# Static equilibrium -- A picture hanging on a wall

• siapola1
In summary, static equilibrium refers to the state of balance achieved when an object is at rest and all forces acting on it are equal and opposite. This concept is often used in physics and engineering to analyze the stability and strength of structures. When hanging a picture on a wall, achieving static equilibrium is important to ensure that the picture stays in place and does not fall. This can be achieved by evenly distributing the weight of the picture on the wall and ensuring that the force of gravity is balanced by the tension in the hanging wire. By understanding the principles of static equilibrium, one can ensure the safe and stable placement of objects in various situations.
siapola1

## Homework Statement

https://imgur.com/v13K6sE
a uniform rod of mass m is placed as shown, with one of its end resting on a smooth wall while 1/4 of the rod's length is sticking out of a rough table. Find the net force the table exert on the rod at the corner.

## Homework Equations

i drew the free body diagram and labeled all the forces. i get stuck when i tried to set up the torque equation
because i don't know what is the force that is responsible for rotating the rod.
i have the picture here:
https://imgur.com/ybSWfcT

3. The Attempt at a Solution
its in the picture

Last edited by a moderator:
There are two things wrong with your torque equation.
1. There is a force missing.
2. Your expressions for the torques for the parts of the rod are wrong. For each part, what is its weight and what is its torque arm?
(Though you don’t really need to treat the rod as two parts. Just find the torque arm for the rod as a whole.)

he didnt give us the weight and is the missing force the normal force at the contact point between the table and the rod?
<a href="https://imgur.com/U6SG6En"><img src="https://i.imgur.com/U6SG6En.jpg" title="source: imgur.com" /></a>

siapola1 said:
he didnt give us the weight
You are told it is a uniform rod of mass m, so you can find the weight(s).
siapola1 said:
the missing force the normal force at the contact point between the table and the rod?
Yes.
Edit: I mean no... it is a normal force but not that one.

Last edited:
what is tikd?

siapola1 said:
what is tikd?
It is a result of fat fingers. Please see edited version.

i still can't figure it out

i check the answer and is this:
mg/3 [(9+ cot2(φ))]

we have never encounter a problem that the answer is cotangent before its way out of my league can someone please just tell me how to do it?

i just checked the answer and it is
mg/3 ( √(9+cot2(φ))

we have never encounter a problem that its answer has cotangent in it. its way out of our league. can someone please just show me how to derive the answer?

siapola1 said:
can someone please just tell me how to do it?
That's not how this forum works. Don't be put off by the cotangent. Just try to answer these questions in sequence:
You are given the mass of the rod. What is the force of gravity on it?
Where does that force act?
What is the moment arm of that force about the point of contact?
Unfortunately I made a mistake in answering a previous post of yours. I'll correct that then continue...

ok, I have edited post #4. You need to look for another force that has a torque about the point of contact between rod and table. The contact forces that act there cannot have a moment about it.

## 1. What is static equilibrium?

Static equilibrium refers to a state in which an object is at rest, with no net forces acting on it. In other words, the object is balanced and not moving.

## 2. How does a picture hanging on a wall demonstrate static equilibrium?

A picture hanging on a wall demonstrates static equilibrium because the weight of the picture is balanced by the normal force exerted by the wall. This creates a state of equilibrium, where the picture remains in place without any additional support or force.

## 3. What factors affect the static equilibrium of a picture hanging on a wall?

The factors that affect the static equilibrium of a picture hanging on a wall include the weight and size of the picture, the strength of the wall, and the method of hanging (e.g. using nails, hooks, etc).

## 4. How can you determine if a picture is in static equilibrium on a wall?

You can determine if a picture is in static equilibrium by checking if there are any net forces acting on it. If the picture is not moving and there are no external forces present, then it is in a state of static equilibrium.

## 5. Can a picture ever be in a state of dynamic equilibrium on a wall?

No, a picture cannot be in a state of dynamic equilibrium on a wall. Dynamic equilibrium refers to a state in which an object is moving at a constant velocity and there are no net forces acting on it. Since a picture hanging on a wall is not moving, it cannot be in a state of dynamic equilibrium.

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