Equilibrium of weight on pulley

[drkidd22]

Homework Statement

A 15lb weight at a on frictionless rod at a distance of 16" from a pulley can move up and down and it has counter-force on pulley of 17lb. What should the height of weight on rod be so that system is in equilibrium

Homework Equations

Cosine Law
Sine Law

The Attempt at a Solution

I have tried to draw the problem so that it would be better to understand. I'm not given any angles and not sure to get started here.

 

[Doc Al]

What's the tension in the pulley cable? What angle must the cable make with respect to the weight on the rod. (Redo your force diagram to show the forces acting on the 15lb weight.)

 

[drkidd22]

I'm having difficulty trying to understand the problem as is. The tension in the cable would be the sum of all components of both weights, but I'm not given angles to find them. Wouldn't the tension be 32lb anyways?

 

[Doc Al]

The tension in the cable would be the sum of all components of both weights,

No, that's not true.

but I'm not given angles to find them. Wouldn't the tension be 32lb anyways?

No.

To find the tension in the cable, analyze the forces acting on the 17lb mass. That mass must be in equilibrium also.

 

[rdl]

I would first analyze the given information and try to understand the physical concept behind the problem. In this case, we have a weight of 15lbs on a frictionless rod, which means that the only forces acting on the weight are gravity and the counter-force of 17lbs on the pulley. The weight is able to move up and down, indicating that there is tension in the rod.

To find the height of the weight on the rod that will result in equilibrium, we can use the principle of moments. This principle states that for an object to be in equilibrium, the sum of the clockwise moments must equal the sum of the counterclockwise moments. In this case, the moments are created by the weight and the counter-force on the pulley.

Using the cosine law, we can calculate the angle between the rod and the horizontal line, which will help us determine the distance between the weight and the pulley. Then, using the sine law, we can calculate the height of the weight on the rod that will result in equilibrium.

It is important to note that the angle and height may vary depending on the position of the weight on the rod. Therefore, multiple calculations may be needed to find the exact height that will result in equilibrium. Additionally, the weight and counter-force may also change, so the height of the weight on the rod may need to be adjusted accordingly.

In conclusion, to find the height of the weight on the rod that will result in equilibrium, we need to analyze the forces and moments acting on the system and use mathematical equations such as the cosine and sine laws. It is also important to consider any potential changes in the weight and counter-force that may affect the equilibrium of the system.