A block of mass $m$, acted on by a force $F$ directed horizontally, slides up an inclined plane that makes an angle $\theta$ with the horizontal. The coefficient of sliding friction between the block and the plane is $\mu$.

Question

A block of mass $m$, acted on by a force $F$ directed horizontally, slides up an inclined plane that makes an angle $\theta$ with the horizontal. The coefficient of sliding friction between the block and the plane is $\mu$.(a) Develop an expression in terms of $m$, $\theta$, $\mu$, $F$, and $g$ for the block’s acceleration up the incline.
, (b) Develop an expression for the magnitude of the force $F$ that will allow the block to slide up the plane with a constant velocity. What relation must $\theta$ and $\mu$ satisfy in order for the solution to be physically meaningful?
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Rita · Accepted Answer

a) $ a = \frac{F (\cos \theta &#8211; \mu \sin \theta) &#8211; mg (\mu \cos \theta + \sin \theta)}{m} $
b) $ F = \frac{\mu m g \cos \theta + \mu F \sin \theta + m g \sin \theta}{\cos \theta} $

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