When we talk about non-conservative forces, it’s important to know how they do work in a physical system.

Unlike conservative forces, which can store energy (like gravity or a spring), non-conservative forces don’t store energy in a way that you can fully get back.

Here are some common situations where non-conservative forces show up:

1. Frictional Forces: A great everyday example of a non-conservative force is friction. Imagine you slide a book across a table. Friction works on the book and turns its moving energy into heat. Once the book stops, that energy is lost as heat and can't be used again.

2. Air Resistance: This force acts like friction but happens in air. For example, when a skydiver jumps out of a plane, air resistance pushes against them as they fall. While gravity is helping them fall, air resistance slows them down. This reduces the skydiver's speed until they reach a steady fall, called terminal velocity.

3. Tension in a Rope During a Swing: Think about a pendulum swinging back and forth. The tension in the rope can do non-conservative work based on how it moves and changes energy. If the swing loses energy because of air resistance or if the rope causes it to twist, that shows non-conservative work.

4. Applied Forces: When you push something, like a car, you’re using non-conservative work. This isn't just about moving potential energy around. Instead, you are changing the car’s state, which often includes fighting against friction and creating heat.

In simpler math terms, we can show non-conservative work as:

$W_{nc} = \Delta KE + \Delta PE$

Here, $W_{nc}$ represents the work done by non-conservative forces. $\Delta KE$ is the change in moving energy, and $\Delta PE$ is the change in stored energy. This helps show how energy changes forms and isn’t just shifted around like in systems with conservative forces.

Understanding these forces and when they happen is important for looking at real-life situations where energy isn't always kept in its original form.