Finding the change in length of a nylon string

[tjohn101]

Homework Statement

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

Homework Equations

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

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!

 

[rock.freak667]

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


what units are E in?

 

[tjohn101]

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


what units are E in?

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

 

[rock.freak667]

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

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.

 

[tjohn101]

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.

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. : )

 

[rock.freak667]

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?

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

 

[tjohn101]

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

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

 

[rock.freak667]

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

1.802481745 what unit is this in?

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

 

[tjohn101]

1.802481745 what unit is this in?

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

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.

 

[rock.freak667]

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.

then 1.802481745cm should be it.

 

[tjohn101]

then 1.802481745cm should be it.

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