Newtonian physics and motion of a wiggling rope

Click For Summary
SUMMARY

Newtonian mechanics applies to the motion of a wiggling rope by treating it as a series of rigid bodies, akin to a wiggling chain. Each link can be analyzed using Newton's laws, and as the link size approaches zero, the rope behaves as a continuous medium. While simulations may seem necessary for complex motions, simplifying assumptions can make differential equations tractable within the framework of Newtonian physics. Additionally, wave equations for strings and ropes can be derived from Newtonian principles, assuming uniform tension.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with rigid body dynamics
  • Basic knowledge of differential equations
  • Concept of wave equations in physics
NEXT STEPS
  • Explore the application of Newton's laws to continuous media
  • Study wave equations for strings and ropes in detail
  • Learn about simplifying assumptions in physics for complex systems
  • Investigate numerical simulations for modeling motion in physics
USEFUL FOR

Students and professionals in physics, mechanical engineers, and anyone interested in the dynamics of flexible structures like ropes and strings.

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 Metal Ball Rolling in a Parabolic Bowl in the presence of a magnet
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad 1:1 versus 2:1 Mechanical Advantage debate
  • · Replies 20 ·
Replies
20
Views
868
High School Analysis of Simple Pendulum Motion
  • · Replies 2 ·
Replies
2
Views
1K
High School What is tension and how does it affect a rope?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Laws of motion while climbing a Rope
  • · Replies 8 ·
Replies
8
Views
7K
Undergrad Why does the apparent weight decrease when a body accelerates down a rope?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad How Does Mass Affect the Direction of Rotational Motion in a Pulley System?
  • · Replies 2 ·
Replies
2
Views
1K
High School Is simple harmonic motion also a pure translatory motion?
  • · Replies 21 ·
Replies
21
Views
2K
Graduate Do we have "Newtonian space-time" in classical physics?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Lecture on Newtonian spacetime
  • · Replies 27 ·
Replies
27
Views
5K