A force of 30 N is required to maintain a spring stretched from its natural length of 12 cm to a length of 15 cm. How much work is done in stretching the spring from 12 cm to 20 cm?

Question

Mathematics

Butter

18 January, 20:55

A force of 30 N is required to maintain a spring stretched from its natural length of 12 cm to a length of 15 cm. How much work is done in stretching the spring from 12 cm to 20 cm?

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Julius Sloan · Answer 1

3.2 J

Step-by-step explanation:

It is convenient to use newtons and meters for the units when calculating work.

The spring constant (k) is ...

k = (30 N) / (15 cm - 12 cm) = (30 N) / (.03 m) = 1000 N/m

For some displacement d, the work done in stretching the spring is ...

W = (1/2) kd^2 = (1/2) (1000 N/m) (.08 m) ^2 = (1/2) (1000) (.0064) Nm

= 3.2 J

3.2 joules of work is done stretching the spring.