Pully/spring equilibrium (statics)

[kirab]

Diagram attached.

The spring is unstretched when theta = 0. Determine the theta for equilibrium.

I'm not quite sure how to get started here. My prof said that we cannot assume that the tension in the 400 N force cable at A is equal to the tension at the spring close to fixed support C (because it isn't a frictionless pulley).

If we could make this assumption, I'd have the answer! But we can't. Any suggestions? Thanks.

 

[PhanthomJay]

The system is in equilibrium at a certain value of theta. If you sum moments about point O and set them equal to zero, you get your first equation with theta and the spring force as unknowns. Your second equation comes from Hooke's law for the spring. How much does the spring stretch at the equilibrium position?

 

[piercas]

my suggestion would be to use the principles of statics to solve this problem. In order to find the theta for equilibrium, we need to consider all the forces acting on the system and ensure that they are balanced. This includes the tension in the 400 N force cable at point A and the tension in the spring at point C.

Since the pulley is not frictionless, we cannot assume that the tensions at points A and C are equal. Instead, we need to take into account the friction force at the pulley, which will be equal and opposite to the tension in the cable at point A.

To find the theta for equilibrium, we can set up equations using the sum of forces and the sum of moments at point A. We can also use the spring's Hooke's law to relate the tension in the spring to the displacement of the spring.

Once we have these equations, we can solve for theta by setting the sum of forces and the sum of moments to zero, indicating that the system is in equilibrium. This will give us the angle at which the system will be balanced.

In conclusion, while we cannot make the assumption that the tensions at points A and C are equal, we can still use the principles of statics to solve for the theta at equilibrium. It just requires a more thorough analysis of the forces and moments acting on the system.