Work Done by Spring on a Body Sliding down a rod

In summary, the conversation discusses the work done by a spring on an object sliding down a rod. The homework equations for this problem are provided, and one equation is corrected. The problem is then addressed, with a suggestion to use integration or conservation of energy. The conversation concludes with a discussion on the validity of using the usual formula for work done by a spring in this scenario.
  • #1
Simon Goster
4
0
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!
 
Last edited:
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  • #2
Your formula for work done by a spring is wrong. Its X2. Not x.
 
  • #3
UncertaintyAjay said:
Your formula for work done by a spring is wrong. Its X2. Not x.
Sorry for this.
Corrected the Formulas
Thanks!
 
  • #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?
 
  • #5
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?
 
  • #6
The second method is easier. When in doubt use conservation of energy. Now try it with that and see what answer you get.
 

1. How is work done by a spring calculated?

The work done by a spring is calculated by multiplying the force exerted by the spring (F) by the distance the spring is stretched or compressed (x), represented by the equation W = Fx. This is known as Hooke's Law.

2. What is the relationship between the work done by a spring and the distance traveled by the body?

The work done by a spring is directly proportional to the distance traveled by the body. This means that the more the spring is stretched or compressed, the more work it does on the body sliding down the rod.

3. How does the mass of the body affect the work done by the spring?

The mass of the body has no effect on the work done by the spring. The work done is solely determined by the force exerted by the spring and the distance traveled by the body.

4. Can the work done by a spring be negative?

Yes, the work done by a spring can be negative if the force exerted by the spring is in the opposite direction of the displacement of the body. This means that the spring is doing work against the motion of the body, resulting in a negative value for work.

5. How does the angle of the rod affect the work done by the spring?

The angle of the rod has no effect on the work done by the spring. As long as the spring is exerting a force on the body and the body is traveling a distance, work is being done regardless of the angle of the rod.

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