# Energy Question.

1. Sep 15, 2006

### 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?

2. Sep 15, 2006

### 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.

Last edited: Sep 15, 2006
3. Sep 15, 2006

### 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.

4. Sep 15, 2006

### 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 shouldnt 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.

5. Sep 15, 2006

### neutrino

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

6. Sep 15, 2006

### MathematicalPhysicist

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

7. Sep 15, 2006

### neutrino

That's correct.

8. Sep 15, 2006

### MathematicalPhysicist

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

9. Sep 15, 2006

### 0rthodontist

Yes, but you have to find x.

10. Sep 15, 2006

### MathematicalPhysicist

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

11. Sep 16, 2006

### MathematicalPhysicist

can someone please tell me if im right here?