# Energy stored in springs

1. Sep 22, 2009

### Skuzzy

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

A particle (4m) is suspended from a fixed point by a spring of stiffness k and natural length l0. An identical 2nd spring is attached to this particle, and a mass (3m) is attached to its end. The system hangs vertically in equilibrium.
Take the datuim of P.E. a in each spring to be the natural length of that spring.

http://img176.imageshack.us/img176/2653/2springsytem.jpg [Broken]

Write down the an equation for the energy stored in the two springs.

2. Relevant equations

3. The attempt at a solution

Spring 1, exerts force H1=k(x1-l0)i

it supports both particles so W1=7mgi

Spring 2, exerts force H2=k(x2-l0)i

it supports only the lower particle so W2=3mgi

The energy function U(x) = - $$-\int(F(x)) dx$$

I dont know how to proceed: Should I be integrating 2 equations for the force? Don't I need 'x' in F(x) to be the same in both cases? Have I just got myself in a muddle and am thinking about this all the wrong way?

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

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 4, 2017
2. Sep 22, 2009

### kuruman

Can you find how much energy is stored in a spring if it stretches by amount x?
Can you find how much a spring stretches by if you hang mass m from it?
The bottom spring has mass 3m hanging from it.
The top spring has mass 7m hanging from it.

Put it together.

3. Sep 25, 2009

### Skuzzy

I managed to make this way more complicated for myself than it needed to be... thanks for the help.

i had been trying to come up with a single equation but with two unknown extensions i was getting myslef in a quite a muddle.

SOLVED. thanks.