INCOMPLETE -- How to Solve Most Energy/Work Problems

NOTE: THIS IS INCOMPLETE, please let me know if you'd like me to finish writing it, or just explain it to you in-person :)

I'm very frustrated with how they teach you to solve energy/work problems — ESPECIALLY the confusing mess on your formula sheet.

Here's a significantly more formulaic, straightforward, and easy-to-remember approach.

[1] Steps⚓︎

Start with the basic equation:

\[K_i + \Delta K = K_f.\]

Where does this come from?

Recall that "delta" (\(\Delta\)) is just a mathematical symbol that indicates the change in some quantity.

For example, we write a "change in position" as \(\Delta x = x_f - x_i\).

Apply the same idea to "kinetic energy" to get \(\Delta K = K_f - K_i\). Rearrange this to get \(\boxed{K_i + \Delta K = K_f}\).

I like putting it in this form because it lets you think of problems in terms of the "story of energy":

\(K_i\) — Is the object moving at the start?
\(\Delta K\) — What's pushing/pulling on the object over the course of its journey? (I'll explain this later on)
\(K_f\) — Is the object moving at the end?

It's easy to expand \(K_i\) and \(K_f\):

Case	\(K\)
Problem states/implies object is still	\(0 \ \rm{J}\)
Problem tells you the velocity of the object	Plug into \(\frac{1}{2}mv^2\)
Problem asks you to find the velocity of the object	Write in symbolic form \(\left( \frac{1}{2}mv^2 \right)\) and move on

But \(\Delta K\) is a little more involved.