The key to this answer is that if we take some fixed configuration of say gravitating bodies, and then consider a test particle, its subsequent motion: a is completely determined by its initial position and velocity; but b the initial position and velocity are free variables which can be changed relatively easily.
It would actually be impossible! But in practice we find that initial velocities are things which we have a lot of freedom to adjust. In more mathematical terms: suppose we believe the motion of a test particle is completely determined by its initial position and velocity, but also that those quantities are free variables which we can choose. If we know just a little about differential equations this suggests some kind of second-order differential equation must be controlling the behavior of the particle.
In particular, the acceleration of the test particle should somehow be a function of the other configuration of matter. This is a pretty conventional story. Two test particles with the same initial position and velocity, but different electric charges, can behave quite differently in the same electric field.
That free parameter would implicitly contain what in the conventional approach we think of as the charge information. Indeed, the new equations of motion would have a conserved quantity, corresponding to the charge.
But the resulting force laws would be quite a bit uglier. Actually, if we ever saw a situation in nature where charges seemed to change over time, this jerk-based approach might be worth exploring! But the left-hand side, the very notion of a force, is subtle indeed. And, of course, other people have figured out other ways of computing force as a function of the distribution of matter and fields. None of these implicit assertions has anything a priori to do with ma.
The math behind this is quite simple. If you double the force, you double the acceleration, but if you double the mass, you cut the acceleration in half. Newton expanded upon the earlier work of Galileo Galilei , who developed the first accurate laws of motion for masses, according to Greg Bothun, a physics professor at the University of Oregon. Galileo's experiments showed that all bodies accelerate at the same rate regardless of size or mass.
Newton also critiqued and expanded on the work of Rene Descartes, who also published a set of laws of nature in , two years after Newton was born. Descartes' laws are very similar to Newton's first law of motion. Newton's second law says that when a constant force acts on a massive body, it causes it to accelerate, i. In the simplest case, a force applied to an object at rest causes it to accelerate in the direction of the force.
However, if the object is already in motion, or if this situation is viewed from a moving inertial reference frame, that body might appear to speed up, slow down, or change direction depending on the direction of the force and the directions that the object and reference frame are moving relative to each other. Let's say we see some m with an a.
So we must insist on some rules about the F 's. The third law says that there needs to be an opposite F on something else, and we can insist that the something else is fairly nearby. More generally, we can insist that the rules for when there should be an F shouldn't be too weird or complicated. Up to a point, that program works. That's a very compressed version of a long discussion.
Feel free to follow up. It seems like this is what Mr. Newton did while experimenting on accelerating objects before he came up with this law, but since he was the head of the British Royal Society of science, no one dared question him. It doesn't have to take an Einstein to realize that, but a willing to be disattached from prejudices. I hope no one gets offended by my questioning as if I attacked their religious beliefs. Historically speaking, humans held unshakable beliefs as facts for hundreds of years before they finally tossed them out as falsehoods, and I believe that there are still lots of falsehoods that will be tossed out of science facts in the future.
Thank you. Rebecca H. I completely agree to the above explanation given by Mr. Intuitively and even logically I understand that force applied to generate a specific acceleration in an object depends on mass of the object.
Let me put my point through a thought experiment. Consider a ball that weighs grams and another that weighs 1 kg. Now make your friend drop them from the balcony of the first floor so that it doesn't gives air resistance enough time to change their accelerations by a lot.
So when the balls fall down they will be having almost similar acceleration and you stand down to catch them. Now from the 1 kg ball you will experience a greater impact on your hands than with the grams. So the forces you applied on 2 balls having different masses gave the same acceleration and the one with the greater mass had the greater force applied on it. Hence F is directly proportional to mass.
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