Kinetic and potential energy, conversion by falling
Ek = ½ m v²
The two energies of the chapter and their conversion. Kinetic energy runs from speed to energy or from energy back to speed; potential energy from height to energy or the reverse, relative to the reference zero you choose; and the fall mode applies conservation of mechanical energy to its most taught case, where mass cancels and the landing speed is √(2gh) for the feather as for the hammer. Gravity is adjustable, Earth, Moon or Mars, and every result recalls the lesson of the square: doubling the speed quadruples the energy.
385864 J
- Calculation
- Ek = ½ × 1000 × 27.78² = 385864 J
At 27.78 m/s, this body carries 385864 J of kinetic energy.
Kinetic energy grows as the square of the speed: doubling the speed quadruples the energy, hence the braking distance. Going from 50 to 100 km/h does not double the danger, it quadruples it. That is road safety in one equation.
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulasEk = ½ m v²
Ek = ½ m v²
Ep = m g h
Em = Ek + Ep
frictionless fall: v = √(2gh)
Mechanical energy, the sum of the two, is conserved as long as no friction does work: what is lost in height is found in speed, exactly. In the equality mgh = ½mv², the mass cancels, and out comes the most counter-intuitive result of the chapter: fall speed does not depend on mass.
- Ek
- · kinetic energy, that of motion, in joules.
- Ep
- · gravitational potential energy, that of position, relative to a chosen zero.
- Em
- · mechanical energy, the sum of both: the conserved quantity.
- g
- · gravity: 9.80665 m/s² on Earth (exact conventional value), 1.62 on the Moon, 3.72 on Mars.
- Joule
- · the unit of energy: lifting an apple by one metre, roughly.
Validity domainThe fall mode assumes frictionless free fall: in air, part of the energy leaves as heat and the real speed is lower, the more so the longer the fall and the lighter the body; a leaf does not follow the formula, a steel ball over a few metres follows it very well.
The fall mode assumes frictionless free fall: in air, part of the energy leaves as heat and the real speed is lower, the more so the longer the fall and the lighter the body; a leaf does not follow the formula, a steel ball over a few metres follows it very well. The formulas hold for speeds far below light and a uniform gravity field, that is, heights small against the planet’s radius. Speed is taken as an absolute value, kinetic energy depending only on its square.
Reading the resultThe square of the speed is the reading that matters: going from 50 to 100 km/h quadruples the energy to dissipate when braking, and a crash at 100 equals four crashes at 50.
The square of the speed is the reading that matters: going from 50 to 100 km/h quadruples the energy to dissipate when braking, and a crash at 100 equals four crashes at 50. For potential energy, only the height difference has physical meaning: changing the reference shifts every value without changing any difference, which is why the tool lets you pick your zero instead of imposing one.