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?

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

Given the following data:

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:

Where:

Substituting the given parameters into the formula, we have;

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:

Work = 45 Joules

For an extension of 6 cm;

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

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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

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

40 J