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

AI Thread Summary
In a spring-block system on a frictionless surface, the energy calculations involve understanding the work done on and by the system. The discussion centers on whether the equations ΔE = Q + W1 and ΔE = Q - W2 are equivalent, where W1 is the work done on the system and W2 is the work done by the system. It is clarified that W2 is the negative of the work done by the applied force, leading to W2 = -∫Fdx. The relationship between W1 and W2 indicates that W1 + W2 does not equal zero, as it relates to the change in kinetic energy. The conversation concludes with a better understanding of the work done by the system, emphasizing Newton's third law in the context of forces.
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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