Understanding Newton's Second Law: Deriving the Equation F=ma

[vysis]

I knew i should have paid more attention in class =/

anyways, We have been studying Newton's second law. And I have a question on my lab that asks for me to "derive equation for a (acceleration) vs F (force) and a (acceleration) vs m (mass)"

a vs F and a vs M are two graphs which we did.

and I am at a complete lost at what to do. I have no idea how to or what to derive. My only hint is a small piece of note I copied from teacher's notes. It goes like this:

It looks like slope is equal to 1/mass. So

a α(alpha) F
a α 1/m
a α F/m
F = ma

does anybody know what a(alpha) stands for? And what it exactly means by "deriving equation?"

thank you very very much.

 

[Snazzy]

Deriving means how someone formulates an equation through other equations or experimental results. The alpha symbol means 'is proportional to'.

 

[vysis]

so would i derive a vs F or a vs m in the same fashion as:

a (alpha) x
a (alpha) y
a (alpha) z
a = xyz

 

[Astronuc]

a α(alpha) F
a α 1/m
a α F/m

That's not α (alpha) but rather \varpropto, which means a is proportional to F, a is proportional to 1/m, and a is proportional to F/m, with the last being a one-to-one proportionality which gives a = F/m.

 

[vysis]

ahh, ic
thank you very much. That might explain why i never got anything by searching up alpha on google :P

can you please tell me what it is called?

 

[Snazzy]

It's called a proportionality symbol.

 

[weitao]

F \varpropto ma? How to say that F=ma? is not F=kma?