How can I calculate the potential energy stored in a compressed spring?

AI Thread Summary
To calculate the potential energy stored in a compressed spring, the work done on the system must be understood in terms of the applied force and displacement. The work done on block A is equal to its kinetic energy, but this does not directly represent the work done on the entire system, which includes the spring. The relevant equation for work is the force applied multiplied by the displacement. The discussion clarifies that the potential energy can be derived from the net external work done on the system without needing to partition it into kinetic energy and elastic potential energy. Ultimately, the calculation simplifies to using the force and displacement directly.
dge
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Homework Statement
Two identical blocks, A and B, on a frictionless surface are connected by a spring of negligible mass. The spring is initially unstretched. During the interval from t1 to t2, block A is pushed through a distance dA by a hand exerting a force of magnitude FA, as shown. Block B is held in place by a wall. The wall exerts a force on block B that varies with time but is always directed to the left.

Write an expression for the net external work done on system ABS by external forces in terms of given quantities (ie. FA, dA, and/or t2). Explain.
Relevant Equations
Work = Force * displacement
I feel like I've gotten stuck on this. I know the work done is equal to the kinetic energy of block A, but I can't figure out how I would find the potential energy stored in the spring without using the spring constant in the equation. W = FA * dA + U
 
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dge said:
Homework Statement:: Two identical blocks, A and B, on a frictionless surface are connected by a spring of negligible mass. The spring is initially unstretched. During the interval from t1 to t2, block A is pushed through a distance dA by a hand exerting a force of magnitude FA, as shown. Block B is held in place by a wall. The wall exerts a force on block B that varies with time but is always directed to the left.

Write an expression for the net external work done on system ABS by external forces in terms of given quantities (ie. FA, dA, and/or t2). Explain.
Relevant Equations:: Work = Force * displacement

the work done is equal to the kinetic energy of block A,
That’s the work done on block A, but it is not the work done on the system "ABS" (S presumably being the spring).
You do not need to care how the work done on the system gets partitioned into KE and EPE.
 
haruspex said:
That’s the work done on block A, but it is not the work done on the system "ABS" (S presumably being the spring).
You do not need to care how the work done on the system gets partitioned into KE and EPE.
So would it just be the force applied * the displacement?
 
dge said:
So would it just be the force applied * the displacement?
Yes.
 
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haruspex said:
Yes.
I guess I overcomplicated that in my head. Thank you!
 
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