Non-Conservative Forces

Energy balance with dissipative non-conservative forces and thermal energy degradation.

General idea of the topic

A force is non-conservative when its work depends on the path followed, such as friction or air resistance. These forces transform mechanical energy into thermal energy, which is not recovered as kinetic or potential energy of the system.

The topic explains the mechanism of dissipation and quantifies it with the work of non-conservative forces, which equals the change in the mechanical energy of the system.

What you will truly understand

By the end you will be able to compute the energy dissipated by friction along a path, use W_nc = ΔE_mech to obtain the final speed and distinguish the work of a driving force from that of a resisting one.

You will also know why two different paths between the same points dissipate different amounts.

Recommended learning route

1. Friction and Dissipation: how friction converts mechanical energy into heat and why its work is always resisting.
2. Work Done by Non-Conservative Forces: balance W_nc = E_final − E_initial applied to bodies that stop, rise or descend with friction.

Physical criterion you must acquire

The essential criterion is that the work of kinetic friction is −μN·d, with d the length traveled, not the net displacement. Static friction in rolling without slipping does not dissipate. If the final mechanical energy turns out greater than the initial one without driving forces, there is a sign error.

Connection with real problems

• vehicle braking.
• parachutes and air resistance.
• machines with friction losses.
• dissipation in shock absorbers.

Final goal of the topic

The final goal is to include non-conservative forces correctly in the energy balance and quantify the mechanical energy that is lost.