Aspring has a natural length of 8 m. if a 12-n force is required to keep it stretched to a length of 10 m, how much work w is required to stretch it from 8 m to 16 m? (round your answer to two decimal places.)

The work is required to stretch it from 8 m to 16 m is 192 N-m

Explanation:

Given that,

Natural length = 8 m

Force F = 12 N

After stretched,

length = 10 m

We need to calculate the elongation

Using hook's law

The restoring force is directly proportional to the displacement.

Where, k = spring constant

Negative sign shows the displacement in opposite direction

Now, The value of k is

When stretch the string from 8 m to 16 m.

Then the elongation is

Now, The work is required to stretch it from 8 m to 16 m

Where, k = spring constant

x = elongation

Hence, The work is required to stretch it from 8 m to 16 m is 192 N-m

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