A student pushes a heavy crate across a warehouse floor at a constant velocity. Explain why the student must apply a continuous force to keep the crate moving at constant velocity, and describe the energy transfers that occur during this process.

The crate is moving at a constant velocity, so by Newton’s first law the net horizontal force on it must be zero. The rough concrete floor exerts a kinetic friction force that acts opposite to the direction of motion. Therefore the student must apply a horizontal force equal in magnitude to the friction force to keep the net force zero.

While the crate moves, the student’s hand does work on the crate: (W=F,d). This work is transferred as mechanical energy to the crate. Because the crate’s kinetic energy does not change (velocity is constant), the energy supplied by the student is not stored as kinetic energy but is dissipated by the frictional interaction between the crate and the floor. The friction converts the mechanical energy into thermal energy, raising the temperature of the crate, floor and the student’s hand.

Thus the continuous applied force balances friction, allowing constant velocity, and the energy supplied by the student is ultimately lost as heat due to friction.