Why are clasical physics formula simple and how accurate are they?

Question

Hi. I've been wondering about this for a while. I find it surprising that most classical physics equation are surprisingly simple. Take for example, the equation, F=ma, D=Vi*t+1/2at^2 or even x' = ( m1x1 + m2x2 ) * (m1 + m2)^-1. 

The reason I find it surprising is because all the numbers and variable are so neatly arranged that it seems far too simple to be true. Why arent there any constant terms in the equation f=ma? Shouldn't it be more like F= 1.05235m*a + 0.0000433? How come classical formulas are so perfect? And although I understand that some classical mechanics equations are more complex to calculate, the constant term are still so easy and simplified it leads me to wonder about the accuracy of these equations.

As for the second question, how accurate are classical mechanics formulas? From my experiences, these equation are still used in modern engineering today. Although other factors are included into their calculations, the very foundation of these classical formula still remains unchanged. So my second question is, how precise are these formulas?

Thanks for taking your time to read through all of this. Im looking forward to hearing your responses.

? · Accepted Answer

F = ma works because the unit of force (the newton) is DEFINED as being the force which gives a 1kg mass an acceleration of 1m/s².

If F is measured in pounds weight, m is in kg and a is in m/s², then the equation becomes:
F = 0.225ma approx. (if my maths is correct!).

The concepts of distance, time, speed and acceleration are human ones, defined to help us describe the way the world behaves.  D=Vi*t+1/2at^2 follows directly from the way speed and acceleration are DEFINED mathematically. 

x' = ( m1x1 + m2x2 ) * (m1 + m2)^-1 is a bit harder to exaplin but I think it is partially a result of geometry.

You said "D=1/2gt^2 will work everywhere on the universe"
That's not true.  It only works perfectly accurately in regions where g is constant.  There is nowhere like this in the universe!  The formula is an approximation that appers to be accurate most of the time, but if measurement are made very accurately it doesn't work perfectly!  'g' is not a fixed numbner - it depends how far away from the centre of a planet you are. It even depends on how fast you are going and the GPS system has to correct for these effects to give accurate positioning.

The reason you get exaclty 1/2 in some formulae usally follows from the derivation. The 1/2 in 1/2gt^2 occurs because we are assuming g is constant and the average velocity is therefore  (initial velocity + final veloicty)/2; that's where the '2' comes in.

You haven't learned enough physics yet, or you would have discovered, for example, that you CAN'T use centigrade for certain calculations BECAUSE it depends on the properties of water. You have to use a different temperature scale that has at least one point which doesn't depend on a material (that's the absolute temperature scale and uses units of kelvin (K)).

As you learn more phyiscs you will understand the answers to your problems better.

However at a deep level there is truth in what you say.  You might like to take a glance at the link.

Dean · Answer

They are axioms, ideal relationships in ideal situations.
force mass and acceleration are related.
f = ma
a = f/m
m = f/a
say predicting the acceleration of a mass under a constant force under ideal conditions
(no air resistance or friction or additional external forces such as gravity)

Trending News

Why are clasical physics formula simple and how accurate are they?

2 Answers