If it requires 4.0 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?

16J

Explanation:

From hookes law

The work done in a spring is given as W = 1/2ke^2

Given that the force constant (k) is constant in the spring material

We have that 2W = e^2

Let W1 = 4J e1 = 2cm e2 = 4cm

Let W2 be the work required to stretch it an additional 4cm

W1 / W2 = e1^2/e2^2

W2 = W1 * e2^2 / e1^2

= 4 * 4^2 / 2^2

=4 * 16 / 4

= 16J