Massless Pulley Spring Problem: Solving for Displacement x at Equilibrium

[jofree87]

Consider the massless pulley connected by a spring at the pivot. What is the displacement x at equilibrium after the mass m has been added? Determine x in terms of m, g, and k.

I drew picture of the problem and tried to work it out in the pic below. The answer should be x = 4mg/k, but I don't understand how they got it. What am I doing wrong?

 

[Doc Al]

It looks like there are two masses hanging from the pulley. What's the mass of each?

 

[jofree87]

only one mass is given. If it reaches equilibrium, wouldn't that mean both masses are the same though?

 

[Doc Al]

only one mass is given. If it reaches equilibrium, wouldn't that mean both masses are the same though?

Not clear to me. Equilibrium may just refer to the spring. (At least that's how I would interpret it.)

What's the exact statement of the problem?

 

[jofree87]

"Consider the massless pulley connected by a spring at the pivot. What is the displacement x at equilibrium after the mass m has been added? Determine x in terms of m, g, and k."

 

[Doc Al]

"Consider the massless pulley connected by a spring at the pivot. What is the displacement x at equilibrium after the mass m has been added? Determine x in terms of m, g, and k."

This is a repeat of what you've already stated up front. I'm still puzzled. Was a diagram included? "after the mass m has been added" to what? That's not enough for me to understand the problem.

Was this a problem from a textbook? Was it part of a larger problem?

 

[BruceW]

The question is badly worded/vague. If the problem is what you've drawn, then you would have got it right, but since its not right, the question must be describing something different to what you're thinking.

 

[jofree87]

ya, I think I might be interpreting the problem incorrectly. I think there is only one block of mass hanging and the other "block mass" is actually a fixed support? Here is the actual picture of the problem

 

[Doc Al]

ya, I think I might be interpreting the problem incorrectly. I think there is only one block of mass hanging and the other "block mass" is actually a fixed support? Here is the actual picture of the problem

Based on this, I'd say that your solution was correct.

 

[Doc Al]

OK, I see the problem. They are defining x as the change in position of the mass with respect to the ground, not as the amount of stretch in the spring. (Although they are related.) The given answer is correct.

 

[BruceW]

yeah, jofree87 has got the answer for the extension of the spring. So next he needs to work out why the mass will descend by twice this.