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# Friction - Mu R Watch

1. Hi. F=Mu R
Why is Mu multiplied by the normal reaction force? I thought it would be more logical to multiply the coefficient of friction by the force in the direction of the ground (below). It especially doesn't make since since the reaction force isn't necessarily always the same as the force acting downwards.
2. (Original post by MathMeister)
Hi. F=Mu R
Why is Mu multiplied by the normal reaction force? I thought it would be more logical to multiply the coefficient of friction by the force in the direction of the ground (below). It especially doesn't make since since the reaction force isn't necessarily always the same as the force acting downwards.
1. The relationship is essentially a rough, empirical thing. If you do experiments with materials pressed together, and dragged relative to each other, then you find that the value of limiting friction is roughly proportional to the normal reaction.

2. "I thought it would be more logical to multiply the coefficient of friction by the force in the direction of the ground (below). It especially doesn't make since since the reaction force isn't necessarily always the same as the force acting downwards."

This is pretty much incomprehensible, I'm afraid. If you want someone to answer this:

a) write some equations using symbols (wordy maths went out around Newton's time)
b) draw some pictures - where is your "reaction force" pointing and what is "the force acting downwards"?
3. (Original post by atsruser)
...
The force acting downwards lets say is the force mass*gravity making it go towards the ground/plane. I.e It's more logical that the equation should be F=Mu*mg (where mg is the mass multiplied by the acceleration [g] (9.8 m/s/s) acting towards the plane/ground.)
It would make more sense saying that friction= the coefficient of friction multiplied by how much force is going downwards. But it's not.
4. (Original post by MathMeister)
The force acting downwards lets say is the force mass*gravity making it go towards the ground/plane. I.e It's more logical that the equation should be F=Mu*mg (where mg is the mass multiplied by the acceleration [g] (9.8 m/s/s) acting towards the plane/ground.)
It would make more sense saying that friction= the coefficient of friction multiplied by how much force is going downwards. But it's not.
My thinking would be

The reaction force and the frictional force are perpendicular to each other so it makes more sense to look for a connection between those as they are never in the same equation of motion

Also, whist the weight does not change the reaction force does when we create a slope - given that friction also changes with slope it cannot be a function of weight
5. also in reality its Fr<= MuR

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