Mechanical
The math behind machines and motion
7 live exhibits. Each one already works. Change a number and see what happens.
Open as board Play with these together. Solving one grows related exhibits.
Linear EquationsHooke’s law: how far does the car sag when you load it?
A spring squeezes in a straight line with the load: twice the weight, twice the sag, until it hits the stops.
Ratios & ProportionsTorque: how hard to pull the wrench, and what an adapter changes
Torque is force times distance. A longer handle takes less push, and an adapter that adds length means you must set the wrench lower.
Linear EquationsPC cooling: passive, air, or water?
Heat flows through the cooler like current through a resistor: temperature rise = watts × °C/W. Water adds mass, so it heats up slower.
Linear EquationsStress and strain: how much does a rod stretch under a load?
Stress is force per area. Divide by the material’s stiffness and you get the stretch, until it yields and stays bent.
Differential Equations & TransformsDoor closer: slam, bounce, or glide
One damping knob turns a slam into a glide. Where two dots (the poles) sit tells you which.
Differential Equations & TransformsWhy the shower goes hot, then cold
You react to water that left the tap seconds ago. Delay plus impatience makes the swing, and one number predicts it.
Exponents & LogarithmsThe Bartz equation: how regenerative cooling keeps a rocket throat from melting
Heating grows with chamber pressure to the 0.8 power and peaks at the throat. The fuel flows through the wall to carry it away.