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Finding the change in length of a nylon string

  • Thread starter tjohn101
  • Start date
  • #1
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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!
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
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[tex]\Delta L = \frac{FL}{AE}[/tex]


what units are E in?
 
  • #3
93
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[tex]\Delta L = \frac{FL}{AE}[/tex]


what units are E in?
I've been trying to find the equation in latex... :/ E is in N/m^2.
 
  • #4
rock.freak667
Homework Helper
6,230
31
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.
 
  • #5
93
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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. : )
 
  • #6
rock.freak667
Homework Helper
6,230
31
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
 
  • #7
93
0
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
 
  • #8
rock.freak667
Homework Helper
6,230
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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.
 
  • #9
93
0
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.
 
  • #10
rock.freak667
Homework Helper
6,230
31
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.
 
  • #11
93
0
then 1.802481745cm should be it.
That it is! Thank you very much for your help, sir.
 

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