Why is the friction between two smooth(not extremely smooth) surfaces low when they can form more bonds between them?
The law of friction that you learn at school was originally formulated by da Vinci in a series of experiments and later verified by Amontons(called Amontons’ law, without giving him due credit) in a very simple form
μ=F/L=
constant (independent of A and V) —————(1)
where A and V are the (“apparent” or macroscopic) contact area and sliding velocity, respectively. The law is phenomenological in the sense that there are’t fundamental like Newton’s law of gravity or Maxwell law of electromagnetism. We also know that the law isn’t valid for a wide range of velocities and loads but still gives an adequate picture for a wide range of surfaces for about 500 years.
Now, coming back to your question, the friction between highly smooth surface comes because of adhesive forces. The original Amontons’ law is valid when there are impurities between the surfaces and the surface molecules “knows” that the impurities are not of his kind, but in case of highly smooth surface the surface fails to know which is which and “thinks”, it is one of its kind and hence clings to it with strong intermolecular force of attraction.
Another thing to note in case of impurities μ
is zero when there is no load or L=0 but in case of highly smooth surface μ is non-zero even when L=0. Take for example two highly smooth copper plate and turn it vertically and notice it doesn’t fall off. This tells us that eq(1) is not applicable for highly smooth surface. The correct(not really though) is
F=σA
—————(2)
where σ
is the shear stress(laterally applied force per unit area) and A is ‘real’ area. You see that (1) doesn’t depend on area but (2) depends on it Why so ? You must understand that when Amontons was saying friction does’t depend on area, he meant ‘apperanent’ area not ‘real’ area. If you look at the contact of two surfaces with impurities in a powerful microscope, and go on to calculate the area of each microscopic dent that is actually in contact with surface you calculate ‘real’ area but when you just do a macroscopic calculation, it is ‘apparent’ area. In highly smooth surface, since the bond is intermolecular, almost chemical, the real area matters and matters too much! Thats why you have so strong friction.
We combine both this law and write the law of friction as
F=μL+σA
and define μ
as μ=dFdL and not otherwise.
The law of friction that you learn at school was originally formulated by da Vinci in a series of experiments and later verified by Amontons(called Amontons’ law, without giving him due credit) in a very simple form
μ=F/L=
constant (independent of A and V) —————(1)
where A and V are the (“apparent” or macroscopic) contact area and sliding velocity, respectively. The law is phenomenological in the sense that there are’t fundamental like Newton’s law of gravity or Maxwell law of electromagnetism. We also know that the law isn’t valid for a wide range of velocities and loads but still gives an adequate picture for a wide range of surfaces for about 500 years.
Now, coming back to your question, the friction between highly smooth surface comes because of adhesive forces. The original Amontons’ law is valid when there are impurities between the surfaces and the surface molecules “knows” that the impurities are not of his kind, but in case of highly smooth surface the surface fails to know which is which and “thinks”, it is one of its kind and hence clings to it with strong intermolecular force of attraction.
Another thing to note in case of impurities μ
is zero when there is no load or L=0 but in case of highly smooth surface μis non-zero even when L=0. Take for example two highly smooth copper plate and turn it vertically and notice it doesn’t fall off. This tells us that eq(1) is not applicable for highly smooth surface. The correct(not really though) is
F=σA
—————(2)
where σ
is the shear stress(laterally applied force per unit area) and A is ‘real’ area. You see that (1) doesn’t depend on area but (2) depends on it Why so ? You must understand that when Amontons was saying friction does’t depend on area, he meant ‘apperanent’ area not ‘real’ area. If you look at the contact of two surfaces with impurities in a powerful microscope, and go on to calculate the area of each microscopic dent that is actually in contact with surface you calculate ‘real’ area but when you just do a macroscopic calculation, it is ‘apparent’ area. In highly smooth surface, since the bond is intermolecular, almost chemical, the real area matters and matters too much! Thats why you have so strong friction.
We combine both this law and write the law of friction as
F=μL+σA
and define μ
as μ=dFdL and not otherwise.
