Calculating Energy Stored in a Two-Spring System

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The discussion focuses on calculating the energy stored in a two-spring system with a particle and an additional mass. The first spring supports a total weight of 7m, while the second spring supports only 3m. The user initially struggled with integrating the force equations for both springs due to the different extensions. Ultimately, they realized that the problem could be simplified by recognizing the distinct forces acting on each spring. The issue was resolved with guidance, leading to a clearer understanding of the energy calculations involved.
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Homework Statement



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

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

Homework Equations


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 don't 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.

Homework Statement


Homework Equations


The Attempt at a Solution

 
Last edited by a moderator:
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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.
 
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.
 

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