How are proportionality constants in physical relations determined?

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Proportionality constants in physical relations, such as the universal gravitational constant (G), are determined through careful experimental measurements, which yield values with associated precision levels. The exact values of these constants are often not precise due to variations in experimental methods. For example, G is known to be the least precisely determined physical constant. Other constants, like "k" in Coulomb's law, initially had empirically derived values but can now be calculated from other constants for greater accuracy. Understanding these constants is crucial for accurate scientific calculations and theories.
Syed Ammar
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I wanted to ask how are the values of proportionality constants in physical relations determined. How do we come to know their exact values ? An explanation with an example please...
 
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Syed Ammar said:
I wanted to ask how are the values of proportionality constants in physical relations determined. How do we come to know their exact values ? An explanation with an example please...
Which proportionality constants do you have in mind?

If you are talking about something like G (the universal gravitational constant), its value is determined through careful experiments. The value obtained is not exact (how could it be?), and there is usually a precision associated with each constant, since different experimental methods have different levels of precision associated with them. For instance, G is the one physical constant which is least precisely known.

http://en.wikipedia.org/wiki/Gravitational_constant
 
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Can you elaborate on constants of other fundamental forces like k in Coulomb's law?
 
While in the beginning, when Charles-Augustin de Coulomb postulated the law named after him, "k" had an empirically derived value, it now has a precise value, because you can calculate it from other constants. The Wikipedia article on the constant lays out the derivation quite nicely.
 
I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

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