Understanding rigid-body equilibrium problem

In summary, the problem is that the person doesn't understand what the mathematical symbols mean, but they can solve the problem without using trigonometry.
  • #1
Kolika28
146
28
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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  • #2
Those are the vertical and horizontal components of the reaction force that the pivot exerts over the the metal pole.
 
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  • #3
Ohh, that makes sense! Thank you so much!
 
  • #4
This can be solved without trigonometry.
 
  • #5
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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  • #6
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.
 
  • #7
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.
 
  • #8
Kolika28 said:
Ohh, that makes sense! Thank you so much!
You are welcome :smile:
 

Related to Understanding rigid-body equilibrium problem

1. What is a rigid-body equilibrium problem?

A rigid-body equilibrium problem refers to a situation where a rigid body is at rest or in a state of constant motion with no net forces acting on it. This means that the body is not accelerating and all forces acting on it are balanced.

2. How do you determine if a rigid body is in equilibrium?

To determine if a rigid body is in equilibrium, the net force and net torque acting on the body must be equal to zero. This can be calculated by summing up all the forces and torques acting on the body and setting them equal to zero.

3. What are the conditions for a rigid body to be in equilibrium?

The conditions for a rigid body to be in equilibrium are that the net force and net torque acting on the body must be equal to zero. Additionally, the body must not be experiencing any linear or rotational acceleration.

4. How can you solve a rigid-body equilibrium problem?

To solve a rigid-body equilibrium problem, you must first identify all the forces and torques acting on the body. Then, apply the conditions for equilibrium to set up equations and solve for any unknown forces or angles.

5. What are some common examples of rigid-body equilibrium problems?

Some common examples of rigid-body equilibrium problems include a book resting on a table, a ladder leaning against a wall, and a bridge supporting the weight of cars. These situations require the forces and torques acting on the bodies to be balanced in order for them to remain in equilibrium.

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