Is Newton's Second Law the Definition of Force and Mass?

[Shing]

hi guys, I just wonder that do we really need the law I?

since that law II, because of F=ma, you need a F such that there exist a a

somehow that I heard that it is related to frames, but I didn't quite understand,

would anyone here be kind enough to elaborate a bit please?

 

[D H]

F=ma is only valid in an inertial frame; it is not true in all reference frames. The first law in part defines the concept of an inertial frame of reference.

 

[mikelepore]

hi guys, I just wonder that do we really need the law I?

since that law II, because of F=ma, you need a F such that there exist a a

The first law is a special case of the second law, the case where both sides of the equation are zero. Zero net force implies zero acceleration, and vice versa.

somehow that I heard that it is related to frames, but I didn't quite understand,

would anyone here be kind enough to elaborate a bit please?

If a frame of reference is accelerating, it will appear to someone inside that frame that objects accelerate for no apparent reason, which they will tend to explain by saying that a force has appeared.

For example, a rocket is coasting and the astronauts are floating inside. Then they turn on the engine, and the rocket accelerates. The astronauts' bodies move toward the floor, which they perceive to be identical to a force of gravity suddenly appearing.

Another example, the centrifugal "force" is a fictitious force invented to explain why objects in a rotating frame of reference move outward, like the water and clothes in a washing machine during the spin cycle.

Someone outside of that frame of reference, and observing the whole frame accerating, will be able to see that the acceleration of the frame and the inertia of the mass are sufficient to explain the effects, and it's not necessary to assume a new force.

 

[jonjacson]

And another question ¿what are the definitions for the concepts of mass and force?

 

[D H]

Newton's second law defines force and mass. Forces are things that make objects accelerate when viewed from the perspective of an inertial frame. How much they accelerate depends on how massive they are.

 

[Shing]

thanks, guys
um... so my understanding is that
the law I is fundamental...
law II can be true if and only if law I is TRUE?

 

[Shing]

And I was thinking that
if mass is merely a coefficient?
Or quite the contrary, we define coefficient for certain propertyies because we know not much about it... and let the coefficient be the "approximate properties" in math.

sorry for my lousy explanation of my thoughts... I can't think of better way of questioning...

 

[D H]

One way to look at it: Newton was a smart guy, a very, very smart guy. He put the first law first for some reason. The first law says an awful lot. First there is the concept of a reference frame which enables an observer to specify the positions of objects. If you can't say where something is, how can you possibly say how fast it is moving, and how that velocity is changing? Those concepts raise another question: What is time? The first law in a sense wraps up the concept of reference frames and time and says that some reference frames, the inertial frames, are very special.

 

[jonjacson]

Newton's second law defines force and mass. Forces are things that make objects accelerate when viewed from the perspective of an inertial frame. How much they accelerate depends on how massive they are.

I can't see that, ¿how could you define two concepts in an equation of three parameters?.

If the definition of mass and force arises from that equation there is a problem, the definition of mass depends on the definition of force , and viceversa, it's the dog that bites his scut.

For the acceleration everithing is clear, you fix de coordinate system, and you can compute the position of the particle, the acceleration is the second derivative.

I think we should have a precise definition of mass to accept that the second law is the definition of force.