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Work Done by Spring on a Body Sliding down a rod

  1. Dec 3, 2015 #1
    1. The Question
    Unable to find the work done by spring on the object sliding down the rod as shown below:

    6KCzFSc.png

    2. Relevant equations
    Work Done by Spring Force : -1/2 * KΔx2 --(1)
    where k = Spring Constant
    Δx = Change in Spring Length


    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!
     
    Last edited: Dec 3, 2015
  2. jcsd
  3. Dec 3, 2015 #2
    Your formula for work done by a spring is wrong. Its X2. Not x.
     
  4. Dec 3, 2015 #3
    Sorry for this.
    Corrected the Formulas
    Thanks!
     
  5. Dec 3, 2015 #4
    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?
     
  6. Dec 3, 2015 #5
    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?
     
  7. Dec 3, 2015 #6
    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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