FμNmaμmgmaμa/gbut i don‘t understand this.more mass creates more downward force therefore more normal so i don‘t understand why mass cancels out.
That mathematical derivation only applies to a moving body in contact with a rough surface with no other forces acting on it. So please remember that that is not a good representation of the coefficient of friction. The coefficient of friction does not depend on the mass because it is intended to make a statement about the nature of the materials involved. For instance, copper and iron have a unique coefficient, and so if you had a copper sheet rubbing on an iron sheet you would use that. But copper and cobalt have a different coefficient than iron and copper, because again, the coefficient depends on the materials involved and on how smooth the surfaces are. So when you right F'mu'N, you are writing, the strength of friction depends on what the surfaces are made of and how polished they are and on how hard you are pushing the surfaces together.
I can understand your confusion. First μ is not basically ratio of accelerations! It is ratio between two forces. One is normal force acting between two faces and the other which is tangential force which comes into play only when there is either relative motion or tendency of motion. μ is the ratio of the maximum frictional force to the normal force. It is just a matter of chance, that the m which occurs in Newton's law of motion and the m that occurs in the expression of gravitational law, is same, which is called equivalence of inertial mass and gravitational mass. So in this special case m is canceling. If e normal force has nothing to with mass as it is in electrostatic and magnetic forces, ten m will not cancel.
you have an equation which points to a very special casethe case where applied force equals the frictional force, or when the object is moving at a constant speed, without acceleration only in such a case, is μ independent of mass mathematically!! and also μ a/g is a mathematical statement . a mathematical consequence physically and a conceptually correct equation would be a μg acceleration u have to give is μ times g . so that object does not accelerate now why is that mass doesnt have an effect? for a given μ , more the mass means more frictional force, but at the same time u will have to exert a more applied force. physically in nature, frictional and applied force vary in the same mannerhence they cancel out the 'm's' in the math . also the fact that μ a/g is off in the logic the case pertains to zero acceleration so how could u have an a? unless we talk in terms of force ur equation should be something like μ F/mg (where a, would be a measure of the force simply!)
