Kinetic & potential energy
In Mechanics, energy usually appears in two forms: energy of motion and energy of position in a gravitational field. The formulae are short; the important step is deciding which energy changes during the motion.
Kinetic energy depends on speed squared
Symbols
- = mass (kg)
- = speed (m s⁻¹)
- = kinetic energy (J)
- Kinetic energy uses speed, so it is never negative.
- Two equal speeds in opposite directions give the same kinetic energy but opposite momenta.
- Doubling the speed multiplies kinetic energy by four.
- A change is always final minus initial: .
Common mistake
Gravitational potential energy uses vertical height change
Symbols
- = mass (kg)
- = acceleration due to gravity; use 10 unless told otherwise (m s⁻²)
- = final vertical height minus initial height (m)
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- A rise gives positive and a gain in GPE.
- A fall gives negative and a loss in GPE.
- Moving distance along a slope of angle changes height by , not by .
- Any convenient zero level may be chosen, but every GPE value in one solution must use the same datum.
Read a story as changes, not isolated formula substitutions
Worked example
A body speeds up while climbing
A 4 kg body speeds up from 3 m s⁻¹ to 7 m s⁻¹ while rising 5 m.
Its mechanical energy has increased by J. Some external agent must have supplied at least that much energy; more would be needed if resistance were present.
When asked for an increase or decrease, write “final minus initial” before inserting numbers. This prevents the common reversal of and .
A 2.5 kg particle moves from point A to point B. Its speed changes from 8 m s⁻¹ to 4 m s⁻¹ and B is 3 m above A. Find the change in kinetic energy, the change in gravitational potential energy and the change in total mechanical energy.