- #1
puzzler7
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I have a problem that might sound simple, but has been bugging me for months. In a physical equation, the units are regarded as multipliers - so to take a very simple example in SI:
1) F[N]=M[kg]a[m/s2]
And, of course, [N] is equivalent to [kg][m/s2], so all is well.
Here's my problem: let's say I want to adjust the equation, so that my mass measurements are in grams [g] rather than [kg].
Direct substitution for 1kg = 1000g into equation 1) gives:
2) F(N)=1000M[g]a[m/s2]
Which is clearly incorrect.
(a mass of 1g accelerated at 1 m/s2 would compute a force of 1000N - wrong - The equation actually needs to be divided by 1000 on the RHS.)
The logic looks perfect - but the result is wrong.
The problem is resolved in *all* equations by regarding the algebraic symbols to be *divided* by the unit - so why do we consider them to be multiplied?
What's my problem!?
1) F[N]=M[kg]a[m/s2]
And, of course, [N] is equivalent to [kg][m/s2], so all is well.
Here's my problem: let's say I want to adjust the equation, so that my mass measurements are in grams [g] rather than [kg].
Direct substitution for 1kg = 1000g into equation 1) gives:
2) F(N)=1000M[g]a[m/s2]
Which is clearly incorrect.
(a mass of 1g accelerated at 1 m/s2 would compute a force of 1000N - wrong - The equation actually needs to be divided by 1000 on the RHS.)
The logic looks perfect - but the result is wrong.
The problem is resolved in *all* equations by regarding the algebraic symbols to be *divided* by the unit - so why do we consider them to be multiplied?
What's my problem!?
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