LaLALa wrote:
> On May 19, 3:42 pm, Rama<
mr.ra...@googlemail.com> wrote:
>
>>
>> So you mean neo will start falling at EXACTLY same moment rope at
>> helicopter is cut. That means info about rope cut at helicopter end
>> travels to neo(who is 1 km away) instantaneously. You want to say this?
>
> Mr. Rama, I believe you are absolutely right. Neo will take a little
> bit before falling. You can think of each bit of rope as a little
> spring so that the whole rope is like a chain of little springs. If we
> like we can mentally divide up the rope into little decimeter segments
> and number them under the cut all the way down to Neo like segment 1,
> 2, 3 and so on. Before the cut segment 2 does not fall because segment
> 1 is holding it up. Segment 1 applies a force on segment 2 because it
> is stretched a little. I do not remember whether this law is Young's
> law or Hooke's law. But I remember that it is that the restoring force
> is proportion to its stretch. In my thinking segment 1 won't stop
> pulling on segment 2 until the other end has moved a little so that it
> is not so stretched. When segment 1 is stretched a little less then
> the force holding up segment 2 will start to decrease and so then the
> top of segment 2 will begin to fall and so segment 2 will be less
> stretched so it will pull a little less hard on segment 3 and so on.
>
> In my mind if this really were a chain of little springs and I moved
> the top end of spring 1 a little then this would result in some kind
> of wave or signal pulse traveling down the chain of springs. It may be
> very possible that in a rope this traveling would be connected to the
> speed of sound in the rope. It makes much sense to me because sound
> after all starts with a little displacement at one end.
>
> I don't believe Neo begins to fall until segment 10 000 no longer
> feels held up by segment 9 999 and that's when segment 10 000 starts
> to fall too. That would be just before Neo starts to fall.
>
> I think one question that would come out of this is what if Neo
> weren't on the end of the rope at all? What if it were just a rope
> hanging there? By the thinking above I would have to believe that the
> top of the rope starts to fall before the bottom of the rope does. Is
> this possible? I think it is. Here is how I think about it. With the
> rope just hanging there is still a force that stretches the rope -- it
> is the force of the helicopter pulling on the top end equal to the
> weight of the rope. When the rope is cut I think what must happen is
> that the center of mass of the rope must start falling with
> acceleration 9.8 m/s/s. That is Newton's second law. But this can be
> satisfied even if the bottom of the rope does not start moving right
> away. This can happen with the rope getting shorter because it is less
> stretched so that the center of mass moves because only the top moves.
> As the rope relaxes the top of the rope surely accelerates FASTER than
> 9.8 m/s/s. This is because there is no force pulling up on the top of
> the rope but there is both the weight of that part of the rope AND the
> stretch force of all the rope under it pulling it down. By this
> thinking the behavior of the rope is that the middle of the rope is
> accelerating down at 9.8 m/s/s and the top of the rope is accelerating
> downward much faster than 9.8 m/s/s and the bottom of the rope is
> accelerating down at must slower than 9.8 m/s/s. So the top of the
> rope could conceivable catch up with the bottom of the rope as the
> whole rope falls. This makes sense to me because that is the kind of
> whiplash that is so dangerous when a taut cable breaks. It is not the
> end far from the break that is dangerous. It is the end near the break
> that can be flying at supersonic speeds and can kill people.
>
> If what I am thinking is right then Neo won't start falling right away
> but he might be killed by the top of the rope coming down and hitting
> him very hard in the head. But someone who is a scientist might tell
> you that I am full of garbage and that nothing I have told you is
> right.
Well, Mr. Lala, although you're clearly no scientist, that does look
like a pretty good way to "think about it".