When working out the Uncertainties, what to do with the constants?

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SUMMARY

The discussion centers on calculating uncertainties in physical equations involving constants, specifically the equation Q=mcT. When constants like c are involved, they typically have negligible uncertainty compared to the measured variables m and T. The consensus is that the uncertainties of m and T should be added together as percentages, while the constant can generally be ignored unless its uncertainty is comparable to that of the experimental measurements. For example, the specific heat capacity of water, c=4186 J/kg, is accurate to over one part in 4000, making it unnecessary to factor in its uncertainty for most experiments.

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Q=mcT, variables with uncertainties are m and T.
If it were only Q=mT, the %uncertainty of Q would be %uncertainty of m + % uncertainty of T.

But c=constant (no uncertainties), so what is the uncertainty of Q when Q=mcT? Do you just multiply the constant to the %uncertainties of m and T?
What generally happens to constants when working out uncertainties?
 
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You would normally ignore it, as the value of the constant found in tables would have a very small uncertainty.
Any uncertainty in the constant would need to be of the same order of magnitude as your experimental uncertainty for it to be necessary to include it.
In your example, if it was water you were using, the value of c can be found from tables to be 4186 J/kg. This is presumably accurate to over one part in 4000. Much more than your readings.
If your experiment used data that was more accurate than this, you would need to get the value of c to even greater accuracy.
 
Oh ok I see...
so eg. v=2as,
then would I need to multiply the 2 to the uncertainties of a and s, or would I ignore it like you said?
 
In that formula, just add the % uncertainties in the things you measure. Ignore the 2.
It is the uncertainty in the measured values that you need to account for.
 
ok, thanks so much!
 

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