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If it requires 5.0J of work to stretch a particular spring by 2.0cmfrom its equilibrium length, how much more work will be required tostretch it an additional 4.0cm?

Respuesta :

jcherry99

Formula

E = 1/2 k * x^2 for a spring.

E = 5

k = ??

x = 2 cm = 2 * [1 m / 100 cm] = 0.02 m

5 = 1/2 k * 0.02^2      Multiply both sides by 2

10 = k * 0.0004

k = 10/0.0004

k = 25000 J/m^2

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x = 6 cm = 6 cm * [1 m/100 cm = 0.06 m

E =1/2 k * 0.06^2

E = 1/2 25000 * 0.0036

E = 45 J

But you had 5 joules which you have to account for.

You need (45 - 5) = 40 Joules to go the extra 4.0 cm

Answer: 40 J

Lanuel

The amount of work required to stretch the string an additional 4.0 cm is 40 Joules.

Given the following data:

  • Work = 5.0 Joules
  • Extension = 2 cm to meters = [tex]\frac{2}{100}[/tex] = 0.02 meters.

To find how much more work will be required to stretch it an additional 4.0 cm:

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

[tex]Work = \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]5 = \frac{1}{2} K(0.02^2)\\\\5 = \frac{1}{2} K(0.0004)\\\\10 = 0.0004K\\\\K = \frac{10}{0.0004}[/tex]

Spring constant, K = 25,000

Stretching it an additional length of 4.0 cm, makes its extension equal to 6.0 cm.

Now, we would find the work required for the above extension:

[tex]Work = \frac{1}{2} (25000)(0.06^2)\\\\Work = 12500(0.0036)[/tex]

Work = 45 Joules

For an extension of 6 cm;

[tex]Work = 45 - 5\\\\ Work = 40 Joules[/tex]

Therefore, the amount of work required to stretch the string an additional 4.0 cm is 40 Joules.

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