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calculate the workdone to stretch an elastic string by 40cm if a force of 10N produces an extension of 4cm in it

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skyluke89
The force of F=10 N produces an extension of
[tex]x=4 cm=0.04 m[/tex]
on the string, so the spring constant is equal to
[tex]k= \frac{F}{x}= \frac{10 N}{0.04 m}=250 N/m [/tex]

Then the string is stretched by [tex]\Delta x=40 cm=0.40 m[/tex]. The work done to stretch the string by this distance is equal to the variation of elastic potential energy of the string with respect to its equilibrium position:
[tex]W= \Delta U= \frac{1}{2}k(\Delta x)^2 = \frac{1}{2}(250 N/m)(0.40 m)^2=20 J [/tex]
Lanuel

The amount of work that would be required to stretch this elastic string by 40 cm is 20 Joules.

Given the following data:

  • Force = 10 Newton
  • Extension = 4 cm to meters = [tex]\frac{4}{100}[/tex] = 0.04 meters.

To find how much work will be required to stretch an elastic string by 40 cm:

First of all, we would determine the spring constant by using the formula:

[tex]F = Ke\\\\10 = k(0.04)\\\\10 = 0.04k\\\\k = \frac{10}{0.04}[/tex]

K = 250 N/m

Mathematically, the work done by a string is given by the formula:

[tex]Work\;done = \frac{1}{2} Ke^2[/tex]

Where:

  • K is the spring constant.
  • e is the extension.

Substituting the given parameters into the formula, we have;

[tex]Work\;done = \frac{1}{2} 250(0.4)^2\\\\Work\;done = 125(0.16)[/tex]

Work done = 20 Joules.

Therefore, the amount of work that would be required to stretch this elastic string by 40 cm is 20 Joules.

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