Conservation of energy — potential and kinetic energy
What we will do: We will release a cart on a track with hills and check how high it gets and how energy converts between potential and kinetic.
What you see on screen: A roller coaster with a cart, a slider for the start height (and mass), and a friction switch. Two bars — potential and kinetic energy — always add up to the same value (without friction); with friction a "heat" bar appears. Readouts: height, speed, Ep, Ek and total energy.
What just happened?
The cart did not climb a hill higher than the start — because it had no energy source to do so. Without friction it reaches at most the height it started from.
Two forms of energy:
at the top the cart has potential energy , at the bottom — kinetic . Rolling down, it converts one into the other.
Conservation of mechanical energy (no friction):
The sum does not change — energy just "pours" between potential and kinetic. Hence the speed at the bottom:
And friction?
Then part of the mechanical energy turns into heat, so the cart returns lower each time — yet the total energy is still conserved, only part of it "escapes" as heat.
Why you need this for the exam:
Ep = mgh, Ek = ½mv² and their sum solve problems about falling, rolling down and speed without computing forces. The trick: equate the energy at two points of the track.
Remember: energy is not lost — it changes form. Without friction you cannot get higher than the starting point. This is the third in the family of conservation laws: mass, momentum, energy.
Theory & formulas
Two forms of mechanical energy
- potential (gravitational):
- kinetic:
The law of conservation of mechanical energy
Without friction the sum of potential and kinetic energy is constant: At the top of a hill the energy is mostly potential, at the bottom — kinetic.
Speed from height
From the conversion of into (): With friction part of the mechanical energy turns into heat, but the total energy is still conserved.
Notation: — potential energy, — kinetic energy, — mass, , — height, — speed.
Frequently asked questions
›What does the law of conservation of mechanical energy state?
Without friction the sum of potential and kinetic energy is constant: Ep + Ek = const.
›How do you calculate the speed of a body falling from height h?
From the conservation of energy: v = √(2gh).
›Where does the energy go when there is friction?
It turns into heat — the total energy is still conserved, but the mechanical energy decreases.
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