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This question already has an answer here:

I have been told always that $F$ is directly proportional to acceleration.

My question is that for finding such a relationship there should be source that produces desired force and in which the force can be adjusted i.e. Twice, thrice and more. But the problem is initially before the discovery of laws of motion how can one say that a force is twice the other, how can he even judge the relationship between two forces without knowing the quantitative definition of force?

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marked as duplicate by Brandon Enright, John Rennie, tpg2114, Alfred Centauri, Qmechanic Nov 13 '13 at 18:08

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ Duplicate of physics.stackexchange.com/q/2644 $\endgroup$ – Kyle Kanos Nov 13 '13 at 15:53
  • $\begingroup$ @kyle kanos that question does not answers the question above $\endgroup$ – user28804 Nov 13 '13 at 15:57
  • $\begingroup$ It does as stated from the title of this question. $\endgroup$ – Ignacio Vergara Kausel Nov 13 '13 at 16:17
  • $\begingroup$ Another possible duplicate: physics.stackexchange.com/q/70186/2451 $\endgroup$ – Qmechanic Nov 13 '13 at 16:22
  • $\begingroup$ @user28804: I disagree. Lubos's answer provides the answer to your question in his last 3 paragraphs. Please read it again. $\endgroup$ – Kyle Kanos Nov 13 '13 at 16:33
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how can he even judge the relationship between two forces without knowing the quantitative defination of force ??

One can't. The concept "Force" is an abstraction from observation and must be well defined before quantitative relationships (once, twice, thrice, etc.) can be established.

But this was Newton's accomplishment, correctly recognizing and defining (net) force as that which acts to change an object's momentum (an abstraction which also must be correctly recognized and defined).

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  • $\begingroup$ can you tell what did newton used as a source of constant force for studying hi relationships ?? $\endgroup$ – user28804 Nov 14 '13 at 11:19

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