Confused which formula to use

1. Oct 14, 2013

anthonyk2013

I have a question I'm having trouble with.

A wire is stretched 1.2 mm by a force of 240n. Calculate the force needed to stretch the wire 2.0mm assuming the elastic limit is not exceeded.

I'm new to physics and I have only used formulas for finding stress, strain and youngs modulas. Should I be able to find the value using one of those formulas?

2. Oct 14, 2013

arildno

Use the fundamental tenet of Hooke's law (for which the limit of elasticity is not exceeded), that the force must be proportional to the stretching of the wire.

The simplest use of this is that the ratio between the two forces must equal the ratio of the two stretchings.

3. Oct 14, 2013

anthonyk2013

I use f=-KX?

4. Oct 14, 2013

arildno

That is indeed Hooke's law!

Since you are not bothering about the directions of accelerations here, you can disregard the minus sign, and say that the magnitude of the force "f" equals "k" times the magnitude of the stretching X.
That is:
F=kX.

Now, you know both the force in the first instance, and the stretching in that instance.
Can you solve for "k", so that you can use that in order to find the magnitude of the force in the second instance?

5. Oct 14, 2013

anthonyk2013

240=K.1.2
K=240x1.2=288N ?

6. Oct 14, 2013

arildno

If you have the equation:
240=K*1.2

How do you solve for K?

Remember that we can switch about the order of factors in a product, and also what we term the LHS and RHS of an equation.

Thus, the above equation can also be written as:

1.2*K=240

Also, do NOT use as multiplication sign "." when you also use "." as decimal point sign!

7. Oct 14, 2013

anthonyk2013

Ok won't do that again.

So K=240*1.2=288N

8. Oct 14, 2013

arildno

Really?

How do you solve the equation:

2*x=4?

9. Oct 14, 2013

anthonyk2013

Sorry my bad, need to get my head in the game here.
K=240/1.2=200.

10. Oct 14, 2013

arildno

Now we are in agreement!

Now that you know the K-value is 200 N/mm, what must the applied force be in the second instance, when you know the stretching is equal to 2.0 mm?

11. Oct 14, 2013

anthonyk2013

F=k*x
F=200*2=400N/mm squared ?

12. Oct 14, 2013

arildno

How does (N/mm)*mm become?

13. Oct 14, 2013

anthonyk2013

Need to concentrate no mm.

400N

14. Oct 14, 2013

arildno

Yup!

15. Oct 14, 2013

arildno

Now, here's how you can do it without bothering to solve for "K" first:

We have, for the first instance, F_1=k*x_1
and for the second instance, F_2=k*x_2

Dividing the second equation by the first, we have:

F_2/F_1=(k*x_2)(k*x_1)=x_2/x_1

That is:
F_2/F_1=x_2/x_1, or, multiplying with F_1

F_2=(x_2/x_1)*F_1

16. Oct 14, 2013

anthonyk2013

Thanks very much for your help. I won't feel too bad in class Thursday evening.
Cheers

Last edited: Oct 14, 2013