# Solving the Sliding Rod Equilibrium Problem on a Wall

• daniel_i_l
In summary, the conversation discussed a question about a rod leaning against a wall and the static friction needed to keep it in equilibrium. The speaker used the method of considering all forces acting on the rod, including gravity, the force from the wall, and the force from the floor. By applying the conditions for translational and rotational equilibrium, the speaker determined that the static friction needed is greater than or equal to 0.5sqrt(3).
daniel_i_l
Gold Member
Here's a question (not homework) that someone asked me a few days ago:
you have a rod with length L and mass M that's leaning against a frictionless wall and makes a 30deg angle with the floor. what does the static friction have to be inorder for the stick to stay inequilibrium?
What i did was to pretend that all the mass was at the center of the rod. then i split the force mg on that point into two parts - "along the rod" and perpendicular to the rod. the force along the rod pushes the bottom of the rod into the ground with and angle of 30 bellow the ground. the perp force induces a normal force which also has two parts - along the rod and perp to the rod going up. this perp force creates a torque which also pushes the bottom of the stick into the ground.
So basically i summed up all these forces and got the answer:
Ustatic >= 0.6sqrt(3)
Ustatuc >= 0.5sqrt(3)
What it the correct way to deal with this problem?
Thanks.

Whether "homework" or not, all textbook/coursework-type questions should be posted in the appropriate "Homework Help" section. I'll move it.

I can't really follow what you are doing here. To solve this, just consider all the forces acting on the ladder:
(1) Gravity, which acts down through the center of mass (you started off with that)
(2) The force from the wall--since there's no friction, it acts horizontally
(3) The force from the floor--break it into two components: friction force (horizontal) and normal force (vertical)

Now just apply the conditions for translational and rotational equilibrium.

thanks, i got it now.

## 1. What is the Sliding Rod Equilibrium Problem on a Wall?

The Sliding Rod Equilibrium Problem on a Wall is a physics problem that involves finding the position at which a rod placed against a vertical wall will remain in equilibrium without falling. This problem is commonly used to demonstrate the concept of torque and equilibrium in introductory physics courses.

## 2. How is the Sliding Rod Equilibrium Problem solved?

The Sliding Rod Equilibrium Problem can be solved using the principle of torque, where the sum of the clockwise torques must be equal to the sum of the counterclockwise torques for the rod to remain in equilibrium. This can be represented by the equation ΣMcw = ΣMccw, where M represents the torque and cw and ccw represent clockwise and counterclockwise directions, respectively.

## 3. What factors affect the equilibrium position of the Sliding Rod?

The equilibrium position of the Sliding Rod is affected by several factors, including the weight of the rod, the distance of the point of contact from the wall, and the coefficient of friction between the rod and the wall. These factors can be adjusted to find the optimal equilibrium position for the rod.

## 4. Can the Sliding Rod Equilibrium Problem be solved in real-world scenarios?

Yes, the Sliding Rod Equilibrium Problem has real-world applications, such as in the design of structures and machines. Engineers and architects often use the principles of torque and equilibrium to determine the optimal placement of beams and columns to ensure stability and prevent collapse.

## 5. Are there any limitations to the Sliding Rod Equilibrium Problem?

The Sliding Rod Equilibrium Problem assumes ideal conditions, such as a perfectly straight rod and a smooth wall surface. In reality, there may be imperfections that can affect the equilibrium position. Additionally, the problem does not take into account the effects of external forces, such as wind or vibrations, which can also impact the equilibrium position of the rod.

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