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**Problem and Data**

three masses conected m1= 800g, m2 =1100g m3=1200g. m2 rest on a table of coefficient μ=0.345. m1 and m3 hang vertically over frictionless/massless pulleys. The system is released from rest. Whats the velocity of m3 after falling 60.0cm

P.S "i know this system can be solve with finding tension and such, but i have to use energy conservation method."

## Homework Equations

W(work)= ΔK+ΔUg(potential gravitational)+ΔUs(Spring energy)

## The Attempt at a Solution

The velocity for m3 would be the same for all three masses because they are connected by a string. There's no k (initial) and spring energy involved.

This is what i have gotten so far;

I made a system of equations for each body:

Δy i defined as the change of height for potential energy.

m1;

W= (1/2)m1v^2+ m1gΔy

m2;

W= (1/2)m2v^2

m3;

W=(1/2)m3v^2-m3gΔy (the minus from negative displacement in height(Δy))

Im not sure about the following, i think I am missing something;

"

*I also know that the system is losing energy by the interaction of M2 w/ the surface of the table...friction.

so friction(f)= N(normal)*μ(K).

In other words: f=m2*g*μ

and Work is also =f*r(displacement by the force)* cos (θ)

θ being the angle between the force and the displacement."

I'm just not sure how to related the energy lost W on all three bodies

Thanks for any input or help you guys can provide on my problem.

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