If 20 J of work is done in compressing a spring from 0 cm to 6 cm, then find the work done in compressing the same from 3 cm to 6 cm.

Question

My solution
If 0.5kx^2= 20, & newx=0.5x,
Should the work done be (0.5kx^2)/4=5 joules ? Pls explain. Thanks.

Answer 1

compressing 0 cm to 6 cm is equivalent to compressing 0 cm to 3 cm, and continuing to compress 3 cm to 6 cm

although the compression lengths are the same for the two parts, the 2nd part takes more work because the resistance of the spring increases with compression

0 to 6 uses 20 J

0 to 3 (with the same starting point) is half the compression, so it takes a quarter of the work...5 J

this means the 3 to 6 compression takes 15 J (20 - 5)