The rope

Referring to his third law, Newton writes: If a horse pulls a stone
tied to a rope, the horse is also equally pulled towards the stone. For
the rope stretched between the two parts, by the same attempt to
slacken, will push the horse towards the stone and the stone towards
the horse; and it will impede the advance of the one by as much as it
will promote the advance of the other.

I have already shown that this is not true at all when the horse
accelerates or brakes and now I will show that it is not true even when
the rope is stationary in a gravitational field.

In the diagram https://www.geogebra.org/classic/pnbsvfuk there is the
hand holding end A of the 2 kg rope and there is end B of the rope
holding the 15 kg bucket full of water.

The hand exerts the blue force +17 (upward) on the rope, and the rope
reacts with the red force -17 (downward).

And the rope exerts the blue force +15 (upward) on the bucket, and the
bucket reacts with the red force -15 (downward).

So, contrary to what Newton says, the rope does NOT exert the same
force on the hand (-17) and on the bucket (+15)!

Luigi fortunati


[[Mod. note --
Newton's 3rd law applies separately at each location where forces are
applied:
* At the top of the top, Newton's 3rd law says the hand force on the
  rope (17 upward) is equal in magnitude and opposite in direction from
  the rope force on the hand (17 downard).
* At the bottom of the top, Newton's 3rd law says the hand force on the
  bucket (15 upward) is equal in magnitude and opposite in direction from
  the bucket force on the hand (15 downard).

But, the top of the rope and the bottom of the rope are different
locations (with different forces applied), so Newton's 3rd law does
not say anything about how the top-of-the-rope forces and the
bottom-of-the-rope forces relate to each other.

There's also another force present which is missing from the diagram,
namely the 2kg Newtonian-gravity weight force acting downwards on the
rope.  Because the rope's mass is spread out along the rope's length,
the weight force is also a *distributed* force -- it acts all along the
rope's length.

To summarize, here are all the (vertical) forces which acting on the rope:
* 17 up applied by the hand at the top of the rope
* 15 down applied by the bucket at the bottom of the rope
* 2 down applied by Newtonian gravity, distributed along the length
  of the rope.
Notice that the sum of all these forces is zero, which is just what it
should be by Newton's 2nd law, since the rope is stationary.
-- jt]]