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. And so the configuration of matter completely determines the acceleration of a test particle. There is no a priori reason this ought to be true. This force is a simple function of the configuration of matter and fields, notably of the positions, velocities and charges of all particles.
That suggests the force should somehow determine the acceleration. Newton's Second Law relates the three quantities. This leaves open the distinction between inertial mass and gravitational mass, but separate experiments can show that they are numerically the same.
At heart, force is "amount of push", but how do you define this? You can't, without making some appeal to a deeper law. Your statement about inertial and gravitational mass belies this -- gravitational mass isn't a thing without a gravitational law. Show 3 more comments. Active Oldest Votes. Suppose that you were to perform the following experiments: 1. Like this: b If you happen to find a ball that is moving with constant velocity, that is it moves in a straight line and it moves equal distances in equal times.
Like this: What we find is that if we are in a place where the ball is not interacting with anything air, gravity, etc.
Now suppose that the ball is not moving and you shot this arrow to move it, you have the same conditions as before: As you can see the ball wasn't moving and now it is moving, so it accelerated. Improve this answer. M Katz 5 5 bronze badges. Keith Keith 6 6 silver badges 22 22 bronze badges.
Add a comment. Floris Floris k 12 12 gold badges silver badges bronze badges. I will be back when I can make a diagram The same approach of yours was followed by A. French, last century's MIT physics professor in his book. You can go here. The famous relation can be deduced intuitively by means of calculus. I would also like to jot down A. French's way to prove the law: A.
French's deduction of 2nd law:- Let an object is placed on a horizontal table pierced with holes through which air is blown from below. Let's see: If we place on the first object a second, identical object, it is observed that all accelerations produced by given arrangements of the sprins are reduced to half of what was obtained with one object alone.
Here, we are not questioning about the validity of second law but rather we have to find the relation between force and acceleration. Now, one can ask whether acceleration is proportional to force or vice versa. So, this is not a circular reasoning. You are not proving the second law but rather using it to find the quantitative picture of the law.
Sparkler Sparkler 3, 3 3 gold badges 28 28 silver badges 52 52 bronze badges. John Hunter John Hunter Featured on Meta. Now live: A fully responsive profile. 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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