How long would it take to fall through the Earth?
This is a classic calculation, and one that’s surprisingly tricky: suppose you could bore a hole all the way through the Earth. If you jumped in, how long would it take you to fall through and come out of the other side?
If you’re taking A-level physics you know pretty much everything you need to do the calculation for yourself, but there are a few fiddly little problems you need to deal with along the way. Most importantly: if you’re falling through the Earth, only some of it is below your feet. The rest of it is above your head, and the force of gravity from that part is pulling you not downwards but upwards. So working out the forces isn’t as simple as you might hope, but you do get something back: when you start picking away at the maths, you’ll find that what happens when you reach the centre of the planet is pretty important.
Have a think about how you’d tackle the problem yourself, then take a look at this video from MinutePhysics.
Tip of the hat to Alom Shaha for pointing us to this.