Why does work by conservative forces equal zero when potential energy doesn't change?

[ikjadoon]

Homework Statement

Work done by conservative forces = -$$\Delta$$U

Homework Equations

Above.

The Attempt at a Solution

Here is the whole equation:

W_c+ W_nc = $$\Delta$$K.

W_nc = $$\Delta$$K + $$\Delta$$U.

So, W_c = -$$\Delta$$U.

But, for example, how does that apply in a situation with no potential energy changes, but still with work done by conservative forces?!

Example: a block slides across a horizontal, flat table and comes to rest due to friction. There was no change in gravitational or spring-related potential energy (the only two forms of potential energy I can think of). However, there was work done (50J or whatever) by friction on the block. Thus, 50J = 0J! There is no change in potential energy, but there was work done by conservative forces.

Where did I go wrong?

Thanks,

~Ibrahim~

 

[PhanthomJay]

Why did you assume that friction was a conservative force? either one of your first 2 equations would be OK to use. The third one says that since there was no potential energy change, there was no work done by conservative forces (no work done by gravity, springs, or other conservative forces).

 

[ikjadoon]

Oh, crap.

Friction is a non-conservative force: it depends on the path.

There are no conservative forces acting, only non-conservative (friction).

0J = 0J.

Got it. Thanks for the solution, however simple!

~Ibrahim~