- Thread starter
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#### karush

##### Well-known member

- Jan 31, 2012

- 2,727

by a force acting along a rope attached to the object

If the rope makes an angle $\theta$ with the plane, then the magnitude of the force is

$

\displaystyle

F=\frac{\mu W}{\mu\sin{\theta}+\cos{\theta}}

$

where $\mu$ is a positive constant called the

*coefficient of friction*

and where $$0<\theta\le \pi/2$$ Show that $F$ is minimized when $\tan\theta=\mu$

this was a problem under min/max values. I was going to find F' or try to graph this

in W|F but got a 3d graph which I didn't understand.

Am sure this is a common problem in Physics but it was put in with exercises in Calculus

Anyway curious how this is solved...