Newton’s Three Laws of Motion, Explained With Everyday Examples
Newton’s first, second and third laws of motion explained simply, with everyday examples, the F = ma formula, worked problems and common misconceptions.
Kinetic vs Potential Energy (With Examples)
Kinetic and potential energy explained: formulas, units, everyday examples, energy conversion on roller coasters and pendulums, and a quick energy calculator.
Key takeaways
- Kinetic energy is energy of motion: KE = ½mv².
- Gravitational potential energy is stored energy due to height: PE = mgh.
- Energy converts between the two, while total energy is conserved (ignoring losses).
On this page
Energy is the ability to do work, and in mechanics it comes in two main forms: energy of motion and stored energy. Understanding how they convert explains everything from roller coasters to bouncing balls.
Kinetic energy
Kinetic energy (KE) is the energy an object has because it’s moving:
KE = ½ m v²
- m = mass (kg)
- v = speed (m/s)
- KE in joules (J)
Because speed is squared, doubling speed quadruples kinetic energy, which is why car crashes at higher speeds are so much more dangerous.
Potential energy
Gravitational potential energy (PE) is energy stored because of an object’s height:
PE = m g h
- g ≈ 9.81 m/s² on Earth
- h = height (m)
Other forms of potential energy include elastic (stretched springs) and chemical (fuel, food).
Quick calculator
Kinetic and potential energy calculator
Energy conversion
- Roller coaster: at the top, mostly potential energy; at the bottom, mostly kinetic.
- Pendulum: swings between maximum PE at the ends and maximum KE at the bottom.
- Falling ball: PE turns into KE as it falls; see our free fall calculator.
In reality, some energy is lost to air resistance, friction and sound; see friction explained.
Worked example
A 2 kg ball dropped from 10 m (ignoring air resistance): PE at the top = 2 × 9.81 × 10 = 196.2 J. Just before landing, nearly all of this becomes KE, so ½ × 2 × v² = 196.2, giving v ≈ 14 m/s.
For how energy relates to work and power, see work, energy and power.
Frequently asked questions
Can an object have both kinetic and potential energy?
Yes. A flying plane has kinetic energy from its speed and potential energy from its height.
What is the unit of energy?
The joule (J).
Is energy ever lost?
Energy is conserved, but it can be transformed into less useful forms, like heat.
Sources
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