Do pistons stop in an engine when reversing direction?

[Chronos]

Ordinarily, I would nitpick that there are an infinite but countable number of derivatives. But (especially with sine and cosine) it’s possible to define a derivative of fractional or even irrational order. So yes, it would actually be uncountable.

[KMS94]

@Great_Dave

If they didn’t stop, they’d fly right out the top of the cylinder, wouldn’t they?

Sometimes, they do. But that is definitely a bug, not a feature. :eek:

[Senegoid]

@Chronos

Although, the fact that the derivatives of sine and cosine are so uninteresting is, itself, quite interesting.

The successive derivatives of e[sup]x[/sup] are even less interesting, hence, even more interesting.

Successive derivatives of f(x)=0 even less and more so.

[Senegoid]

@Riemann

Have we discussed a photon in a vacuum? If you hold up a mirror, is the photon stationary as it bounces off the mirror?

Is this true? When a photon “bounces” off a mirror, is it even the same photon?

[Melbourne]

@Mangetout

There has to be a point at which the fly’s motion goes from eastward to westward - and this transition involves traversing zero - so if the fly is momentarily motionless, and is still in contact with the train, the train must also be considered to be motionless in that moment.

I mean, I don’t think it works like that in reality - this is supposed to be an argument that gets you thinking about what really happens
(which I think is):

Not really. The engine is stiff compared to the fly at any scale: assuming an almost free atom of fly (carbon, oxygen, nitrogen or lead) hits a bound atom of engine (Iron, oxygen) it is unlikely that the Engine comes to an infinitesimal stop at any scale.

And even if the Engine had the surface hardness and mass of a fly, it’s not necessary for both to come to an iinfinitesimal stop /relative to a stationary observer/