MHB What is the equation linking force and extension for a stretched spring?

[DeusAbscondus]

I have come across a question in my text which I feel completely at sea about. could someone have a look and see if they can give me some orientation?

The question starts by stating:
"The force required to stretch a spring is proportional to the extension. If a spring is normally 25 cm long and force of 100 N is required to stretch it 0.5cm, find the equation linking force and extension."

Then:
"The work (W) done in stretching the spring is given by:
$$W=\int^{x_2}_{x_1} F\ dx$$
Find the work done extending the spring from 27 cm to 30 cm."


Some important points I've extracted and noted (just to show I don't just want an answer, but understanding and practice is construing these problems for an exam in 2 weeks):

1. I need a equation linking force and extension which will then become the integrand in above Work equation
2. In this equation, force will be the dependent value, extension the independent; the equation will be a ratio, hence a derivative of the anti-derivative Work function provided
3. the increment of .5cm is obviously to be worked into this equation, as is the value of 100N
4. finally, the "27cm to 30 cm" will obviously provide the boundaries for the integral:
$$W=\int^{30}_{27}F(e)\ de\ **$$

Beyond that, I am flumexed and feeling pretty defeated!

Deus Abs

** I'm guessing that the equation sought must be a ration between Force (dependent variable) and Extension (e), independent variable, hence $$F(e)\ de$$??

 

[MarkFL]

This may be the missing piece of the puzzle. Hooke's Law states that:

$\displaystyle F=-kx$ where $\displaystyle 0<k$.

You may they use the given information to determine k.

 

[DeusAbscondus]

This may be the missing piece of the puzzle. Hooke's Law states that:

$\displaystyle F=-kx$ where $\displaystyle 0<k$.

You may they use the given information to determine k.

Thanks Mark.
Just worked it out: k is the constant linking extension and force

Cheers,
D