The force acting upon the spring to compress it by 3 cm is equal to 20 N. What is the work when compressing the spring

Question

The force acting upon the spring to compress it by 3 cm is equal to 20 N. What is the work when compressing the spring

Answer 1

Hi Gabrielius T.,

So, you are given a force resulting from a specified spring compression. And you know that the work done is the result of the product of the instantaneous force times the distance moved through, integrated over the distance moved through.

Now, you could do this formally -- first find the spring constant (k = 20 N / 0.03 m), then apply that to the expression for the spring force as a function of displacement (F= kx), over the specified interval (= 0 to 0.03 m). But, why bother? The spring force is "triangular" with respect to displacement. So the average force, over the range of 0 to 0.03 m, was 10 N. Just multiply that average by the displacement, therefore (= 10 N * 0.03m) to get the work done on the spring.

Never do more work than you have to (unless you are trying to fatigue that spring to failure in the shortest possible time, and I wouldn't blame you if you did!)

-- Cheers, --Mr. d.