Definition of Force.

Force is some natural phenomenon that changes the state of the motion of the body that is it accelerates the body. Now let us define a unit of Force arbitrarily (e.g. a standard spring being stretched 1 cm under elastic limit and select a stone, make it standard. it serves as a unit of mass.

This force produces some acceleration on that unit mass.

Now if we take two of such stones and both identical and let a unit force act on each of them such that they move together in parallel. Now bring the two stones close together such that they are almost coincident and a unit is acting on force on each stone.

Obviously will accelerate as much when unit force acted on one stone. Now here come the crucial point Consider two stones close together as one big stone of 2 units of mass and two unit forces acting in the same direction together as single 2 unit force. Here we have to define additive property of forces. This experiment can be repeated with 'n' number of stones in parallel and then combining together. We will always find

"Force is proportional to mass when acceleration is constant.

Now to see the effect of Force with acceleration, for a constant mass, we can do this experimentally Because we have a unit of force and we can make many of such springs exactly And force being defined to follow the law of addition, we can attach two springs to the unit mass, and pull it from the other side until they both are stretched at 1 cm.

Repeating this we can find the relationship between force and acceleration. It turned out to be linear and hence in classical physics we Could have "Force = Mass * Acceleration".

But we know this is wrong. the correct definition is.. F = dp/dt...And all concepts of Force and Mass gained earlier have to be redefined!!

I believe that Newton had not only wanted to explain the uniform force. Indeed, he would also like to explain the change in momentum one object when there is an elastic collision with other. this great force acts on the objects very short interval of time, so the change in the momentum could be only measure to define the team force. Also for non uniform forces.

The basic definition of force is, that it changes or tend to change the momentum of the body.

Take the same put a stone of 1kg on top of a table neither its mass nor the velocity is changing but still it is experiencing two force, gravity & normal reaction.. Hence the picture of dp/dt comes when there is an unbalanced force and the funda is change in the momentum is in the direction of unbalanced force

Thus, he definitely didn't want to explain force with mass alone, since mass is a scalar , but force is a vector and so momentum.