Calculating Energy Stored in a Spring

In summary, the energy stored in a spring with a spring constant of 400N/m and a maximum stretch of 12cm can be calculated using the equation U = 1/2k(x^2), resulting in an answer of 2.88J. However, when considering significant figures, the answer should be rounded to 3J. The computer may not always account for significant figures in its answer acceptance.
  • #1
aligass2004
236
0

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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  • #2
This looks correct, what's your question exactly?
 
  • #3
If I'm not mistaken, that's the energy of just one particle from the spring.
 
  • #4
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.
 
  • #5
Well I tried the answer, and it was wrong. I don't know what other equation I would use.
 
  • #6
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).
 
  • #7
It would be (N/m)(m^2) = Nm = J
 
  • #8
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.
 
  • #9
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!
 

What is the definition of "Energy stored in a spring"?

Energy stored in a spring is the potential energy that is stored in an elastic material, such as a spring, when it is stretched or compressed. This energy is stored in the form of potential energy due to the displacement of the spring from its equilibrium position.

How is the energy stored in a spring calculated?

The energy stored in a spring can be calculated using the formula E = 1/2kx^2, where E is the energy stored, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

What factors affect the amount of energy stored in a spring?

The amount of energy stored in a spring is affected by the material and shape of the spring, as well as the amount of displacement from its equilibrium position. The spring constant, which is a measure of the stiffness of the spring, also plays a role in determining the amount of energy stored.

How is the energy released from a spring?

The energy stored in a spring is released when the spring returns to its equilibrium position. This can happen through the release of tension in a stretched spring or the compression of a compressed spring. The released energy can be used to do work, such as powering a mechanical device.

What are some real-life applications of the energy stored in a spring?

The energy stored in a spring has many practical applications, such as in various types of springs used in everyday objects like mattresses, trampolines, and car suspensions. It is also used in more complex systems, such as shock absorbers and mechanical watches. Additionally, the energy stored in a spring is utilized in many scientific and engineering experiments, such as in testing the properties of materials and designing structures that can withstand stress and strain.

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