**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
The reality is, you already understand multiple unit math, you just don’t realize it yet.
Let’s say you have a big box of apples that you weigh, and find out there 100 lbs of apples in the box. You take out each apple and count it, and find out the box was holding 400 apples, you could take the average density of apples as:
400 apples / 100 lbs = 4 apples per pound, or 4 apples/lb
Then if you have another box that holds 200 lbs of apples, you could multiply it by the apple density you know of to find that the number of apples is: 200 lbs * (4 apples/lb) = 800 apples.
So the above is an example of units divided, IE apples / pound. Similar commonly used divided units are pressure, IE lbs/ square inch.
Let’s say you’re on a teeter-totter, and balancing with another friend. If each end of the teeter-totter is 4 ft from the pivot, and you’re sitting on it with a weight of 150 lbs, you’re applying a moment (torque) of M = F X R = 150 lbs * 4 ft = 600 ft*lbs.
If you add another 100-lb person to your side of the teeter-totter, you added a total torque of 100 lbs * 4 ft, or 400 ft * lbs.
So you’ve added 400 ft * lbs to 600 ft * lbs to get 1000 ft * lbs. So though the units are multiplicative (ft * lbs), because the sums you’re adding are the same, you can safely add them.
When you multiply, it doesn’t matter what the units are, it always works the same. You multiply both the numbers and the units. If it’s “4 cookies” times “$2 per cookie”, then the result is $8, because “cookies” * “per cookie” cancel out.
If you multiply “3 feet” by “3 feet”, the result is 9 square feet.
If you multiply “10 miles per second” with “60 seconds”, the result is 600 miles, because the “per second” and “seconds” cancel out.
It’s no different with any of the other examples you’re giving.
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If you want to visualize it, multiplication always adds a dimension. If you multiply two values which are one-dimensional, e.g. 3 meters and 2 meters, which are just “lengths” of a one-dimensional line, the result is two-dimensional: a rectangle of 2 by 3 meters length, i.e. an “area”. If you then multiply that again by another 4 meters, which again is a one-dimensional value, the result is three-dimensional, i.e. a block of 2 by 3 by 4 meters called “volume”. It’s easier to visualize if all three components have the same type of unit, but it doesn’t actually matter at all for the concept itself. Energy consumption is measured in kWh, which can be visualized as the two-dimensional area of a rectangle with some amount of Energy (kW) in one dimension and some other amount of time (h) in another dimension. Whether it’s 1 hour of 2000 kW consumption or 2000h of 1kW consumption doesn’t matter, the total energy consumption (i.e. the area of the rectangle) is the same in both cases.
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How do you know if you have to multiply something? That’s easy – correlation. If something grows when something else grows, you have to multiply it. If something gets smaller while something else grows, you have to divide by that. Like the formula for gravity. Gravitational force gets bigger the bigger the two masses are, so both masses have to be multiplied. The force gets smaller the bigger the distance is between those masses, so we have to divide by the distance. We actually see that this reduction is not just proportional, but actually exponential, so it’s really divided by distance squared. Then you only need to calibrate the formula with some constant factor to make the numbers work out, and there you go – Newton’s formula of gravitic force, derived quite easily just from basic observations.
Do not look at basements directly look at them in steps via other units.
force in newtorn = kg m /s^2 not kg / m×s2,
A force is coming that can accelerate a mass. You ned more force to accelerate a larger mass at the same rate as a smaller mass. If on the other hand, the force is constant a larger mass will get accelerated slower then a small mass
Force = mass x acceleration.
Mass is in kg and acceleration is m/s^2
Distance will be in meter
Speed is how distance changes with time or meter/second.
Acceleration is how speed changes with time so speed/second = meter/second/second = m/second^2
Another way to say it is speed is the first derivate of distance in regard to time and acceleration is the second derivate
So a force is something that can accelerate a mass and the units will be kg m /s^2
F=m x g is the weight of an object. m is the mass and g is the acceleration du to gravity on a mass
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
If I drive a speed of 50 miles per hour (that is a unit of speed) for 2 hours, that is 100 miles.
Speed X Time = Distance
Something about this formula is that speed is already expressed as a ratio of distance / time.
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