Homework Help: Simple Pulley Spring Problem

1. Sep 24, 2011

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 dont understand how they got it. What am I doing wrong?

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2. Sep 24, 2011

Staff: Mentor

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

3. Sep 24, 2011

jofree87

only one mass is given. If it reaches equilibrium, wouldnt that mean both masses are the same though?

4. Sep 24, 2011

Staff: Mentor

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?

5. Sep 24, 2011

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."

6. Sep 25, 2011

Staff: Mentor

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?

7. Sep 25, 2011

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.

8. Sep 25, 2011

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

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9. Sep 25, 2011

Staff: Mentor

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

10. Sep 25, 2011

Staff: Mentor

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.

11. Sep 25, 2011

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.