Mechanics · Quick Reference

Energy Cheat Sheet

Mechanics · Lesson 10/19

In one line: energy is the capacity to do work — it comes in many forms, and one of physics' most powerful ideas is that total energy is always conserved, even as it changes form.

Key Ideas

1Kinetic Energy (KE). The energy of motion: KE = (1/2)*m*v^2.

2Potential Energy (PE). Stored energy due to position or configuration; gravitational PE = m*g*h, where h is height above a reference point.

3Conservation of Energy. In a system with no external losses (like friction), total mechanical energy (KE + PE) stays constant, even as it converts between forms.

4Energy Transformations. Energy constantly converts between forms -- a falling object converts PE into KE; a pendulum swings between KE and PE at each end and midpoint of its swing.

5Units of Energy. Measured in joules (J), the same unit as work, since work is the transfer of energy.

Worked Examples

Find the kinetic energy of a 4 kg object moving at 5 m/s.

50 J

Find the potential energy of a 3 kg object held 10m above the ground (g=10 m/s^2).

300 J

A 2 kg ball is dropped from a height of 5m (g=10). Use energy conservation to find its speed just before hitting the ground.

v = 10 m/s

Formulas

KE = (1/2)*m*v^2

PE = m*g*h

Total mechanical energy = KE + PE (conserved without friction)

Practice Yourself

Find KE of a 2 kg object at 10 m/s.

100 J

Find PE of a 5 kg object at height 4m (g=10).

200 J

A ball is dropped from 20m (g=10). Find its speed at the bottom using energy conservation.

v^2=2*10*20=400, v=20 m/s