Re: The rope

pglpm wrote on 2025-05-27 08:44:03:

You are confusing momentum with velocity. If mass is zero (more precise=

ly:

negligible), then momentum is zero even if velocity is different from z=

ero=20

and varies over time. So the rope can accelerate, yet the forces on the=

 two

ends are equal and opposite. More precisely: their difference is neglig=

ible

Decide: is the difference zero or is it negligible?

They are not the same thing at all: an increase of x% by zero remains=20
zero, an increase of x% by a negligible amount y does not remain y.

If the rope accelerates, you cannot tell me that its momentum *does=20
not* increase!

It will increase a little but it certainly cannot stay the same!

If we start with the wrong assumptions, everything else is wrong.

I will show you where you are wrong.

The rope (even if massless) is constrained to particle A (with mass) of=20
the horse and particle B (with mass) of the stone.

Particles A and B have momentum because they have mass.

When the horse accelerates, the momentum of its particle A increases=20
but that of particle B of the rope does not (that is, not at the same=20
time) because it is distant from A.

Only after a certain time will particle B also have increased its=20
momentum but, in the meantime, particle A will have achieved another=20
increase that particle B will receive only later.

So, at any instant, the momentum of A is *greater* than the momentum of=20
B which for the entire time of the acceleration will have to chase the=20
increases of A.

The two values =E2=80=8B=E2=80=8Bwill stabilize at the same level only wh=
en the horse=20
stops accelerating.

This is why the momentum of the ends of the rope cannot be equal during=20
the acceleration.

Luigi Fortunati.