How height turns into speed
Energy never disappears. It just changes form. Watch a marble swap stored height for speed.
Why does a roller coaster climb a huge hill at the start, and then never need an engine again? The answer is one of the biggest ideas in all of science: energy.
Two kinds of energy
Energy is what makes things happen. It comes in many forms. Two of them are in every marble run:
- Stored energy. A marble held up high has energy stored in it, because gravity is ready to pull it down. The higher it is, the more it has. Scientists call this potential energy.
- Motion energy. A marble that is moving has energy because of its speed. The faster it goes, the more it has. Scientists call this kinetic energy.
Try it
Press Release marble. Watch the energy bar under the picture. The blue part is stored energy, the orange part is motion energy and the grey part is energy lost as heat.
Release it again from a different height. What did you notice?
- At the top, the bar is all blue. The marble is not moving yet.
- As the marble rolls down, blue shrinks and orange grows. Height turns into speed.
- At the bottom, the marble has its fastest speed.
- Going up the hill, orange turns back into blue. The marble slows down.
The marble from the higher start is faster at the bottom. More height means more stored energy, which means more speed.
Energy changes. It does not vanish.
Look at the bar again. The total length is always the same. Stored energy and motion energy swap, but the total stays the same. This is called the conservation of energy.
So what is the grey part? Rolling is never perfectly smooth. The marble and the track rub, a tiny bit. That rubbing is friction, and it turns a little energy into heat. The heat is not lost forever. It just spreads out into the track and the air, where we can't use it any more.
That is why:
- A marble can never climb higher than where it started. It has no extra energy to spend.
- A bouncing ball bounces a bit lower each time.
- A roller coaster's first hill is the tallest of the ride.
In Marble Machine Mission 1, you build any track you like. But the speed at the bottom depends only on how far the marble dropped. A steep drop and a long gentle ramp give the same speed, if they lose the same height. (The gentle ramp just takes longer to get there.)
Why a marble is slower than you might think
If you slid a block down a ramp, it would go faster than a rolling marble from the same height. Why? A rolling marble has to spin as well as move forward, and spinning also takes energy. About 2/7 of the marble's motion energy goes into the spin.
In the game, the marble's energy is worked out for a real rolling ball. From a 3 m drop, a rolling marble reaches about 6.5 metres per second. A sliding block would reach about 7.7.
Stored energy is g × height (for every kilogram). A rolling ball's motion energy is 0.7 × speed². With no friction, they swap exactly, so 0.7 × speed² = g × height lost. That gives speed = √(g × height lost ÷ 0.7). Try it: from 3 m, √(9.81 × 3 ÷ 0.7) is about 6.5 m/s.
Try it in the game
- Downhill dash: which pieces give the fastest finish? Does the steep one win?
- Up the hill: why can't the marble climb all the way back to 3 m?
- In Free Build, switch Friction to None, then High. Watch the grey part of the bar.