Calculating Energy Stored in a Spring

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The discussion centers on calculating the energy stored in a spring using the formula U = 1/2k(x^2), where k is the spring constant and x is the maximum stretch. The initial calculation yielded 2.88 Joules, which was later corrected to 3 Joules due to significant figure considerations. Participants noted the importance of including units in calculations, confirming that the energy is measured in Joules. A misunderstanding regarding the placement of a decimal point led to confusion over the correct answer. The thread highlights the challenges of precision in physics problems and the impact of significant figures on computer-based grading systems.
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Homework Statement



How much energy can be stored in a spring with k = 400N/m if the maximum possible stretch is 12cm?

Homework Equations



U = 1/2k(x^2)

The Attempt at a Solution



I tried using the above equation. U = 1/2(400)(.12^2) = 2.88.
 
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This looks correct, what's your question exactly?
 
If I'm not mistaken, that's the energy of just one particle from the spring.
 
The mechanical energy is stored uniformly in the spring for the most part (assuming uniform material properties, e.g. elastic modulus), but that is the energy that would be imparted to any mass at the end of the spring (with respect to the other end) if the spring were released and pushed or pulled the mass.
 
Well I tried the answer, and it was wrong. I don't know what other equation I would use.
 
aligass2004 said:
Well I tried the answer, and it was wrong. I don't know what other equation I would use.
what units should you use for the stored energy? (You left them out).
 
It would be (N/m)(m^2) = Nm = J
 
aligass2004 said:
It would be (N/m)(m^2) = Nm = J
OK try 2.88J or 2.9J (I'm not good at significant figures) and see if the computer buys it.
 
As far as sig figs go, I think it should be 3 Joules. We only know the spring constant to one significant digit.
 
  • #10
hotcommodity said:
As far as sig figs go, I think it should be 3 Joules. We only know the spring constant to one significant digit.
Yes, I think you're right, webassign gets very picky.
 
  • #11
Holy crap everyone! I am so sorry about this problem. I was just going to try entering 3, when I noticed that I didn't put the decimal point into my original answer. BIG difference between 288 and 2.88! Sorry again!
 
  • #12
aligass2004 said:
Holy crap everyone! I am so sorry about this problem. I was just going to try entering 3, when I noticed that I didn't put the decimal point into my original answer. BIG difference between 288 and 2.88! Sorry again!
Great, just when I learn how to do significant figures, the computer wasn't looking for 'em. That figures!
 

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