Calculating Work Done on a Spring-Block System: Equivalent Equations?

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Discussion Overview

The discussion revolves around calculating the work done on a spring-block system, particularly examining the equivalence of two energy equations involving work done on and by the system. Participants explore the implications of force constancy and the definitions of work in this context.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant asks if the equations ΔE=Q+W1 and ΔE=Q-W2 are equivalent and seeks to calculate W2.
  • Another participant questions whether the force F is constant during the displacement.
  • A different viewpoint suggests that the work done on the system can be represented as W1=∫Fdx, regardless of the constancy of F.
  • One participant proposes that W2, the work done by the system, is equal to W2=-1/2kx², attributing it to the spring force.
  • Another participant counters that if the block is pulled with a force F, then the block exerts an equal and opposite force, leading to the conclusion that W2 should be calculated as W2=-∫Fdx.

Areas of Agreement / Disagreement

Participants express differing views on the definitions and calculations of W1 and W2, with no consensus reached on the equivalence of the two energy equations or the correct formulation of work done by the system.

Contextual Notes

There are unresolved assumptions regarding the constancy of the force F and the definitions of work in relation to the spring force and external force applied to the block.

daigiaga1994
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Consider a system with a spring and a block. The block moves on a frictionless surface. At the equilibrium position, the speed of the block equals to 0. Now i pull the block by a force F with a displacement of x. Assuming that the speed at the final position is v.
Can you calculate the energy of the system after the process ?

If i apply the equation: ΔE= Q+W1 ( with W1 is the work donr on the system )
Is the above equation equivalent with the eqution: ΔE=Q-W2( with W2 is the work done by the system)

( Q is the heat that is transferred to the system)
If these equations is equivalent, please tell me how to calculate W2 ?
thank
 
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daigiaga1994 said:
Now i pull the block by a force F with a displacement of x.
Is the force constant over that displacement?

(The work done by the system is just the negative of the work done on the system.)
 
Doc Al said:
Is the force constant over that displacement?
I think it is not important if F is constant or not. Because we can represent the work done on the system by W1=∫Fdx.

In my opinion, W2 is the work done by the system, so it is done by the spring force ( This is only force created by the system) and equals to W2=-1/2kx2.

If the two equation is equivalent, W1+W2=0. It is clearly wrong because W1+W2=ΔK=1/2mv2.

This is my confusion
 
daigiaga1994 said:
In my opinion, W2 is the work done by the system, so it is done by the spring force ( This is only force created by the system) and equals to W2=-1/2kx2.
This is where you are going wrong. If you pull the block with a force F, then the block is pulling you with a force -F. (Newton's 3rd law.) So the work done by the system W2= -∫Fdx.
 
Thank you so much Doc Al. Now i know what is the work done by the system.
Hope that i can learn more from you. Thank again :D
 

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