# What does unstretched/natural length mean?

1. Jul 27, 2011

### flyingpig

1. The problem statement, all variables and given/known data

A spring with a spring constant k = 50 N/m has an unstretched length of 20cm. Find the work required to stretch the spring to a length of 30 cm.

3. The attempt at a solution

It feels like some measurement to the equilibrium point, but i can't get it right.

Does that mean

[PLAIN]http://img696.imageshack.us/img696/1253/unledcel.jpg [Broken]

Or

[PLAIN]http://img856.imageshack.us/img856/6496/unledovi.jpg [Broken]

Last edited by a moderator: May 5, 2017
2. Jul 27, 2011

### flyingpig

$$\sum W = \int_{x = 0}^{x = 10} -kx dx = \frac{-k}{2}(10^2) = -2500 \cdot 10^{-2} J$$

3. Jul 27, 2011

### ehild

The work done on the spring is the question. If x is the change of the length the external force is F = k x. This is the same with opposite sign as the force of the spring. The net force is zero, so the end of the spring moves with constant velocity. In reality, the work needed is slightly more, as the force has to bring the spring into motion, but it can be ignored if the mass of the spring is very low and/or it moves very slowly.

ehild