F=ma.

"A man may imagine things that are false, but he can only understand things that are true, for if the things be false, the apprehension of them is not understanding." - Sir Isaac Newton

Newton, considered to be one of the most inspiring and influential scientists to have ever lived. My opinion however differs, as I consider Einstein and Witten to be. Nevertheless Newton was a fascinating man.


One of his most famous equations; F=ma. Quite a simple theory to understand, if you know your variables, and how to rearrange it.


The equation is part of Newtons 2nd Law of Motion and states that Force = Mass x Acceleration.

Lets say you're a professional race car driver, and you run out of fuel. Oh no. What do we have here? A car in need of pushing.


Let M = 750kg, 750 000 grams. 


M is the the mass of the thing which is acted upon, in this case the car. 


And let a = 0.5 m/s/s (Metres a second, per second) - this is the speed (acceleration) you are pushing the car at.


So F?


F = m(*)a.


So F = 750 x 0.5.


So F = 375 Newtons!


So 375 N acting on the car!


This is a very basic way of using F=ma, as we do not know of the surface - if it is rough etc. We only need F in one direction.


However, if you are pushing forward at 400 newtons, on an object of 750kg. With a resistance of 25, what is the acceleration?


Well, F=ma. So we have F and m, we need a. So lets rearrange: A=f/m.


F = (400-25) m = 750kg.


A = 375/750.


A = 1/2 = 0.5m/s/s (m/s^2)


There we go! It works both ways!


And finally, lets work out m in another version of this question.


If you are pushing an object at 450N, with a resistance of 75N, at a rate of 0.5m/s/s. How much does your object weigh?


Well M=f/a, so...


F = (450-75) a = 0.5


M = 375N/0.5m/s/s


M = 750kg!


So there we have it, it works in all 3 ways!


Thanks for reading, Ben.