RE: Flat Earther, and other conspiracy theories. Are they mostly atheists?
March 4, 2021 at 2:22 pm
(March 3, 2021 at 10:30 pm)polymath257 Wrote: Very seldom do we have reason to multiply bunches of apples, although I will give an example where it happens below. But, we *do* have reason to multiply meters and meters--it gives us an area. We can even multiply meters by meters by meters to get a volume.
Seconds (s) are frequently multiplied by seconds, although typically it is divided by seconds twice in a row. So, a meter divided by a second is a measure of velocity and dividing by seconds again gives an acceleration. Doing it again gives something called the jerk.
Densities are often measured in mass per volume, in other words kg/m^3. But, for example, the units of energy are kg*m /s^2.
It is less common to have to multiply by kelvins or to divide by them twice, but it does happen. For example, if you are interested in how something expands on heating, the appropriate units would be m^3/K. If you want to know how that coefficient of expansion changes as the temeprature changes, that would give something like m^3/K^2.
Another situation is where you want to talk about entropy, which has units of energy/kelvin, or kg*m/(s^2 K). But, if you want to know the rate at which the entropy changes with temperature, that would be kg*m/(s^2 K^2).
As for apples, if you want to know a price per apple, that would be something like dollars/apple. But, if you want to know how that price changes for more apples, that would be something like dollars/apples^2.
Yes, acceleration, expressed as m/s^2 corresponds to something in our reality. However, s^2 doesn't correspond to anything.
What would it mean if I do 1/(9.81546 m/s^2 / 23.5 m) = 2.39418223904 s^2
--Ferrocyanide
Well, s^2 naturally comes up when you want to go from acceleration to a distance traveled. (1/2)gt^2. You are multiplying the acceleration (g) by the square of a time (t^2). That second term has units of s^2.
All that an s^2 would mean is that you are multiplying two times together. That happens frequently in physics.
