# Stretching a Spring

RGBolton95
Hey everyone,

I'm really hoping somebody will be able to help me with this problem. I've searched all through my textbook, notes, and the Internet, but I keep getting the wrong answer. Here's the question:

If it requires 6 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 cm?

I start by finding k, the spring constant. I do this by using the equation W = 1/2kx^2. I plug in the known values of work and x in the equation, which gives me 30,000 Nm (I changed 2 cm to 0.02 m). Now that I know k, I find the total work to pull the spring down 0.06 m (the original 0.02 m plus the additional 0.04 m). I use the same W = 1/2kx^2 equation, with W being the unknown, k = 30,000 Nm, and x = 0.06. This gave me a W = 54 J. From there, I know that to find the additional work needed to pull down the spring from 0.02 m to 0.06 m I should just subtract 6 J from 54 J, which gives me a final answer of 48 J. However, I keep getting told that this is the wrong answer. Any idea where I'm making my mistake?

Orodruin
Staff Emeritus
Homework Helper
Gold Member
$$2W_2 = k x_2^2 = k(3x_1)^2 = 9kx_1^2 = 18W_1$$