# Definition of Work

My mechanics textbook defines work such that it involves a force that is exerted as the point of application moves through some distance. I'm confused how to apply this definition.

Suppose you slide your hand across a table, such that friction exerts a force on the table but the table remains stationary due to external forces. If the work is based on the motion of the point of application, it appears that the point of application moves, so work from the hand on the table should be nonzero. However, the table has no change in kinetic energy, and external forces (for example, a static friction between the table and the floor) also exert zero work since the point of application on those external forces do not move, so the work due to the hand on the table should be 0. How do I resolve this?

• Yes, it would probably be more correct to say that work involves forces on specific particles, when those specific particles move through a distance. It's always particles moving. A "point of application" moving like in your example doesn't count, that just means which particles are primarily getting pushed is changing over time. Jan 20, 2022 at 5:23

## 1 Answer

First, consider the hand: The force of friction on the hand is acting in the opposite direction of the hand’s velocity. (Specifically the velocity of the material of the hand where the force is applied) So the mechanical work is negative meaning that mechanical energy is leaving the hand.

Next, consider the table: the force of friction on the table is equal and opposite to the force of friction on the hand, by Newton’s 3rd law. However, the table is motionless (specifically the material of the table where the force is applied), there is no mechanical work done on the table. Mechanical energy is not entering the table.

So we have mechanical energy leaving the hand but not entering the table. This mechanical energy is lost and becomes heat generated at the interface between the hand and the table. It then moves into the hand and the table according to the laws of thermodynamics and based on their respective temperatures and other thermodynamic properties.

• Does this mean that it doesn't matter that the point of application of the frictional force moves, because the table as a whole is not moving? Jan 20, 2022 at 5:03
• What matters is the motion of the material at the point of application of the force. I will be more specific in the answer
– Dale
Jan 20, 2022 at 5:13
• We are consider force/ work on table. So consider displacement of point on table Jan 20, 2022 at 5:17