Kinetic and potential energy, conversion by falling
Ek = ½mv² and Ep = mgh both ways, and the fall converting one into the other with v = √(2gh), independent of mass.
Result
385 864 J
- Calculation
- Ek = ½ × 1000 × 27.78² = 385 864 J
Energies
- Kinetic energy
- 385 864 J
- Potential energy
- 0 J
- Total mechanical energy
- 385 864 J
State of the body
- Speed
- 27.78 m/s
- That is, in km/h
- 100.008 km/h
- Height
- 0 m
Notes (2)
At 27.78 m/s, this body carries 385 864 J of kinetic energy.
Doubling the speed quadruples the kinetic energy.
Calculation, assumptions and sources
OverviewKinetic energy is computed from speed or the reverse, gravitational potential energy from height or the reverse, relative to a chosen zero.
Kinetic energy is computed from speed or the reverse, gravitational potential energy from height or the reverse, relative to a chosen zero. The fall mode applies conservation of mechanical energy without friction: the landing speed is √(2gh), whatever the mass. Gravity is adjustable (Earth, Moon, Mars).
Method & formulasEk = ½ m v²
Without friction, mechanical energy is conserved. In the equality mgh = ½mv², the mass cancels and v = √(2gh) does not depend on it.
- Ek
- kinetic energy, in joules.
- Ep
- gravitational potential energy, relative to a chosen zero.
- Em
- mechanical energy, the sum of both, conserved without friction.
- g
- gravity: 9.80665 m/s² on Earth (exact conventional value), 1.62 on the Moon, 3.72 on Mars.
- Joule
- unit of energy.
Validity domainThe fall mode assumes frictionless free fall.
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. The formulas hold for speeds far below that of light and a uniform gravity field, hence heights small against the planet’s radius.
Reading the resultFrom 50 to 100 km/h, the kinetic energy to dissipate when braking quadruples, and so does the braking distance.
From 50 to 100 km/h, the kinetic energy to dissipate when braking quadruples, and so does the braking distance. For potential energy, only height differences have physical meaning: changing the zero shifts every value without changing their differences.