Work, Energy, and Power (Grade 12 NSC Matric Physical Sciences): Revision Notes

Conservation of Energy

What is a conservative force?

A conservative force is a special type of force where the work done depends only on where you start and where you finish - not on the path you take to get there. This is a fundamental concept that helps us understand how energy behaves in physical systems.

The most important example of a conservative force is gravity. Whether you walk up a mountain via a gentle winding path or climb straight up a cliff face, gravity does exactly the same amount of work on you. The only thing that matters is the change in height.

When a conservative force acts on an object, we can define something called potential energy for that force. The work done by a conservative force is always equal to the negative change in potential energy:

$W_{\text{conservative}} = -\Delta E_p$

Understanding work done by gravity on slopes

Let's examine how gravity works when objects move along different inclined surfaces. Consider pushing a ball up several slopes of different angles, all reaching the same height $h$.

The diagram shows three different slopes with the same vertical height. Using trigonometry, we can see that $\sin \alpha = h/d$ for each slope, where $d$ is the length of the slope and $\alpha$ is the angle.

When analysing forces on an inclined plane, we need to consider the components of gravitational force:

The component of gravitational force parallel to the slope is $F_{gx} = F_g \sin \alpha$. When we push an object up the slope against gravity, the work done by gravity is:

$W_g = -F_g \cos \theta = -(F_g \sin \alpha) \times d = -F_g \times \frac{h}{d} \times d = -F_g h$

This diagram illustrates how different paths between the same two points result in the same work done by conservative forces.

What is a non-conservative force?

A non-conservative force is one where the work done depends on the specific path taken by the object. The most common example is friction.

Unlike conservative forces, non-conservative forces cannot have potential energy defined for them. When non-conservative forces do work, mechanical energy is typically converted to other forms like thermal energy, which cannot be easily recovered.

Effects of friction

This image shows a real example of friction in action - a football player sliding on grass, where friction gradually slows down the motion.

Work-energy theorem with non-conservative forces

When both conservative and non-conservative forces act on an object, we can derive a powerful relationship. The total work done by all forces equals the change in kinetic energy:

$W_{\text{net}} = W_{\text{conservative}} + W_{\text{non-conservative}}$

Since $W_{\text{conservative}} = -\Delta E_p$, we can substitute:

$\Delta E_k = -\Delta E_p + W_{\text{non-conservative}}$

Rearranging this equation gives us:

$W_{\text{non-conservative}} = \Delta E_k + \Delta E_p$

This is the work-energy theorem for systems with non-conservative forces. It tells us that the work done by non-conservative forces equals the change in total mechanical energy of the system.