M2 June 06 Q6

which is when M = 48/61.

True.



False.

The rod is resting in equilibrium, yes, but it's not limiting equilibrium. The frictional force is NOT Fmax.

If it was limiting equilibrium then yes, you'd have M = 48/61, but as it's not the the coefficient of friction could be higher.

So even though in our working out we are using the notation MR, we are still not talking about Fmax and the highest upper limit of friction?

So what's the difference between equilibrium and limiting equilibrium? :

Equilibrium is when all forces are equal and limiting is when they're all equal AND it has to be Fmax?

Thanks, this has had me confused for ages.

...

Also, should we be using the notation MR to work out M = 48/61.

Because it seems weird to go M = 48/61, then all of a sudden M $\geq$ 48/61.

So could we call the coefficient of friction M when it is only in equilibrium, as we have already stated that this value doesn't necessarily equal M

Or would we call the coefficient of friction something else, like $\alpha$, then we can rightly state $\mu \geq \alpha$.

I don't like the idea of $\mu = \frac {48}{61} \Rightarrow \mu \geq \frac{48}{61}$.

I'd use $F\le\mu R$, with equality if it's in limiting equilibrium.

I thought its F = MR in limiting, and F $\leq$ MR for resting?

Resting?

Do read my post carefully: That is what I said without using the word "resting".

By resting I meant resting equilibrium.

I thought that was the difference between limiting and resting equilibrium. That is what I gathered from your post:

"The rod is resting in equilibrium, yes, but it's not limiting equilibrium. The frictional force is NOT Fmax"

I presumed resting meant it only had to be friction, and not Fmax, because then M $\geq \frac {48}{61}$ would make sense to me.

Damn, seemed to have gone in one big circle

Resting is just a verb, you could say it was sitting in equilibrium, reclining in equilibrium, etc., which is why I didn't understand you.

The key phrse is "in equilibrium", which is how you know F<=MR. If it says "limiting equilibrium" then F=MR.

"limiting equilibrium" is still "in equlibrium"

"In equlibrium, F<=MR means F<MR OR F=MR; it could be limiting, but you're not told that, so all you know is F<=MR

If it's in equlibrium but not limiting equilibrium, then yes, the frictional force is not Fmax.

Hmm I was also under the belief that you use the inequality if it is not in limiting equilibrium, but use the equality if it is =\ .