Potential Energy & Conservation
Roller coaster designer. Builds on Work & Kinetic Energy.
A roller coaster car starts from rest at the top of a 30-meter hill, goes through a loop, and reaches a second hill that's 25 meters high.
How fast is it going at the top of the second hill? (Ignore friction.)
About 9.9 m/s! Energy conservation makes this simple: the car converts potential energy (mgh) to kinetic energy (½mv²). From 30m to 25m, it has 5m worth of kinetic energy: ½mv² = mg(5), so v = √(2g·5) ≈ 9.9 m/s. The track shape, loops, curves — none of it matters!
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Watch the energy bars as the car moves. KE + PE always equals the same total — no matter what the track looks like.
½mv² + mgh = const
Notice: mass cancels in every energy conservation problem with only gravity! That's why a marble and a bowling ball on the same track reach the same speed.
The first hill MUST be the tallest — there's no motor after that. Each subsequent hill must be shorter, because friction steals a bit of energy each time.
Water falls from height h, converting PE to KE to electrical energy. The Hoover Dam's 180m height gives each kg of water 1,764 J of energy.
A snowboarder can only reach the height they started from (minus friction losses). Energy conservation sets the absolute maximum air height.
“Energy conservation is the greatest shortcut in physics. Forget about forces, accelerations, and paths. Just compare energies at start and finish. The universe keeps perfect books.”
Roller Coaster Designer
Draw your own roller coaster track! Watch the car ride it while energy bars show the KE/PE exchange in real time.
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Make a track with two hills — the second slightly lower. The car will make it over. Now make the second hill taller than the first — the car can't make it! Energy conservation forbids it.
The path doesn't matter — only the heights. A straight drop and a winding track from the same height produce the same final speed. Energy doesn't care about the route.