Friction

[NA19]

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A person applies a horizontal force F on a block of mass m resting against a vertical wall. If the block slides vertically down the wall at a constant speed, what must be true about the coefficient of kinetic friction between the block and the wall?

The answer to this is coefficient of kinetic friction = mg/F.

But I don't understand why...

 

[FeinMS]

.............l
F----> &#12609;l<----N and mg down friction up
.............l
It's not moving side ways so F=N. Friction=N*(mu_k) and Friction=mg because it's moving at a constant velocity (a=0, f=0).

N(mu_k)=F(mu_k)=mg ->> Mu_k=mg/F

 

[NA19]

How is N pointing downwards? I don't get why F = N.

 

[FeinMS]

N is not pointing downward, it's pointing to the left (opposite to F). Mg points downward and friction points up. F=N because the box is not moving to the right or left (it's in equilibrium horizontally. Fnet=F-N=0)