Topic: Dynamics
Concepts: Inclined plane, Newton’s laws

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Solution:

Since the block slides down at constant speed with gravity and friction alone, we have

Because $N=W\cos\theta$ and $f=\mu N$,

Thus,

When a horizontal force $P$ is applied to the box, it moves up the ramp at constant speed so the net force on the box is still zero. Balancing forces,

From the free-body diagram, note that $\tan\varphi=W/P$ so

It remains to find $\varphi$ using the other angles. We have

We are given $\theta=30^{\circ}$ and we have

which means $\phi=\theta=30^{\circ}$ also. Thus,

so the answer is D.