Freshman Electric Engineer Explores Meaning of F=ma

[gma]

I'm a freshman who majors in electric engineering.

Before several days, I studied for my exam on mathematics.

Accidently, an interesting idea hit me!

If my idea is wrong or meaningless, I welcome threads to explain why.

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The meaning of F=ma??

I studied F=ma in my high school, but I only recited this formula until my pencil point was worn out. F=ma, F=ma, F=ma, ...

When I took a look on F=ma, I thought that Force and mass is not natural conception, but only a conception defined by people. Contrary to F and m, acceleration is a natural conception, because it can be induced from the conception of time and space.

But, I heard that F=ma is a great formula explaining the motion of all of things. This formula is a definition of force and mass or a great formula explaining the nature??

my idea is, 'F=ma' means that there exists a quantity of 'a' in every time, every space. Therefore, all of time-velocity graph is continuous graph in nature, because there exists the value of the derivative of 'v'. Experimentally, you know, there is no t-v graph that is not continuous.

As a result, it explains why F=ma is a formula explaining the character of the nature.

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If my English is hard to read, sorry. I'm Asian.
but, my English score is not bad :)

 

[chaoseverlasting]

I think that's right. I don't know what you mean that a t-v graph is discontinuous. Everything could be accelerating, even if the acceleration is zero, but that concept too is relative. The acceleration is zero or positive or negative in a frame with respect to some other defined frame. There is no absolute acceleration. Only relative acceleration. Dunno if that helps you or not or even answers/refutes your question/suggestion.

 

[Danger]

I suspect that once again the language barrier rears its ugly head.
Welcome to PF, Gma. I'm assuming that English is not your first language, based upon your phraseology. If that is in error, I apologize.
I don't know that there even exists a category called 'natural conception'. Even if there is, though, all of physics would fit within it. Force and mass are not human constructs, although the measurement systems used to define them are. By the same token, how could you consider acceleration to be in that category while mass and force aren't? You can't have acceleration without both of those.

edit: I just saw your tag at the bottom. Yes, you do very well for having English as an alternate language. In fact, your grammar and spelling are better than some native Anglophones. (Take a bow, Hypatia. )

 

[olgranpappy]

When I took a look on F=ma, I thought that Force and mass is not natural conception, but only a conception defined by people. Contrary to F and m, acceleration is a natural conception, because it can be induced from the conception of time and space.

It is not at all clear why acceleration should be a "more natural" quantity than
mass. The most basic properties *of the object* are its mass and charge.

But, I heard that F=ma is a great formula explaining the motion of all of things. This formula is a definition of force and mass or a great formula explaining the nature??

No, it's not just an empty definition because we have independent ways of computing the LHS of the equation. This is what makes the equation important. For example, I put a charged mass in an electric field. Then I can calculate the LHS of the equation and if only I knew the value of the mass then I could predict the accleration of the object. But I can determine the mass of the object by simply weighing it which is actually another implementation of F=ma where now the LHS is given by Hooke's spring-force (or some other expression depending on the scale). Thus I can predict how the object accelerates. Then, because my independent expression for the force is given for all times I can integrate to find the velocity and then the position of the object at all times. So, everything I want to know follows from F=ma.

 

[Claude Bile]

You ought to consider too, that F = ma is actually a special case of the more general equation F = dp/dt (p = momentum).

F = dp/dt has another interesting special case when F = 0, namely the law of conservation of momentum.

Claude.