Work Done by Spring on a Body Sliding down a rod

AI Thread Summary
The discussion revolves around calculating the work done by a spring on an object sliding down a rod, highlighting confusion over the application of the work formula due to changing angles and force components. The original formula for work done by a spring, -1/2 * KΔx², is questioned in light of the dynamic situation. Participants suggest alternative approaches, such as using integration of the spring force or applying the principle of conservation of energy to find potential energy changes. The consensus leans towards using conservation of energy as a simpler method to solve the problem. The conversation emphasizes the need for clarity in applying physics concepts to dynamic systems.
Simon Goster
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1. The Question
Unable to find the work done by spring on the object sliding down the rod as shown below:

6KCzFSc.png


Homework Equations


Work Done by Spring Force : -1/2 * KΔx2 --(1)
where k = Spring Constant
Δx = Change in Spring Length[/B]

3. Where the problem occurred
While seeing the solution of the problem, it was mentioned that we can simply take
WSpring = -1/2 * K(X22-X12) --(2)
But my problem is that if the position of ring on rod is changing, the angle of spring with the rod is changing and thus the force components on rod is changing, then how the usual formula
Work Done by Spring Force : -1/2 * KΔx2
is also valid for the given condition.
PS: I also tried to understand this using concept of conservative force, but couldn't get it.
Thanks!
 
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Your formula for work done by a spring is wrong. Its X2. Not x.
 
UncertaintyAjay said:
Your formula for work done by a spring is wrong. Its X2. Not x.
Sorry for this.
Corrected the Formulas
Thanks!
 
Okay so , ignore the fact that you've seen the solution for a moment. Assume you don't know what the answer is. How would you approach the sum?
 
UncertaintyAjay said:
Okay so , ignore the fact that you've seen the solution for a moment. Assume you don't know what the answer is. How would you approach the sum?

1. Integration =>∫(force of spring along rod)*dx or ∫(force of spring along rod as function of angle)*dθ
2. As Work Done = - Change in Potential Energy
Find Potential Energy due spring for both the positions and use the above relation

Are these meathods right.
Wont consider using integration method
Can we use other concepts like conservative forces or just like that?
 
The second method is easier. When in doubt use conservation of energy. Now try it with that and see what answer you get.
 
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