Question

The coefficient of friction between the wall and the weight shown in the figure is 0.25. What force P is necessary to keep the body in place? What force P will keep the body moving up uniformly?

Answer 1

Answer on Question #64160, Physics / Mechanics | Relativity

The coefficient of friction between the wall and the weight shown in the figure is 0.25. What force P is necessary to keep the body in place? What force P will keep the body moving up uniformly?

Solution:

We will draws two free body diagrams for this problem

To keep the body in place

$\sum F_{x} = 0$

$\sum F_{y} = 0$

$N = P\cos \theta$

$P\sin \theta +f_s - mg = 0$

with $f_{s} = \mu_{s}N$

$mg = P\sin \theta +P\mu_{s}\cos \theta$

$mg = P(\sin \theta + \mu_s \cos \theta)$

$P = mg / (\sin \theta + \mu_s \cos \theta)$

$P = mg / (\sin \theta + 0.25 \cos \theta)$

The body moving up

$\sum F_{x} = 0$

$\sum F_{y} = 0$

$N = P\cos \theta$

$P\sin \theta -mg - f_s = 0$

with $f_{s} = \mu_{s}N$

$mg = P\sin \theta -P\mu_{s}\cos \theta$

$mg = P(\sin \theta - \mu_s \cos \theta)$

$P = mg / (\sin \theta - \mu_s \cos \theta)$

$P = mg / (\sin \theta - 0.25 \cos \theta)$

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