**Title: What does it mean to multiply units?**
I can’t grasp what it represents in the real world
Addition/Subtraction: only makes sense in same units and increases/decreases the value like moving forwards/backwards or inreasing/decreasing the amount of force on an object etc…
Division: a ratio, how much of x per y: how many meters you move in one second, how much force is put on an area etc….
Multiplication: no idea. The unit of force: kg / m×s^(2,) mass per whatever m×s^(2) means or F = m×g what does m*g represent? Obviously there is a mathematical proof for this equation but what is the actual reason beyond: the math works out
Or imagine I am in the process of figuring out a brand new equation (in Physics/Chemistry/Geometry/…) how do I know that I need a multiplication right here beyond it’s the math?
**EDIT:** An Attempt to clarify the problem I have
At some point in school we learn that multiplication can describe areas: 7*5 = 35 is the number of pieces in a rectangle if said rectangle is divisible into 7 rows with 5 pieces each or 7 columns with 5 pieces each or the opposite.
Multiplication can also describe an event occuring multiple times if I run 5 km in 7 hours then I ran 35 km total
in probability multiplication can also describe the number of possible uniqe iteration
and I definitly forgot a few things.
But what does Multiplication describe in nature sciences or physics especially? Perhaps in the example of F = m*g but also in general
In: 0
Ok, let’s start with an example you gave. Let’s take a force being exerted on a body, the unit for that is Newtons
Newtons can be written as Kg*m/s*s, but that’s hell of confusing, so let’s break it down. If we do you see it has Kilograms, Meters, Seconds and m Seconds again. This is still hard to put together though, so let’s built up to it from something smaller.
Let’s for example, first define speed. Speed is how far a given body moves in a given amount of time, it is therefor expressed in m/s, or how many meters a body moves PER second (Think of the division as the word per).
But what if we want to measure how the speed of a body changed? Well, then you measure the difference between its starting speed V1, and final speed V2 in a given period of time and see how it changed. We call that acceleration.
To stick to metric units, say a body is static (so it has a speed of 0m/s) and that it suddenly starts speeding up so that after a minute it’s moving at 600 m/s. Well, in that case we divide that difference (600) by the unit we want to measure acceleration in (seconds) and arrive at our value.
600 / 60 = 10
So we know the speed in m/s changes by 10 m/s PER second.
So we now have m/s/s. But that is the same as writing m/(s*s) or m/s^2 so for ease of understanding we present it like that.
Now for a body to suffer acceleration we need to exert a force on it, and forces are likewise defined by their ability to change the speed of an object. So how do we measure forces? For convenience we defined that a force capable of imparting 1m/s^2 acceleration on a 1kg body is called 1 Newton. So for example, if you can make a 20kg body suffer a 5m/s^2 acceleration by shoving it, then we can calculate that you should be able to impart an acceleration of 1m/s^2 on 100kg body. That means when you shove an object your using 100 Newtons of force.
So how do we write it? Well, if Newtons are defined by how fast you can accelerate a certain mass you simply grab the value of the mass (kg) and multiply it by the acceleration (m/s^2)
That’s how you arrive at kg * m/s^2
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