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Context

I am thinking about the physics of the movement of a rope in the context of a person running and grabbing a rope in one hand (the other end is "free", there is nothing attached).

When the person is just standing, the rope simply falls down vertically.

Update after comments: the rope does not stay on "horizontal state" (wrong original assumption was that when the person is running, the rope looks like it follows the direction of the person hand, that is, if the person runs forwards (horizontally), the rope hangs horizontally from the hand.)

When the person is not running, I asume that the main ideas that explain why the rope "falls down" vertically are gravity.

Main question

What physics principles / ideas can explain the movement of the rope, when the person is running?

I guess that air friction might be one. Am I right? What would others be? Tension?

Side question

While running, the person moves its arm upwards. The rope transitions from horizontal to diagonal (switching from one height to the current hand's height) and then returns to horizontal. What principles are involved in these transitions / movements?

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  • $\begingroup$ When the person is running, the rope is NOT hanging horizontally. $\endgroup$
    – David White
    Commented Jan 13, 2019 at 16:28

1 Answer 1

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The rope can be modeled as an elastic system consisting of individual massive elements connected by springs. Each massive element moves under the action of elastic forces, gravity and air resistance. Let's consider the task: at the initial moment of time, the rope hangs vertically, in the next 1 second the upper end of the rope moves with acceleration 2, after that it moves at a constant speed 2. We solve the problem with air resistance and without resistance. Both versions are presented in animations 1,2. We see that in the presence of resistance, the rope deviates from the vertical both when accelerating and when moving at a constant speed. Without resistance, the rope is deflected during acceleration, and then oscillates relative to the vertical.

With resistance

fig1

Without resistance

fig2

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  • $\begingroup$ Thanks for the animations. So, the key ideas are gravity, elastic forces and air resistance. $\endgroup$
    – Jesus
    Commented Jan 13, 2019 at 21:04
  • $\begingroup$ I thought in the case of a rope it would look like moving totally horizontal, but I see I was wrong. In the case of clothes or a flag, the transition from "hanging down" to horizontal might have to do more with wind (air resistance) than the "pulling force"? $\endgroup$
    – Jesus
    Commented Jan 13, 2019 at 21:08
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    $\begingroup$ In the case of a flag, there is a flagpole, which creates a stream of air behind the cylinder, in which the cloth makes a wave-like movement. $\endgroup$
    – Alex Trounev
    Commented Jan 13, 2019 at 23:19
  • $\begingroup$ Thanks for the answer. I deduce the key to these movements is related to "force" (acceleration). At first, the acceleration of the person (or a strong pull movement) may make the rope to temporarily reach horizontal state. When the movement becomes uniform, the rope looks "diagonal". When wind is involved, the stream of air acts like a continuous force that might keep the flag horizontal (with a wave-like movement) $\endgroup$
    – Jesus
    Commented Jan 14, 2019 at 16:00

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