Suppose that 2 Joules of work is needed to stretch a spring from its natural length of 35 cm to a length of 54 cm. How much work is needed to stretch it from 50 cm to 55 cm?
First change cm to m.
W = the integral from Xi to Xf of kx dx
so W=(1/2)k(Xf^2) - (1/2)k(Xi^2)
So solve for k
2=(1/2)(k(.54^2) - k(.35^2))
them solve for W with your new k value but with a different distance
W=(23.6546/2)(.55^2 - .50^2)
But the answer is wrong....