Friction as a conservative force

AI Thread Summary
Friction is discussed as a nonconservative force, raising questions about its decomposition into components when acting at an angle. In a horizontal plane, the equations of motion for a ball launched at 45° are examined, highlighting the challenges posed by friction's dissipative nature. The validity of using Lagrangian mechanics in the presence of friction is questioned, with suggestions to simplify the problem to one dimension. It is noted that if friction is isotropic, decomposing it into components may not be necessary. Overall, the discussion emphasizes the complexities of incorporating friction into mechanical equations.
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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,
 
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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
 
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When dealing with lagrangian mechanics it is always best to minimise the number of dependant 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.
 

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