Understanding rigid-body equilibrium problem

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SUMMARY

The discussion centers on solving a rigid-body equilibrium problem involving a metal pole and the reaction forces at a pivot. Participants clarify that ##F_h## and ##F_v## represent the horizontal and vertical components of the reaction force exerted by the pivot. The problem can be approached without trigonometry, although some parts may require basic trigonometric understanding, particularly due to the use of a 37-degree angle, which approximates a 3-4-5 triangle. The ambiguity regarding the height of the nail and the direction of the forces is also addressed, highlighting the need for clearer problem statements.

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Kolika28
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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
1591197597563.png

The soultion to the problem gives me this drawing
1591197708186.png

But I don't understand what ##F_h## and ##F_v## is
 
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Those are the vertical and horizontal components of the reaction force that the pivot exerts over the the metal pole.
 
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Ohh, that makes sense! Thank you so much!
 
This can be solved without trigonometry.
 
Halc said:
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.
 
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haruspex said:
... 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.
 
Halc said:
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.
 
Kolika28 said:
Ohh, that makes sense! Thank you so much!
You are welcome :smile:
 

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