Understanding rigid-body equilibrium problem

[Kolika28]

Homework Statement

I don't understand the forces $F_h$ and $F_v$

Relevant Equations

$\sum F_x=0$
$\sum F_y=0$
$\sum \tau =0$

So I have this problem

The soultion to the problem gives me this drawing

But I don't understand what $F_h$ and $F_v$ is

 

[Lnewqban]

Those are the vertical and horizontal components of the reaction force that the pivot exerts over the the metal pole.

 

[Kolika28]

Ohh, that makes sense! Thank you so much!

 

[Halc]

This can be solved without trigonometry.

 

[haruspex]

This can be solved without trigonometry.

... except to find the height of the nail?

Btw, @Kolika28 , problem setters often choose 37 degrees because it is a close approximation to an angle in a 3,4,5 triangle. Knowing that will make the trig trivial.

 

[Halc]

... except to find the height of the nail?

They don't ask for the height of the nail, and don't give enough information to compute it if they did ask, but I still stand corrected.
Part (a) does not require trig but computing fV, part of the (b) answer requires a bit of trig, which as you point out, can be done in your head due to the choice of angle.

 

[haruspex]

They don't ask for the height of the nail, and don't give enough information to compute it

You’re right, there's not enough information for that, which means I misinterpreted "outward" force. I would have banged the nail in pointing up into the wall, but then the question would would make no sense, so I took it to be horizontal. Outward from the wall is then also horizontal, but then you would need to be able to find the height of the nail.
This leaves only that the nail was inserted in the same straight line as the cable. Not only is that an incompetent installation, but the question could simply have specified a maximum tension in the cable and avoided the ambiguity.

 

[Lnewqban]

Ohh, that makes sense! Thank you so much!

You are welcome