Unit 4, lesson 21. About 15 minutes.

Energy is never lost

Where does a roller coaster get its energy once the chain lets go?

Play

Getting the experiment ready…

Explain

Energy changes, but it never goes away.

High turns into fast.

Energy can't be made or destroyed. It can only move or change form.

A roller coaster has lots of height energy at the top. As it falls, that turns into movement energy. As it climbs again, it changes back.

Watch the bars as the car moves. Now add friction, and see the car stop lower down each time.

Conservation of energy: in a closed system, total energy stays constant.

With no losses, mgh = ½mv². The mass cancels out, so v = √(2gh).

Worked example: a coaster drops 20 m. So v = √(2 × 9.8 × 20) ≈ 20 m/s, whatever its mass.

Top: all height energy
Bottom: all movement energy
Total stays the same

Want the full story?

Friction doesn't destroy energy. It turns it into heat and sound, which spread out, so we say it is dissipated. The sim shows energy per kilogram of the car, in J/kg, so that mass doesn't matter. It also runs the same track shape for each start height.

The Formula

height energy at the top = movement energy at the bottom

m g h = \tfrac{1}{2} m v^2 \Rightarrow v = \sqrt{2 g h}

$v$: the speed after dropping, measured in metres per second (m/s)
$g$: the acceleration due to gravity, measured in metres per second squared (m/s²)
$h$: the height dropped, measured in metres (m)
$m$: the mass, which cancels out, measured in kilograms (kg)

Try the numbers

Drop height: 20 m

Speed at the lowest point, with no energy lost: 19.81 m/s

Try it at home

You need a ball, a smooth curved bowl or a large bent card.

You need: a ball, a smooth curved bowl or a large bent card.

Roll a ball in a bowl. Up and down!

Hold a ball near the rim of a smooth bowl.
Let go and watch it roll.
Notice how high it gets each time.

What's happening: height energy becomes movement energy, then height energy again. Each time a little goes to heat and sound, so it never quite reaches the same height.

Physics is life

Your body

Your body warms up when you run.

Your body changes chemical energy to movement, but most of it ends up as heat. That is why you get hot.

Daily life

Bike brakes get warm.

Brakes change movement energy into heat. Some electric cars store it in the battery instead.

Nature

Waterfalls turn height to movement.

Water at the top of a waterfall has height energy, which turns into movement and sound on the way down.

Space

The Sun's energy reaches us.

The energy in a bowl of cereal began in the Sun, then passed through a plant and into you.

Quick check

Question 1 of 3

What happens to energy as a coaster goes down?

Words to know

Conservation of energy: Energy can move and change form, but never appears or disappears.

Conservation of energy: Energy can move and change form, but never appears or disappears.
Kinetic energy: The energy something has because it is moving.
Potential energy: Energy stored, ready to be used, like a ball held up high.

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