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

In summary, the conversation discusses finding the potential energy stored in a spring without using the spring constant. The equation for net external work done on system ABS is determined to be the product of the force applied and the displacement. It is noted that the work done on block A is not the same as the work done on the system, and the partitioning of this work into kinetic energy and potential energy is not relevant.
  • #1
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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  • #2
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.
 
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  • #3
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?
 
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  • #4
dge said:
So would it just be the force applied * the displacement?
Yes.
 
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  • #5
haruspex said:
Yes.
I guess I overcomplicated that in my head. Thank you!
 
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What is spring compression?

Spring compression is the process of applying a force to a spring, causing it to compress or become shorter in length. This is typically done by pushing or pulling on the ends of the spring.

How does spring compression relate to work?

When a force is applied to compress a spring, work is done on the spring. This is because the force is causing a displacement in the spring, and work is defined as force multiplied by displacement. The work done on the spring is stored as potential energy in the spring.

What is the formula for calculating the work done on a spring during compression?

The formula for calculating the work done on a spring during compression is W = 1/2 * k * x^2, where W is work, k is the spring constant, and x is the displacement of the spring. This formula is derived from the equation for potential energy, U = 1/2 * k * x^2.

How does the spring constant affect the work done on a spring during compression?

The spring constant is a measure of the stiffness of a spring. A higher spring constant means that more force is required to compress the spring a certain distance. Therefore, a higher spring constant will result in more work being done on the spring during compression.

What factors can affect the amount of work done on a spring during compression?

The amount of work done on a spring during compression can be affected by the magnitude of the applied force, the spring constant, and the displacement of the spring. Additionally, factors such as friction and air resistance can also affect the amount of work done on the spring.

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