What Friction Coefficient is Required for Outward Sliding at Points A and C?

[lwc729]

Homework Statement

The unstretched length of a spring is 1.5 ft. What friction coefficient,μ, at A and C is needed so that P=500 lb would tend towards points A and C sliding outward? Given spring constant k=70 lb/ft

Diagram-
Inverted triangle such that height is 4 ft to point B. Force P points directly down at the tip of triangle (point B). Width at base between points A and C is also 4 ft. Spring is located 1 ft off horizontal between two legs of triangle.

Homework Equations

Friction=μ*Normal force

F(spring)=kΔx=(70 lb/ft)Δx

The Attempt at a Solution

I drew a free body diagram of half the system showing the P=500 lb downward, the spring force, the friction force and the normal force. Summing the forces in the y, I came to the Normal force equal to 500 lb. Then summing the forces in the x you have the friction force equal to the spring force. Here is where I get stuck. If you are trying to find μ what should the value of Δx be such that the system would tend towards sliding outward?

 

[KataKoniK]

Hello, thank you for your question. It seems like you are on the right track with your free body diagram and summing of forces. To find the required friction coefficient, you will need to use the equation Friction = μ*Normal force. As you mentioned, the normal force in this case is equal to the force P of 500 lb. Now, to find the friction force, you will need to use the spring force equation, F(spring) = kΔx. Since you are trying to find the value of Δx that will result in the system tending towards sliding outward, you can set the friction force equal to the spring force. This will give you the equation μ*500 lb = (70 lb/ft)Δx. Solving for μ, you will get μ = (70 lb/ft)Δx/500 lb. To find the value of Δx, you can use the given information that the unstretched length of the spring is 1.5 ft. This means that when the system is in equilibrium, the spring will be stretched to a length of 1.5 ft. Therefore, Δx = 1.5 ft. Plugging this value into the equation for μ, you will get μ = (70 lb/ft)(1.5 ft)/500 lb = 0.21. This is the required friction coefficient for the system to tend towards sliding outward. I hope this helps!