In all the objects we have present in our reaching we can see that without friction, it will be uneasy for a certain object to stay in its position without slipping. In many physics problems we assume there is no friction to make the problem easier but the reality is that there will always be friction. In mathematical purposes we see that friction is proportional and perpendicular to the normal force. As we know, we are usually provided with a table of the coefficient of frictions for both rough and smooth surfaces [1]. The interval in which the coefficients take place is usually 0 to 1, but as everything else in science and in math there will always be an exception. The science world usually starts with making assumptions of certain theories to then proceed to the experimentation to see if it passes as a law or now.
What happens if you are not provided with the table of coefficients of friction? You can always assume it’s in the interval (0, 1) and see if it’s less or greater than the Normal force by how rough or smooth the surface is. The rougher the surface is than greater the force you need to produce movement and the lesser force you need to keep the object at its stationary position [1]. The case for smooth surfaces is opposite to those of rough surfaces. When the surface in which the object lies is a smooth surface then the force you’ll need to move the object will be less than its normal force and to keep the object at its stationary position then the force needed will be greater than its normal force. The coefficient of friction is a number which represents the friction between two surfaces. Between two equal surfaces, the coefficient of friction will be the same, it’s a constant only for a given pair of sliding materials under a given set of ambient conditions and varies for different materials and conditions.
However, we can use these definitions and known theorems of friction to create a new approach. A general idea that can be used in many engineering disciplines under certain, but common conditions.
The proposed idea consist of neglecting the existence of the coefficient of static friction when 0.9 ≤μs ≤ 1, specifically when calculating frictional forces. Let’s begin with the mathematical explanation for frictional force which is: Ffr= μs FN. So for small values of μs, we will have almost identical values of Normal Force. For example: if μs = 0.95 and FN =3N, the Ffr= 2.85N, almost the same as the original Normal Force. Therefore for ranges very close to this interval of 0.9 ≤μs ≤ 1, one will have a percent of error around 5%.
Some benefits from this assumptions are mainly that it is practical, because many engineers can estimate their Friction Forces faster. It can also be proved mathematically (like discussed above) that under certain conditions this is true and facilitates calculations. That it can be applied to different surfaces as long as μs is between intervals stated.
Future work can include further study of the coefficient of kinetic friction, and how it can be analyzed so under certain conditions it can be negligible or easier to calculate under special cases.
References:
[1] Giancoli, Douglas C. Physics for Scientists & Engineers. Upper Saddle River, NJ: Prentice Hall, 2000. Print.
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