## How to understand the work-energy theorem?

How to understand the work-energy theorem?

I took a short lecture on physics for engineering last week. The lecturer emphasized that the work done on an object will cause the kinetic energy change as

$$W = Delta text{KE}.$$

I know this concept might be so common to you but to me, as a beginner, it is pretty hard to understand the reason. My understanding is that ‘work’ is the energy an external object ‘injects into’ the object or is the energy an external object ‘takes away’ from the object. I think the work done by the object should equal to the total energy changed on that object, which could be in any form (heat, potential or kinetic energy.) Why does the theorem only explicitly refer to kinetic energy? Will this theorem work in some cases or in all cases?

The total work can be split up into two parts:

$$W_{net} = W_{conservative}+W_{non-conservative}.$$

With the

conservativepart you can associate a potential energy:$$W_{conservative}=-Delta PE$$

(this is in fact the

definitionof a conservative force) so that the Work-Energy theorem becomes$$W_{non-conservative}=Delta KE + Delta PE = Delta E.$$

This is another way of writing the Work-Energy theorem and in my mind it’s a little bit clearer. Restated, the work done by non-conservative forces is equal to the overall change in energy of the system.

For example, work done by friction is negative, so it dissipates energy away from a system.

On the other hand, gravity is a conservative force. Imagine the motion of a falling ball. Unless something doing work on the ball to slow it down (for example, air) the ball will speed up as it falls. In this case, the equation

$$W_{gravity} = -Delta PE = Delta KE$$

is equivalent to that statement. (As the potential energy becomes more negative, kinetic energy becomes more positive.)