A Fistful of Brain Teasers

Get 2 cans of beer. Open and drink one. Roll them both down an incline. The full one will get to the bottom first, Open it and drink it.

They don’t both weigh the same though. But taking a limit case is often a good way to visualise the behaviour.

So visualise a solid cylinder mounted on a spindle with a handle. And a very large wheel with most of the weight around the rim, again mounted on a spindle with a handle. Which one would experience suggest would be the hardest to get going? Or once you had got them both going, if you stopped turning the handle, which would stop first? That is also the one that would accelerate under a constant force (gravity) fastest and so reach the bottom of an inclined plane first....

best

David

The centre of gravity of the cylinder and prism is identical, as is the force acting at the centre of gravity.

I don't think the flywheel example above applies to a cylinder rolling down an incline. But I'm not 100% sure.

The lead one will still float on water ?

Could you simply try bending them, or does that count as damaging them? It shouldn’t do, as because lead is bendy and titanium isn’t, the lead one could be straightened out again. 

Get two people to lick one each. If one falls ill after a while then bobs your uncle.

TOBYJUG posted:

The lead one will still float on water ?

Not sure whether this was intended to be a serious question or not, but it will only float it is displaces enough water to compensate for the weight of the lead that is there, which given that lead is much more dense than water seems unlikely.

best

David

hungryhalibut posted:

Could you simply try bending them, or does that count as damaging them? It shouldn’t do, as because lead is bendy and titanium isn’t, the lead one could be straightened out again. 

If you bend it, then you have stretched the metal on one side and it’s very hard to unstretch bent metal, cf if you have ever tried straightening out a dent in a car. So I think that is damaging it....

Lead is very heavy.  Given a certain size the ratio of density versus the amount of air inside could could cancel out and leave it floating or sinking slowly rather than the aluminium one dropping like a lead balloon.

TOBYJUG posted:

Lead is very heavy.  Given a certain size the ratio of density versus the amount of air inside could could cancel out and leave it floating or sinking slowly rather than the aluminium one dropping like a lead balloon.

No this is completely wrong.  They are identical in size and they both weigh the same, so the volume of water they displace will be the same. The fact that one is hollow is unknowable from an immerse-in-water point of view!

best

David

Mike Sullivan posted:

The speed of rotation is dependent on the distance of the mass from the centre of rotation.

The hollow cylinder has a higher mass away from its centre. If you spin both cylinders, the flywheel effect should keep the lead cylinder spinning longer.

David Hendon posted:

TOBYJUG posted:

The lead one will still float on water ?

Not sure whether this was intended to be a serious question or not, but it will only float it is displaces enough water to compensate for the weight of the lead that is there, which given that lead is much more dense than water seems unlikely.

best

David

It won’t - the overall density of the entire cylinder including the internal void is the same as one of solid titanium, so densrvthan water.

Mulberry posted:

Mike Sullivan posted:

The speed of rotation is dependent on the distance of the mass from the centre of rotation.

The hollow cylinder has a higher mass away from its centre. If you spin both cylinders, the flywheel effect should keep the lead cylinder spinning longer.

Good point - but not sure that a cylinder will be easipy to start spinning on one end?

David Hendon posted:

hungryhalibut posted:

Could you simply try bending them, or does that count as damaging them? It shouldn’t do, as because lead is bendy and titanium isn’t, the lead one could be straightened out again. 

If you bend it, then you have stretched the metal on one side and it’s very hard to unstretch bent metal, cf if you have ever tried straightening out a dent in a car. So I think that is damaging it....

And we have no idea of size - it might be just a few mm in diameter, many cm - the latter would not be easy to bend!

TOBYJUG posted:

Get two people to lick one each. If one falls ill after a while then bobs your uncle.

Inthink the paint on both is identical... But teresting way of discovering someone’s uncle’s name!

Chuck them both on a bonfire and see which one melts first..

TOBYJUG posted:

Chuck them both on a bonfire and see which one melts first..

Assuming you have paint capable of  withstanding at least lead’s 328ºC melting point, you have a 50-50 chance of success: put just one in the fire (pizza oven etc), just above that temp, and wait: if it doesn’t melt and comes out undamaged you know the answer and have not failed - but if the lead one goes in and melts it will be damaged so you’ll fail!

Drop them both at a height of 1500 ft. The one that lands first should determine the other before being damaged..

Put them both in a freezer. One might reach zero before the other.

TOBYJUG posted:

Put them both in a freezer. One might reach zero before the other.

Yes that would work, they have different heat capavities, though only slightly different so may need a high precision thermometer.

Hit them with a drumstick. The lead hollow one will not resonate as long as the aluminium one. With different tones. 

TOBYJUG posted:

Drop them both at a height of 1500 ft. The one that lands first should determine the other before being damaged..

They’ll  hit simultaneously...

TOBYJUG posted:

Hit them with a drumstick. The lead hollow one will not resonate as long as the aluminium one. With different tones. 

Even the titanium one...!  They will sound different.

A drumstick is another object. So using each to hit one another to determine a difference in tone. The lead one will not sound hollow as such but will have a different tone to the other. If they both have the same tone - a trained ear will easily tell the difference from harmonics and overtones from a hollow body.

Don’t forget we are not allowed to damage them or to use any other object.......

best

David