# Mechanics Elastic springs question

A particle of mass m is attached to one end of an elastic spring of natural length l and modulous lambda ..The particle and spring rest on a rough horizontal surface and the other end of the spring is fixed..Th coefficient of friction is mu .the particle is held at rest with the spring compressed to a length 2/3l and then released.Show that the particle is instamtenously at rest when it has a moved a distance x where,..lambda=Y,mu=P
$x=\frac{2Yl-6Plmg}{3Y}$

Can some one check if my assumptions are right?..

First of all they want me to show the velocity is 0..
I use conservation of energy
$\frac{Yl}{18}=\frac{Yx_1^2}{2l}+\frac{1}{2}mv^2$
where $x_1=\frac{2Yl-6Plmg}{3Y}-\frac{l}{3}$
After that I get into big muddle as they don't equal to 0
thanks.

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Redbelly98
Staff Emeritus
Homework Helper
Can some one check if my assumptions are right?..

First of all they want me to show the velocity is 0..
I use conservation of energy
$\frac{Yl}{18}=\frac{Yx_1^2}{2l}+\frac{1}{2}mv^2$
where $x_1=\frac{2Yl-6Plmg}{3Y}-\frac{l}{3}$
After that I get into big muddle as they don't equal to 0
thanks.
Energy is not conserved here, because of the friction. However, the energy will decrease by an amount equal to the work done by friction.

Energy is not conserved here, because of the friction. However, the energy will decrease by an amount equal to the work done by friction.