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Energy conservation in free fall
Beginner
Potential energy converts to kinetic energy as an object falls.
v = √(2gh)During a fall potential energy converts to kinetic: mgh = ½mv², so v = √(2gh), independent of mass.
Dropped from 20 m: v ≈ 19.8 m/s.
This ignores air resistance.
In more detail
In free fall, energy conservation gives the speed at any height: ½mv² + mgh is constant. An object dropped from height h hits the ground at v = sqrt(2gh), regardless of mass.
Real-world uses
- Estimating the impact speed of a dropped phone.
- Calculating how fast a diver hits the water from a given height.
- A dropped ball reaches a speed of about 10 m/s after falling 5 metres, which can be checked with energy conservation.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Does mass affect the impact speed?
No, if air resistance is ignored, because mass cancels out.
Why is air resistance important?
At larger heights it changes the speed significantly, reducing the impact velocity.
Does the mass of the ball affect the impact speed?
Not if air drag is ignored. The mass cancels out, so all objects dropped from the same height hit the ground at the same speed.
Related topics in Work, Energy & Power
Potential energy curves · Equilibrium types · Conservation of mechanical energy · Energy on a pendulum · Energy in spring-mass systems · Roller coaster and loops