Mechanics Elastic springs question

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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
[itex]x=\frac{2Yl-6Plmg}{3Y}[/itex]

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
[itex]\frac{Yl}{18}=\frac{Yx_1^2}{2l}+\frac{1}{2}mv^2[/itex]
where [itex]x_1=\frac{2Yl-6Plmg}{3Y}-\frac{l}{3}[/itex]
After that I get into big muddle as they don't equal to 0
thanks.
 

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anyone please?
 
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Redbelly98
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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
[itex]\frac{Yl}{18}=\frac{Yx_1^2}{2l}+\frac{1}{2}mv^2[/itex]
where [itex]x_1=\frac{2Yl-6Plmg}{3Y}-\frac{l}{3}[/itex]
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.
 
  • #4
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Energy is not conserved here, because of the friction. However, the energy will decrease by an amount equal to the work done by friction.
I forgot about friction thanks..
 

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