Question

If you were to double the compression of a spring, what effect would that have on the force required to produce this change?

If you were to double the compression of a spring, what effect would this have on the energy stored by the spring?

Answer 1

Since F = k.x here F is applied force , k is force constant and x is compression.

Here we see force is direcldi proportional to compression .

Hence we have to doubled the applied force to double the compression.

Mathematically , F' = k.(2x) = 2kx

=) F' = 2F

Now for stored energy ,

Since U = 1/2 .kx^2

That means stored energy U is directly proportional to square of compression x

Hence on doubling the compression, stored energy will be 4 times of initial stored energy.

=) U' = 4U .