Microvolts over degrees->degrees over microvolts

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To convert -72 microvolts per degree Celsius to degrees per microvolt, the reciprocal must be taken, resulting in -1/72 degrees per microvolt. This process involves switching the numerator and denominator while maintaining the magnitude. The analogy of earning money illustrates the concept of reciprocals in unit conversion. The discussion emphasizes the importance of correctly applying unit transformations. Understanding this principle is crucial for accurate calculations in scientific contexts.
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Microvolts over degrees-->degrees over microvolts

If I have -72 \mu V / degrees C... how do I change that to degrees per microvolt? just
-72 degrees C / \mu V?
 
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What have you done to the units??
Do the same to the magnitude as well!
 
72 degrees per microvolt?
 
Umm...no.

If I earn ten dollars per hour, how many hours do I work per dollar I earn? The answer is that I earn a dollar in one tenth of an hour (= 6 min). I hope this is obvious. So what did I do to change my figure in units of money earned per unit time to time worked per unit money? I took the reciprocal.

'Nuff said...
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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