Answers

The physics underneath

The handful of quantities that do not change while everything else does, and what goes wrong in the arithmetic when a calculation loses one of them.

1. How can light travel through empty space if there's nothing to wave?Light is a self-sustaining ripple of electric and magnetic fields, each one creating the other, so it needs no material to travel through.
2. How can you predict the shape of a plucked string a moment after you let go?Write the starting corner as a sum of the string's allowed standing shapes, let each shape oscillate at its own rate, then add them back together.
3. Why is momentum conserved in a collision when kinetic energy is not?Momentum is conserved because the internal pushes in a collision cancel in pairs, while kinetic energy can be turned into heat and deformation.
4. Why does a planet speed up when it gets closer to the Sun?A planet speeds up near the Sun because its fixed angular momentum forces its sideways speed up as its distance falls, and gravity does work as it falls inward.
5. Why does an object speed up as it falls?Because a falling object has a fixed total of height energy plus motion energy, so every bit of height it loses turns into speed. Gravity converts rather than adds.
6. Why does pushing a swing at just the right moment make it go much higher?A swing goes higher when each push arrives in step with the motion already there, so many small pushes add up instead of cancelling.
7. Why does a wave on a string travel at the same speed no matter how hard you pluck it?A harder pluck makes a bigger wave, but the speed of the wave is fixed by the string's tension and mass per length, so amplitude does not change it.
8. Why is the fastest way down a hill not a straight line?Because time is distance divided by speed, and a steeper path gives the bead more speed early even though it is longer.
9. Why do two waves moving in opposite directions make a standing wave that doesn't go anywhere?Two travelling waves going opposite ways add point by point; where one rises the other falls they cancel permanently, so the pattern stays put even though both waves keep moving through it.
10. Why does a spinning book suddenly start tumbling instead of staying on its axis?Spinning a book about its middle-sized axis is unstable: the conserved quantities still allow it to turn over, and any tiny wobble grows until it flips.

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