How are these derived for an inclined plane?

[catzmeow]

I'm utterly lost on this and would appreciate any help!

I'm given mechanical advantage= 1/(sin(theta)+mu_k*cos(theta))

And efficiency = 1/(1+mu_k*cot(theta))

These are for an inclined plane and theta is not specified, I'm just supposed to show how those equations were derived.
Thanks!

 

[barryj]

You might start by drawing an incline plane at an angle of theta with a mass on it, call it m as it doesn't matter in the end. Then draw the forces required to push the mass up the ramp. Compare this with the force required to raise the mass straight up. This should be the mechanical advantage.

 

[catzmeow]

Thanks barryj! I did that and now I have MA= (Mgsin(theta))/(input force-mgcos(theta)...

Is this close(er)?

 

[catzmeow]

Oops I meant all that I have equal to mu_k

 

[barryj]

Well, I think the MA = force required to lift the mass with no incline divided by the force required to push the mass up the incline. So, the force required to lift the mass with no incline would be mg, now you figure out the force required to push the mass up the incline and do the division.

 

[catzmeow]

Oh ok- that makes since. Thanks Barryj!