2 ms·

Way back in undergrad I asked why the conversion ratio between electromagnetic and electrostatic charge had the dimensions of meters per second (it's the speed

Way back in undergrad I asked why the conversion ratio between electromagnetic and electrostatic charge had the dimensions of meters per second (it's the speed of light, for those who haven't had to drag themselves through Maxwell). The prof pointed out that if you had a soap factory and measured output in pounds per day and also in dollars per day, the conversion ratio of the two output measures would have the dimensions of dollars per pound, which would also happen to be the price of a pound of soap. I just always thought that was neat.

bonzini 3y ago
The instant consumption of electric cars can be measured as kW which is power, but the overall consumption will more commonly use something like kWh/km which is a force unit (equal to 3600 N); and the ratio between the two is the average speed measured in km/h. Is this related to the answer of your original question? [Yes technically you'd more likely see kWh/100km or Wh/km, but the result is a silly unit for speed].
- bandrami 3y ago
  Yeah it gets to the kind of weirdness that a kWh has the same dimensions as a Joule: power is an instantaneous measurement and when integrated over time yields energy: (mass * distance) / (time squared) vs (mass * distance) / (time), to use the engineering sense of d / dt meaning "dividing by a little bit of t" (we were supposed to avoid saying that around people from the mathematics department). Where it got really interesting was Heisenberg, because the indeterminance relationship doesn't just hold for position and momentum but for any two units whose dimensions multiply out to (mass * distance squared) / (time). So famously meter vs kilogram * meter / second, but more usefully in real life second vs Joule. Or weird combos like mass vs change in area over time, whatever that would mean...
pjc50 3y ago
Similarly for the petrol consumption case, once you convert "liters per 100km" to normalized units, you get "square meters". Usually for most cars a value of a few square milimeters. You can intuit this as "sweep the volume of the fuel injector across the distance travelled"; imagine all the petrol used as a very thin cylinder lying along the length of the trip.

bonzini 3y ago

The instant consumption of electric cars can be measured as kW which is power, but the overall consumption will more commonly use something like kWh/km which is a force unit (equal to 3600 N); and the ratio between the two is the average speed measured in km/h. Is this related to the answer of your original question? [Yes technically you'd more likely see kWh/100km or Wh/km, but the result is a silly unit for speed].

bandrami 3y ago
Yeah it gets to the kind of weirdness that a kWh has the same dimensions as a Joule: power is an instantaneous measurement and when integrated over time yields energy: (mass * distance) / (time squared) vs (mass * distance) / (time), to use the engineering sense of d / dt meaning "dividing by a little bit of t" (we were supposed to avoid saying that around people from the mathematics department). Where it got really interesting was Heisenberg, because the indeterminance relationship doesn't just hold for position and momentum but for any two units whose dimensions multiply out to (mass * distance squared) / (time). So famously meter vs kilogram * meter / second, but more usefully in real life second vs Joule. Or weird combos like mass vs change in area over time, whatever that would mean...

pjc50 3y ago

Similarly for the petrol consumption case, once you convert "liters per 100km" to normalized units, you get "square meters". Usually for most cars a value of a few square milimeters. You can intuit this as "sweep the volume of the fuel injector across the distance travelled"; imagine all the petrol used as a very thin cylinder lying along the length of the trip.