Friction and the non-conservation of mechanical energy

When mechanical energy is no longer conserved

As soon as a non-conservative force acts on a system, such as friction (solid or fluid, e.g. air resistance), mechanical energy is no longer constant: it decreases as the system moves. This energy is not destroyed; it is transferred into another form, mainly heat.

Energy balance

The change in mechanical energy is therefore equal to the work done by the frictional forces, which is negative (as these forces always oppose the motion):

Em(final) – Em(initial) = W(friction), where W(friction) ≤ 0

Example

A skier of mass 70 kg is skiing down a slope subject to friction. If they lose 500 J of mechanical energy due to friction over the entire descent, this energy has been converted into heat in the skis and the snow.

Limit case: constant velocity

If an object moves at constant velocity on a horizontal plane subject to friction, its potential energy (Ec) does not change, but its kinetic energy (Em) still decreases because a driving force constantly compensates for the friction (energy is supplied and dissipated simultaneously).

Pitfalls to avoid

• Believing that energy disappears: it is transformed, notably into heat.
• Forgetting that Ep can remain constant (horizontal motion) whilst Em decreases due to friction acting on Ec.
• Confusing the sign of the work done by friction (always negative or zero in the direction of motion).