Measurement of force According to Newton's Second Law,
$F=ma$
which is based on the fact that force is proportional to acceleration for a constant mass.
But how will someone measure force to confirm this?
Suppose one observed that for a certain push(force), object accelerated by $1$$m{s}^{-2}$. Now we again pushed the same object, this time acceleration is $2$$m{s}^{-2}$. But how can we conclude that the force is also double the previous amount?
 A: An useful experiment to prove Newton's second law is the one in which you have a mass on an inclined plane attached to a dynamometer which is the instrument by which you can measure the force and therefore define it. You can attach an $m_{1}$ mass and measure the intensity of the force. Then you attach a $m_{2}$ mass which can be, for example, double the first mass and then you can again check for the intensity of the force on the dynamometer. The proportion between mass and force is then proven.

A: I think your question is kind of circular.
Physical "laws" are simply formulations of observable phenomena that seem to hold under the observed circumstances.
Newton proposed that a body will not change its momentum unless acted on by a force.
He also proposed that the rate of change of momentum IS directly proportional to the force.
Thus the magnitude of the force is DEFINED by the acceleration it produces, and therefore your question is not a valid one.
A: Is Newton's second law a real law of nature or is it a definition of force?  If it is a law, telling us something about the way things are in the world, rather than what certain words mean, then force must have a definition (or at least a means of measuring it) independent of the law.
The Principia reads as if Newton thought of the statement as a law. We can, indeed, think of some informal ways in which force could be measured independently of the rate of change of momentum that it causes. For example we could stretch several identical springs by the same amount and put them in parallel with each other. It might be considered obvious that the force exerted by the combination is proportional to the number of springs. [In the UK, not so very long ago, students were invited to 'discover' $F=ma$ by attaching such spring combinations to trolleys. I don't think this it bad science.]
What is the accepted view today? We probably define the magnitude and direction of a force by the rate of change of momentum brought about by the force (acting alone). But I draw the line at defining the concept of force as rate of change of momentum. We still, surely, regard a force as an agency that brings about a change of momentum. Consider a charge in an electric field. We may write
$$q\mathbf E = m\ddot {\mathbf r}.$$
Do we not still regard the left hand side as the force, and the right hand side as its effect?
