Spring constant, which equation to use??

[A_Student_03]

I'm really rusty on physics, and it seems that the people who write physics books are the most terrible people on the planet for explaining concepts.

In any case, how do you know which equation you are supposed to use? The two I'm referring to are F = k|x| and PE=(.5)k(x)^2. I don't even understand WHY I can't use either of them whenever I want.

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[A_Student_03]

Oh. I think I get it now. If given, for instance, some work done(joules) and the distance the spring went, you can't change that back into how much force you placed on it because the spring is resisting the push/pull.

 

[huseyin]

I'm really rusty on physics, and it seems that the people who write physics books are the most terrible people on the planet for explaining concepts.

In any case, how do you know which equation you are supposed to use? The two I'm referring to are F = k|x| and PE=(.5)k(x)^2. I don't even understand WHY I can't use either of them whenever I want.

Hi:

The two formulas that you are referring to can be used at the same time however, as F = k|x| gives you the FORCE that is needed to shrink the string, PE=(.5)k(x)^2 gives you POTENTIAL ENERGY. So, according to what they ask in the question, you can use any of them. Also, these formulas are interchangable. You can calculate the potential energy change in the spring by calcualting the force needed to shrink the spring from the eq state to the shrinked stage. If you want the proof of these equations or more insight, let me know.
huseyin

 

[PKP719]

Please note potential energy is energy before action has actually occured.
Ex. A ball in your hand raised to some height. That is potential energy , once you release the ball .. as the ball is dropping that is reffered to as kinetic energy.

 

[A_Student_03]

Hi:

The two formulas that you are referring to can be used at the same time however, as F = k|x| gives you the FORCE that is needed to shrink the string, PE=(.5)k(x)^2 gives you POTENTIAL ENERGY. So, according to what they ask in the question, you can use any of them. Also, these formulas are interchangable. You can calculate the potential energy change in the spring by calcualting the force needed to shrink the spring from the eq state to the shrinked stage. If you want the proof of these equations or more insight, let me know.
huseyin

What about the example I gave? Say you had a problem like this: 400 joules of work is done stretching a spring 20 cm. What's the spring constant?

See, before Iwas thinking I could use either of them tosolve this, but if you try, you will get the wrong answer.

 

[tank you]

What about the example I gave? Say you had a problem like this: 400 joules of work is done stretching a spring 20 cm. What's the spring constant?

See, before Iwas thinking I could use either of them tosolve this, but if you try, you will get the wrong answer.

you would use the PE=0.5kx^2 because it gives u the work done, remember work is change in energy.

 

[A_Student_03]

you would use the PE=0.5kx^2 because it gives u the work done, remember work is change in energy.

Right, that's sort of what I was talking about. The confusion is if you can take work done and get the force that was applied to create it by using work = F d. Then use that force in the other formula to get the constant. It doesn't work.

 

[huseyin]

Right, that's sort of what I was talking about. The confusion is if you can take work done and get the force that was applied to create it by using work = F d. Then use that force in the other formula to get the constant. It doesn't work.

Alright, I think I understand the confusion:

So, if you calculate "k" in the way that you suggest here, you get k=10,000
however if you use PE=(.5)k(x)^2 you get k=20,000.

The problem here is
In your first solution, you are assuming that you are stretching the spring with a constant force over the time. Of course, then you may conclude that the force should be A from the W=k*x formula but this may not be true in all the questions. As an example, you may do the same work by a non constant force over the same period. On the other hand, when you use PE=(.5)k(x)^2 you are not putting a force variable into the equation.

huseyin