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So, will F=ma work if mass is in pounds mass and acceleration in ft/s^2, or will a proportionality constant need to be introduced to the equation? The same question applies to most if not all physics equations
What about gauss, statcoulombs, etc., the units of the cgs system?Some physical properties have only SI definitions (like volts, amps, coulombs, and such where there are no non-SI units of measurement).
Of course. Newton's second law says force is proportional to rather than equal to the product of mass and acceleration. Newton viewed force as some distinct quantity and his second law as a law of nature.So, will F=ma work if mass is in pounds mass and acceleration in ft/s^2, or will a proportionality constant need to be introduced to the equation? The same question applies to most if not all physics equations
I should have said 'Metric' system to cover its many different flavors.What about gauss, statcoulombs, etc., the units of the cgs system?
On a side note: that c is not unitless in the SI, simply means that according to the SI length is physically different from time. [added:] However, indeed c and G could have been given the value 1.[..] That c is not 1 *and unitless* means that the International System is an inconsistent set of units. The same goes for F=GMm/r2. A consistent set of units has G=1, and once again, unitless.
People don't use it much, but the English system actually had a unit of mass, the slug, which was defined so that 1 pound (force) = 1 slug * 1 foot/second^2. So a slug weighs 32 pounds on Earth.Most equations work no matter what units you use. However, many electromagnetic equations change depending on what units are used.
In your case, you can use F=ma to get the force in units of pounds[mass]*ft/s^2. One problem with imperial units is that force is usually measured in pounds[force], and you need a conversion constant to go from pounds[mass]*ft/s^2 to pounds[force] since they are totally different.
The original poster specifically asked "will a proportionality constant need to be introduced to the equation?" Depending on how the basic units are defined, you certainly do need to introduce proportionality constants in some cases.Yes, of course it works, this is like asking does mathematics work in another base system, of course it does.
I don't see how SI units are inconsistent. It's not like you're required to set c=G=1. Planck units are just a convention that physicists find convenient to work with. You won't get a contradiction if you work in SI units.However, from this perspective, SI units are not consistent either. We have to write E=mc2 (better: E2=(mc2)2+(pc)2). If SI truly was a consistent set of units we would write that as E2=m2+p2. That c is not 1 *and unitless* means that the International System is an inconsistent set of units. The same goes for F=GMm/r2. A consistent set of units has G=1, and once again, unitless.
I don't think it's quite fair to view Newton's "F = ma" as a definition. Without ever measuring any accelerations, one could imagine coming up with a concept of force, in terms of how much weight various "pushes" and "pulls" can lift. With springs and ropes and pulleys and so forth, you can develop an entire science of "static" forces without ever thinking to connecting it to acceleration. This might be a counterfactual (because I have no idea to what extent the concept of "force" was used for static calculations prior to Newton), but one can certainly imagine developing a theory of forces without ever realizing that there is a simple relationship between forces and acceleration. In that case, "F = ma" would be a discovery about the effects of forces, rather than a definition.Force is a measure of mass and acceleration according to classical physics, and mass is a measure of energy content according to relativity. Also, for centuries weight was used as a measure of mass (and bathroom scales still use that). Proportional doesn't mean identical.
You won't get a contradiction in any set of units, that isn't what consistency is about.You won't get a contradiction if you work in SI units.
I agree, I only hinted at that because I already mentioned another issue with a side topic.I don't think it's quite fair to view Newton's "F = ma" as a definition. [..] you can develop an entire science of "static" forces without ever thinking to connecting it to acceleration. [..]
Many people use the word "consistent" to mean "free of contradiction". That's certainly how it's used in mathematics.You won't get a contradiction in any set of units, that isn't what consistency is about.
That isn't how it's used in the context of determining whether a set of units is consistent. The issue here is whether the system of units is consistent with modern physics. F=kma is not while F=ma is.Many people use the word "consistent" to mean "free of contradiction". That's certainly how it's used in mathematics.
Agreed. It is a "recycled" word where they probably should have come up with a new one. Same with the "dimensionality" of a unit.Many people use the word "consistent" to mean "free of contradiction". That's certainly how it's used in mathematics.
Nothing is stopping you from doing that.Why can't you use F=ma in English units, with mass measured in slugs, force measured in pounds, and acceleration measured in ft/s^2?
In a parallel thread ghwellsjr makes use of nanoseconds and (very big) feet to make c=1 ft/nsWhy can't you use F=ma in English units, with mass measured in slugs, force measured in pounds, and acceleration measured in ft/s^2?