Applications of Physics and Engineering: Stretching Spring

[krisaldine]

How do I approach this problem?

If 6 J of work is needed to stretch a spring from 10 cm to 12 cm and another
10 J is needed to stretch it from 12 cm to 14 cm, what is the natural length of the spring?


I know for this one I can assume the spring lies along the x axis with it’s base at 0. But where do I go from here?

Thanks so much!

 

[Count Iblis]

Re: Applications of Physics and Engineering: Stretching Spri

How do I approach this problem?

If 6 J of work is needed to stretch a spring from 10 cm to 12 cm and another
10 J is needed to stretch it from 12 cm to 14 cm, what is the natural length of the spring?


I know for this one I can assume the spring lies along the x axis with it’s base at 0. But where do I go from here?

Thanks so much!

If you integrate the force needed to stretch a spring you find that the work needed to stretch a string from
\(\displaystyle x_{1}\) to \(\displaystyle x_{2}\) is:

\(\displaystyle W = \frac{k}{2}\left[\left(x_{2}-x_{0}\right)^{2}-\left(x_{1}-x_{0}\right)^{2}\right]\)

where \(\displaystyle x_{0}\) is the natural length of the string.

Ton solve the problem, you just use the aboove formula to write down the two equations for the workneeded to stretch the string over the two doistances. If you divide the two equations then the spring constant \(\displaystyle k\) drops out. In both the numerator and the denominator you rewrtite the difference of the squares as the product of the sum and difference. In the "difference factor" \(\displaystyle x_{0}\) drops out. Then multiply both sides by he denominator to obtain a linear equation for \(\displaystyle x_{0}\).

 

[galactus]

Here's how I would tackle it. Seems OK.


\(\displaystyle \L\\\int_{10-L}^{12-L}kxdx=6\)......[1]

\(\displaystyle \L\\\int_{12-L}^{14-L}kxdx=10\)....[2]


Solve [1] for k and sub into [2], then solve for L.

 

[krisaldine]

Can you show me how to do this problem? I am still confused... Please tell me, if possible in steps. I am having difficulty figuring this out. I appreciate the help! ^_^

 

[stapel]

Can you show me how to do this problem?

You've been given the complete set-up, and instructions for the last step. Where are you stuck? You can integrate kx, right?

Thank you.

Eliz.

 

[krisaldine]

Is it possible to show me this step by step so I know how I can do these types of problems? I am having a difficult time with this particular one. I really appreciate the time and help!

 

[galactus]

k is a constant. Don't let that trip you up. Suppose you wanted to integrate 2x.

How would you go about it?. Let's see some of your atempts and we'll see where

your hung up. Once the integral is set up, it isn't that bad. The integral itself is

about as easy as they come. Some algebra when you solve for k and L, but not

monstrous.