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Problem 44 Medium Difficulty

An object with weight $ W $ is dragged along a horizontal plane by a force acting along a rope attached to the object. If the rope makes an angle $ \theta $ with a plane, then the magnitude of the force is
$$ F = \dfrac{\mu W}{\mu \sin \theta + \cos \theta} $$
where $ \mu $ is a constant called the coefficient of friction. For what value of $ \theta $ is $ F $ smallest?

Answer

$\theta=\arctan \mu$

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Video Transcript

Okay. We know that we're trying to find the maximum value of the denominator. So what we know we can do is we can take the derivative of the denominator derivative Sinus co sign derivative of coastline is negative sign and said this equal to zero solve. When we get there, that is work 10.