Question

if a spring is compressed 2.0 cm from its equilibrium position and then compressed an additional 4.0 cm, how much more work is done in the second compression than in the first?

Answer 1

Step-by-step explanation:

Work of compressing a spring = 1/2 k x^2

where k is the spring constant and x is the displacement

For 2 cm displacement w = 1/2 k 2^2 = 2k joules

For 4 cm displacement , TOTAL work = 1/2 k 4^2 = 8k joules

but the work was already done compressing it to 2 cm...so subtract that amount from the total 8k - 2k = 6k joules

so work compressing from 0-2 is 2k joules

compressing from 2-4 cm is 6k joules more

or 3 times more as the original work