# Springs and Mechanical Energy

1. Oct 20, 2013

1. The problem statement, all variables and given/known data
When a .5kg mass is suspended from a spring, the spring stretches 4cm. The mass is then displaced 2cm from its equilibrium position and released.
(a) What is the spring constant? (b) What is the mechanical energy of the mass? (c) What is the speed of the mass as it passes through its equilibrium position going down and going up?

2. Relevant equations
F=kx (k is spring constant)
W= .5(k)x2
KE= .5mv2

3. The attempt at a solution
For part A I used F=kx:
mg=kx
(.5kg)(9.8m/s2) = k (.04m)
k= 122.5N/m

For part B I used W= .5kx2:
W= .5(122.5N/m)(.02m)2
W= .025J

For part C I used KE = .5mv2
.025J = .5(.5kg)v2
v= .32m/s

I just need to make sure that I'm on the right track with this problem. I can get confused as to when to use .04m and .02 and generally with using formulas.

Last edited: Oct 20, 2013
2. Oct 20, 2013

### Zondrina

How much gravitational energy is there when the mass is displaced 2cm = 0.002m from its equilibrium position? Hint: The spring originally stretched 0.0004m when the mass was suspended.