Friction as a conservative force

Click For Summary

Discussion Overview

The discussion revolves around the nature of friction as a force, specifically whether it can be treated as conservative or nonconservative, and how to appropriately decompose frictional forces in different coordinate systems. Participants explore the implications of these concepts in the context of Lagrangian mechanics and the equations of motion for a ball launched at an angle.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether the friction force can be split into components when acting at an angle, suggesting equations for motion in x and y directions.
  • Another participant argues that if the frictional force is isotropic, there is no need to decompose it and suggests rotating the frame instead.
  • A different participant advises minimizing the number of dependent variables in Lagrangian mechanics by simplifying the problem to one dimension along the slope.
  • A subsequent reply asks if it is still valid to split forces into components when the situation is not conveniently one-dimensional.
  • Another participant responds that it seems acceptable to split the forces and encourages experimentation with the approach.

Areas of Agreement / Disagreement

Participants express differing views on the treatment of friction as a conservative versus nonconservative force, and whether it is appropriate to decompose the frictional force into components. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants do not reach a consensus on the treatment of friction in Lagrangian mechanics, and there are assumptions about the isotropy of the frictional force that are not explicitly defined.

kizzie
Messages
3
Reaction score
0
friction as a nonconservative force

I was wondering, can the friction force be split up? Suppose you have a friction force working under an angle alpha, can you just say Fx = Ffric*cos(alfa), Fy = Ffric*sin(alfa)

Suppose you're working in a flat horizontal plane, and you launch a ball in 45° direction, what are the equations of the ball in x and y?
mx" = -Fx = -Ffric cos (alfa)
my" = -Fy - -Ffric sin(alfa)

It seems that this does not works since the friction force is a nonconservative force ... Is Lagrange method still valid?

regards,
 
Last edited:
Physics news on Phys.org
If the frictional force is the same in all directions ( isotropic) then there's no reason to decompose it as you suggest. Just rotate your frame.

As far as the Lagrangian goes, clearly the frictional force is dissipative. There are good lecture notes here -

http://tabitha.phas.ubc.ca/wiki/index.php/Dissipative_Forces
 
Last edited by a moderator:
When dealing with lagrangian mechanics it is always best to minimise the number of dependent variables, i.e. just make your situation 1D such that it is up and down the slope. So then you don't have to break up the force, you just have to alter (thru trig) the force from gravity.
 
And when it is very inconvenient to consider it 1D, is it still correct to split the forces into Fx and Fy?
 
It seems ok to do so. Give it a go. See where you end up.
 

Similar threads

Undergrad Is Mechanical Energy Conservation Free of Ambiguity - follow up
  • · Replies 77 ·
3
Replies
77
Views
6K
Undergrad Conservative forces and internal and external forces
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad System, potential energy, and nonconservative forces
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Conservative forces, Nonconservative forces and Potential Energy
  • · Replies 9 ·
Replies
9
Views
4K
High School Why does friction decrease with repeated force application?
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Solving Wheel Coming to a Stop: FBD, Friction & Hysteresis
  • · Replies 22 ·
Replies
22
Views
5K
High School Normal Force Discrepancy for Wedge Vs. Ramp
  • · Replies 9 ·
Replies
9
Views
4K
Undergrad Momentum of a Water Jet Impacting Plate
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Ball rolling down a ramp, no slipping, + friction (conceptual question)
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Frictional Force Equation Doesn't Make Sense
  • · Replies 8 ·
Replies
8
Views
3K