Energy Bar Charts

A force diagram tells you what's pushing on an object right now. An energy bar chart tells you the whole story of a process: what kind of energy the system had at the start, what kind it has at the end, and whether anything from outside added or removed energy in between. Because the total height of the bars must be the same before and after, you can often find a missing speed or height without ever touching Newton's second law. That's the payoff: energy bookkeeping turns a messy multi-step force problem into simple arithmetic.

To build the chart, first choose your system. Draw one column of bars for the initial state and one for the final state, with separate bars for kinetic energy, gravitational potential energy, elastic potential energy, and so on, each bar's height representing that energy's value. If a force from outside the system does work during the process, you add a work bar between the two columns, positive if it adds energy, negative if it removes energy, like friction draining energy as heat. A ball dropped from a roof, with gravity treated as part of the system, needs no work bar at all: it starts as pure potential energy and ends as pure kinetic energy of equal total height.

This same chart is just a picture of the work-energy theorem and conservation of energy from earlier in the unit, so switching between equations and bar charts should feel like translating, not relearning. The one rule that makes it all work: no bar can appear or vanish between the two columns on its own. Every change in total height must be accounted for by a work bar crossing the system boundary from outside.