# Finding the change in length of a nylon string

1. Oct 19, 2009

### tjohn101

1. The problem statement, all variables and given/known data
A nylon tennis string on a racket is under a tension of 225 N. If its diameter is 0.97 mm, by how much is it lengthened from its untensioned length of 29.6 cm?

Li= 29.6cm =.296 m
r= 4.85e-4 m
A= 7.389811319e-7
F= 225 N
E= Young's Modulus for Nylon= 5 x 10^9
Solving for deltaL

2. Relevant equations
A=pi(r)^2
F= E (delta L/Li) A

3. The attempt at a solution
I've found the area and tried using the equation above but did not get a correct answer. I may well have messed up the calculations because that equation confuses me a little and I seem to be algebraically challenged this fine morning.
All my incorrect answers so far are:
14.5e-8 cm
7.470483757e-8 cm
14.506204362e-7 cm
7.470483757e-6 cm (the last three answers came from the equation above)

Any help is greatly appreciated! Thank you!

2. Oct 19, 2009

### rock.freak667

$$\Delta L = \frac{FL}{AE}$$

what units are E in?

3. Oct 19, 2009

### tjohn101

I've been trying to find the equation in latex... :/ E is in N/m^2.

4. Oct 19, 2009

### rock.freak667

I was just checking to see what units the value of E you quoted were in.

But try plugging the number back in and checking again, you aren't supposed to get such small changes in length.

5. Oct 19, 2009

### tjohn101

Okay I plugged everything into it and got an answer but I need to be sure it's right. I only have one more try. :/ Would the answer be 1.802481745?

PS: I love your signature. Makes everything so much simpler. : )

6. Oct 19, 2009

### rock.freak667

If you mean 1.8025 cm, then I believe so as that looks better than 14.506204362x10-7 cm

7. Oct 19, 2009

### tjohn101

Where did that answer come from? And sorry about the long numbers. My homework website is extremely picky

8. Oct 19, 2009

### rock.freak667

1.802481745 what unit is this in?

for the other number, I just quoted one of your above answers.

9. Oct 19, 2009

### tjohn101

Centimeters. The final answer is supposed to be in centimeters so I multiplied the answer from the equation by 100.

Oh yeah I forgot about that one. :/ That was early this morning.

10. Oct 19, 2009

### rock.freak667

then 1.802481745cm should be it.

11. Oct 19, 2009

### tjohn101

That it is! Thank you very much for your help, sir.