# Velocity of a spring

1. Feb 16, 2008

### Batman4t

[SOLVED] velocity of a spring

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

A spring is stretched a distance of Dx = 40.0 cm beyond its relaxed length. Attached to the end of the spring is an block of mass m = 8.00 kg, which rests on a horizontal frictionless surface. A force of magnitude 40.0 N is required to hold the block at this position. The force is then removed.

When the spring again returns to its unstretched length, what is the speed of the attached object?
2. Relevant equations

http://wug.physics.uiuc.edu/cc/IAState/Phys221/spring08/course info/FS.pdf

3. The attempt at a solution

change in X=.4m
mass=8kg
F=k*dx
calculated k=100N/m
w=f*dl
work=.5mv^2
v=?
projected v=2m/s

How come 2m/s is not working for my speed did I make an error?

Last edited: Feb 16, 2008
2. Feb 16, 2008

### PhanthomJay

Your problem statement is incomplete. What's the question? At what point are you looking for the speed (if that's the question)? Also, calculating work as the given force of 40N times its displacement is not correct. We can assist further once you clarify the problem and note all givens, and have made another attempt at a solution.

3. Feb 16, 2008

### Batman4t

Sorry, When the spring again returns to its unstretched length, what is the speed of the attached object?

4. Feb 16, 2008

### Batman4t

I solved it:

Using the spring constant that I found:
F(x) = kx

I found the new Work (W) done for the new distance using:

W = (1/2)k(x2)^2 - (1/2)k(x1)^2

Then with the new amount of work done used the equation Wtotal = (delta)K. So...

W(new) = (1/2)m(v2)^2 - (1/2)m(v1)^2

Starting form it's stretched point the velocity is zero so you're just left with

W(new) = (1/2)m(v2)^2

$$\sqrt{2}$$

5. Feb 16, 2008

### PhanthomJay

OK, I see what you may have done, you set the work done by the spring equal to the KE, which is good, but you incorrectly calculated the work. The spring force is variable (it is 0 at the unstretched length), so you can't use a constant 40N as the force...what shouldyou use? Or it is better to use conservation of energy, since only conservative forces are involved..

Edit: OK, you got it.

Last edited: Feb 16, 2008