# Springs and Mechanical Energy

## Homework Statement

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?

## Homework Equations

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

## 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.

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## Answers and Replies

Homework Helper
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.