How did this definition come to Newton's mind? Force seems to be the effort we apply. So, qualitatively, more the effort, more the force. How to understand intuitively that this formula given by Newton gives a quantitative measure of Force? And, how do we know that Force does not depend on more variables? I think an infinite number of formulas can be given to measure the 'effort' we make. For example, I could give a formula to measure roughness of a surface and could define the unit force as the amount of force required to move a body of unit mass through a distance of 1m on a surface of unit roughness. I think that this definition could also measure the effort. Also, why not |m|+|a| or |m|^|a|. Why this particular definition of force?