# What is the meaning behind multiplication in Physics?

## Main Question or Discussion Point

I understand the meaning behind Division fundamentally, such as one Magnitude being proportional to another. For example, v=m/s means meters per second. Or as a ratio, it means for every one second there is one meter.

What I can't seem to wrap my brain around is the concept of multiplying different types of Magnitudes together. Take for example Amp Hours (Ah) or A*h. What is the significance or meaning behind this? It is not a ratio, and have trouble understanding the meaning behind different types of units being multiplied together as opposed to one being divided by the other.

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phinds
Gold Member
Your example of amp-hours is a good one. Suppose you have a battery that will produce 1/2 amp at 24 volts. OK, that's nice to know, but suppose you need it to power a 24 volt light that requires 2 amps and you need it to do that for 10 hours. Will it do it? You have no idea.

BUT ... if you know that it is rated for 5 amp-hours, then you DO know whether or not it will do what you need it to do.

russ_watters
Mentor
Say it like this: 5 amp-hours is 5 amps for an hour.

rcgldr
Homework Helper
Suppose you have a battery that will produce 1/2 amp at 24 volts. OK, that's nice to know, but suppose you need it to power a 24 volt light that requires 2 amps and you need it to do that for 10 hours. Will it do it?
Probably not. I think you want the 24 volt light to also require 1/2 amp.

If you know that it is rated for 5 amp-hours
Then it can drive a 1/2 amp load for about 10 hours.

Since you know it's a 24 volt battery, then you know that the total energy stored in the battery is:

(24 volts) x (1/2) (amp) x (5 hours) x (3600 seconds / hour) ~= 216000 Joules

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A.T.
I understand the meaning behind Division fundamentally, such as one Magnitude being proportional to another. For example, v=m/s means meters per second. Or as a ratio, it means for every one second there is one meter.

What I can't seem to wrap my brain around is the concept of multiplying different types of Magnitudes together.
So you understand v=d/t but don't understand d=v*t ?

Take for example Amp Hours (Ah) or A*h. What is the significance or meaning behind this? It is not a ratio,
A is the ratio here: A=C/s So: C=A*s or: 3600*C=A*h

Chestermiller
Mentor
Ampere-hours is a measure of the amount of charge.

$$C(coulombs)= A(\frac{coulombs}{sec})×3600(\frac{sec}{hour})×h(hours)$$

In general it sort of means "Applied over..."

As A.T. pointed out, d=v*t is basically read, "Distance is equal to the velocity applied over t amount of time"

Or "Mass is equal to the density of the fluid applied over some volume, V."

A metaphor:
Suppose there are two rectangle cakes. For them, everything is the same excepte the shape: the first one with side length 2 inchs and 2 inchs, the second one with side length 1.7 inchs and 2.35 inches. Now if we want to choose the bigger one and we are allowed to choose one of them but have no chance to see them directly. which one we can choose?
Now we need to define a new quantity area Ω
Ω=a*b
where a and b denot length and width of cakes. We use this quantity measure the size of cakes. When we compare this quantity Ω , we know the relation in size between the two cakes.