Conservation: The Skate Park Rule

Lesson 4 of 10 · 7 min · Free, no account needed

What you will learn

In a closed system with no friction the total energy never changes: mgh + ½mv² stays the same.
So the speed at any spot depends only on how far below the start it is, not on the shape of the track.
From a drop h, starting at rest: v = √(2gh). A 5 m drop gives about 9.9 m/s.

Two slides of the same height, one straight, one twisty. Which kid is faster at the bottom?
Drag a speed marker under each slide.
Draw your own slide from the start down to the ground, and ride it. Then draw a very different one.
Read the speedometer at the bottom each time.
A long wavy track. Press Play and watch the total bar.
This is one of the biggest rules in physics.
Conservation of energy: energy is never made or destroyed, it only changes form. Here: mgh + ½mv² = the same number at every spot.
A closed system is one where no energy comes in or leaks out. Our skate park without friction is one. Real ones leak a little, as heat (next lesson).
Starting from rest, all of mgh becomes ½mv² at the bottom. The m cancels, so v = √(2gh), the same for every skater and every shape.
The green spot is marked. Tap every other spot where she moves at the same speed.
Game: Skate puzzle. Put each star where she is fast enough to grab it.
A star needs its speed. Three levels.
AI: a training step works like a ball on an error curve. Dial the friction so the ball settles in the lowest point.
Play after each change. 20 seconds to come to rest in the green zone.
A slide 5 m high, starting at rest, no friction. What is the speed at the bottom, in m/s?
Race: your slide against a straight one of the same height. Press Play.

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