# Why Multiply?

1. May 9, 2012

### optics.tech

Why F = m * a?

Why not F = m + a?

2. May 9, 2012

### Integral

Staff Emeritus
Adding acceleration and mass is just like adding apples and oranges, it can't be done.

Look at the units involved and combine them in a manner which makes sense.

3. May 9, 2012

### HallsofIvy

Of course, it would be (mathematically) possible to have something like $F= C_1mz+ C_2a$ where $C_1$ and $C_2$ are constants with the correct units ($C_1$ would have to have units of "Newtons per kg" or "meters per second squared" and $C_2$ has units of "Newtons-seconds square per meter" or "kilograms".

But the only good Physics explanation as to why a specific formula is true is "that is what the experimental evidence shows".

4. May 9, 2012

### huntoon

From: http://en.wikipedia.org/wiki/Newton's_laws_of_motion