Question

If it requires 9.0 j of work to stretch a particular spring by 2.0 cm from its equilibrium length, how much more work will be required to stretch it an additional 4.0 cm?

Answer 1

As we know that work done to stretch the spring will be given as

$U = \frac{1}{2}kx^2$

so here we have

$9 = \frac{1}{2}k(0.02)^2$

so we have

$k = 45000 N/m$

now we need to find the work done to stretch the spring from x = 2 cm to x = 4 cm

here we have

$U = \frac{1}{2}k(x_1^2 - x_2^2)$

now we have

$U = \frac{1}{2}(45000)(0.06^2 - 0.02^2)$

$U = 72 J$