Frictional Work

Defining a system for a block sliding across a table with friction, where friction is an Internal Force our normal equation might be:

However, force of friction will cause a change in energy to the system, so a Work from friction is applied. We may be tempted to define this work as:

But because this equation is for particles moving in one dimension with a constant force, it is incorrect. Furthermore, friction is not a Conservative Force, so the path the block takes matters. Taking into account the changes in Energy as a result of friction:

is a positive quantity, since the block heats up as it is dragged across the table, gaining energy. The work derived from our previous equation is actually larger than our current equation.

Think of this as the block capturing some of the energy as it is moved.

This is an oversimplified description of friction, so we will not go further than this for now.