Calculating Mechanical Energy Loss in Block-Spring System

[MathematicalPhysicist]

a block of mass M slides along a horizontal table with speed v0 at x=0 it hits a spring with spring constant k and begins to experience a friction force. the coefficient of friction is variable and is given by u=bx where b is a constnat.
find the loss in mechanical energy when the block has first come momentarily to rest.

i got to this equation (im not sure it's correct):
fx+kx^2/2-mv0^2/2
is this correct?

 

[StatusX]

1) That is not an equation.
2) What is fx?
3) Energy is not conserved (edit: you could probably still do it this way)

Just try finding all the forces and then finding and solving the resulting differential equation.

 

[0rthodontist]

Another way to do it, you could:
1. Find the distance it takes to stop
2. Since friction is the only non-conservative force acting on the block, find the work done by friction over that distance.

 

[MathematicalPhysicist]

fx is the is the work done by the friction force over the displacement x.

so by orthodontist the loss of mechanical energy equals the work of friction.
but shouldn't the equation be:
W_f=E_0-E_v0=kx^2/2-mv0^2/2
then what is the equation of the loss of ME.

 

[neutrino]

What's the work done by friction? (not fx, but in terms of the coefficient of friction)

 

[MathematicalPhysicist]

f=bxmg
then the work equals bmgx^2/2

 

[neutrino]

That's correct.

 

[MathematicalPhysicist]

is this answer to my original question, the loss of M.E is the work done by the friction on the block.

 

[0rthodontist]

Yes, but you have to find x.

 

[MathematicalPhysicist]

then i should use the equation i typed on post #4, right?

 

[MathematicalPhysicist]

then i should use the equation i typed on post #4, right?

can someone please tell me if I am right here?