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Power of engines and climbers
Intermediate
Power needed to lift a body at constant speed.
P = mgvClimbing steadily at speed v needs P = mgv (plus losses). Engine power at constant speed balances drag: P = Fv.
An 80 kg climber ascending 1 m/s needs 784 W of mechanical power.
Hill climbing power depends on vertical speed only.
In more detail
The power of a person climbing stairs or an engine lifting a load is the rate of change of gravitational potential energy. For steady climbing, P = mgv.
Real-world uses
- Estimating the power output of an athlete climbing a flight of stairs quickly.
- Crane specifications state the power needed to lift a given load at a set speed.
- A cyclist climbing a steep hill needs much more power than on the flat, because the energy to rise against gravity is supplied continuously.
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Frequently asked questions
How much power does a person produce?
A fit adult can sustain roughly 100 to 300 watts for an extended period, depending on fitness.
Does climbing faster need more power?
Yes, power is proportional to speed for a fixed load.
Why does power depend on mass when climbing?
Lifting a heavier body at the same speed needs more force, so the rate of doing work and the power are higher.
Related topics in Work, Energy & Power
Units of power · Efficiency · Energy and power bills · Escape from a potential well · Work in rotation · Rotational kinetic energy