Massless Pulley Spring Problem: Solving for Displacement x at Equilibrium

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Homework Help Overview

The discussion revolves around a massless pulley system connected to a spring, focusing on determining the displacement x at equilibrium after a mass m is added. Participants are attempting to clarify the setup and the relationships between the components involved, particularly regarding the equilibrium state and the interpretation of the problem statement.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning the number of masses involved and the interpretation of equilibrium in the context of the spring and pulley system. There is discussion about whether the problem statement is clear and whether the diagram accurately represents the scenario.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some have suggested that the wording may be vague, while others are trying to clarify the relationship between the mass and the spring's displacement. There is recognition of a potential misunderstanding regarding the definition of displacement x.

Contextual Notes

Participants note that the problem may lack clarity, particularly regarding the setup and the roles of the masses involved. There is also mention of a diagram that may help in visualizing the problem, but its absence is acknowledged as a limitation in understanding.

jofree87
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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?
 

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It looks like there are two masses hanging from the pulley. What's the mass of each?
 
only one mass is given. If it reaches equilibrium, wouldn't that mean both masses are the same though?
 
jofree87 said:
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?
 
"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."
 
jofree87 said:
"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?
 
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.
 
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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jofree87 said:
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.
 
  • #10
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
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.
 

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