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

In summary, the conversation is about deriving equations for acceleration versus force and acceleration versus mass. The person is unsure of how to derive these equations and is seeking clarification on the use of the alpha symbol and the concept of "deriving equations". The expert summarizes that deriving an equation means formulating it through other equations or experimental results, and the alpha symbol means "is proportional to". They also clarify that it is a proportionality symbol, not the Greek letter alpha. Finally, they explain that the equation for force, F=ma, is not the same as F=kma.
  • #1
vysis
28
0
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.
 
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  • #2
Deriving means how someone formulates an equation through other equations or experimental results. The alpha symbol means 'is proportional to'.
 
  • #3
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
 
  • #4
a α(alpha) F
a α 1/m
a α F/m
That's not α (alpha) but rather [itex]\varpropto[/itex], 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.
 
  • #5
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?
 
  • #6
It's called a proportionality symbol.
 
  • #7
F [itex]\varpropto[/itex] ma? How to say that F=ma? is not F=kma?
 

1. What is the meaning of F=ma in physics?

The equation F=ma is known as Newton's Second Law of Motion. It states that the force (F) acting on an object is directly proportional to its mass (m) and its acceleration (a). This means that the greater the mass of an object, the more force is required to accelerate it, and the greater the acceleration of an object, the more force is needed to achieve it.

2. How is F=ma used to calculate acceleration?

To calculate acceleration using F=ma, you must rearrange the equation to solve for a. This can be done by dividing both sides of the equation by the mass (m), giving the formula a = F/m. This means that the acceleration of an object is equal to the force acting on it divided by its mass.

3. What units are used for each variable in F=ma?

The unit for force (F) is measured in Newtons (N), the unit for mass (m) is measured in kilograms (kg), and the unit for acceleration (a) is measured in meters per second squared (m/s^2). It is important to use consistent units when using this equation for accurate calculations.

4. How does a relate to F in F=ma?

In the equation F=ma, a is directly proportional to F. This means that as the force acting on an object increases, its acceleration also increases. Similarly, if the force decreases, the acceleration will also decrease. However, it is important to note that the mass of the object will also affect the overall result.

5. What is the difference between a and F in F=ma?

The variable a represents acceleration, which is the rate of change of an object's velocity. This means that it measures how quickly the object's speed or direction is changing. On the other hand, F represents force, which is a push or pull on an object that can cause it to accelerate. In other words, a is the result of F acting on m in accordance with Newton's Second Law of Motion.

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