Newtonian physics and motion of a wiggling rope

Click For Summary

Discussion Overview

The discussion revolves around the applicability of Newtonian mechanics to the motion of a wiggling rope. Participants explore whether Newton's laws can adequately describe such motion, considering both theoretical and practical implications.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether Newtonian mechanics is limited to rigid bodies and expresses uncertainty about its application to a wiggling rope.
  • Another participant argues that Newtonian mechanics can apply to a rope by conceptualizing it as a series of rigid links, suggesting that as the link size approaches zero, it can be treated as a continuous medium without changing the underlying physical laws.
  • A participant raises concerns about the complexity of applying Newtonian mechanics to a wiggling rope, questioning whether simulations are the only viable method for analyzing such motion.
  • Another response suggests that while Finite Element Analysis may be inefficient, simplifying assumptions could make the differential equations more manageable, still within the framework of Newtonian physics.
  • There is mention of wave equations for strings and ropes that derive from Newtonian physics, contingent on the assumption of uniform tension.

Areas of Agreement / Disagreement

Participants express differing views on the practicality of applying Newtonian mechanics to a wiggling rope, with some supporting its applicability through theoretical models and others questioning the complexity and efficiency of such approaches. No consensus is reached regarding the best method for analyzing the motion.

Contextual Notes

Participants acknowledge the potential limitations of their approaches, including the need for simplifying assumptions and the challenges posed by complex motion. The discussion does not resolve these limitations.

Fascheue
What types of objects does Newtonian mechanics deal with? Is it just rigid bodies? I’m not sure how Newton’s laws could explain something like the motion of a wiggling rope.
 
Physics news on Phys.org
It may not seem obvious, but Newtonian mechanics to apply to a rope.

To make is easier to visualize, imagine it as a wiggling chain. Each link is a rigid body and you can use Newton's laws in their familiar form. Make the link size arbitrarily small and you have a continuous rope. The physical laws don't change with link size.
 
  • Like
Likes   Reactions: Fascheue
anorlunda said:
It may not seem obvious, but Newtonian mechanics to apply to a rope.

To make is easier to visualize, imagine it as a wiggling chain. Each link is a rigid body and you can use Newton's laws in their familiar form. Make the link size arbitrarily small and you have a continuous rope. The physical laws don't change with link size.
Isn’t that too complicated to be useful though? Or is the only way to find something like the complicated motion of a rope with simulations on a computer?
 
Fascheue said:
Isn’t that too complicated to be useful though? Or is the only way to find something like the complicated motion of a rope with simulations on a computer?
Finite Element Analysis is probably too clunky to use on such a problem -- possible, but inefficient. One could make simplifying assumptions so that the differential equations are tractable. That's still Newtonian physics.

There are wave equations for strings and ropes that are based on Newtonian physics plus the simplifying assumption of uniform tension.
 

Similar threads

Undergrad 1:1 versus 2:1 Mechanical Advantage debate
  • · Replies 20 ·
Replies
20
Views
2K
Undergrad Metal Ball Rolling in a Parabolic Bowl in the presence of a magnet
  • · Replies 1 ·
Replies
1
Views
2K
High School What is tension and how does it affect a rope?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Laws of motion while climbing a Rope
  • · Replies 8 ·
Replies
8
Views
7K
High School The application of Newton's laws to fluid equilibrium
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad Why does the apparent weight decrease when a body accelerates down a rope?
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Do we have "Newtonian space-time" in classical physics?
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Can analytical mechanics be deduced from Newtonian mechanics?
  • · Replies 22 ·
Replies
22
Views
3K
High School Normal force in case of inclined plane and banked turn
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Lecture on Newtonian spacetime
  • · Replies 27 ·
Replies
27
Views
5K