed other measurable quantities.

Homework Equations

F=ma[/B]

The Attempt at a Solution

I figured out for the normal force of this block at an inclination at rest, the equation would be n=mgcos(θ)I think that the magnitude of the frictional force of this block at an inclination at rest (in terms of m, g, and theta), would be Fs=tan(θ)(mgcos(θ). I got this from the equation Fs=μ*n. We had already found what n would be, so I inputted that. The question wants it in terms of theta, so I think the coefficient of static friction would have to be tan(θ). So, I believe the magnitude of the friction force would be Fs=tan(θ)(mgcos(θ)). But I'm not positive.So, writing an equation for the coefficient of static friction for the point of inclination when the block just begins to slide, using this angle... I think the equation would be... μ=F/N > μ= tanθ(mgcosθ)/mgcosθ. If the mgcosθ cancel.. we would be left with μ= tanθ. But I'm just not sure if this is correct with what the question is looking for and if my previous equations make sense?

 

[BvU]

Hi Tim, I think you did just fine. Your explanation is taking a few shortcuts (where the $\tan\theta$ comes from isn't made explicit) but you get the benefit of the doubt from me. Up to you to guess if teacher will be equally benevolent ...

Note that $F_{s,{\rm max}} = \mu N$. If there is no sliding then $F_{s} \le \mu N$.