Force Defined: First vs. Second Newton's Law

[jayeshtrivedi]

Can we say that the First law of Newton defines the force whereas the Second law gives the magnitude of force?

 

[olgerm]

No, Newton's I law only states that In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.
If you accept mass and acceleration as primitive notion, then Newton's second law (In an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma.) defines force.

 

[fresh_42]

I'd say the first law defines the absence of force and the second has not only magnitude but also direction in it. Turned into the positive direction, the first law says that the change in motion requires a force. It doesn't say what force is.

 

[DrStupid]

Can we say that the First law of Newton defines the force whereas the Second law gives the magnitude of force?

All three laws together define force.

 

[olgerm]

All three laws together define force.

Are you sure? First Newton's law concludes from the second Newton's law (you also have to assume that if force is not acting then F=0). Therefor the first Newton's law is not needed to define force.

$\begin{cases} \text{Newton's II law} \\\text{force does not act} \to F=0 \end{cases}\Rightarrow$
$\begin{cases} \ a=\frac{F}{m} \\\text{force does not act} \to F=0 \end{cases}\Rightarrow \text{force does not act} \to a=0 \Rightarrow \text{force does not act} \to _\Delta v=0 \Rightarrow \text{Newtons I law}$

 

[DrStupid]

Are you sure? First Newton's law concludes from the second Newton's law (you also have to assume that if force is not acting then F=0). Therefor the first Newton's law is not needed to define force.

According to the first law force is the reason for changes of motion. This causality doesn't follow from the second law. You can omit the first law if you have no problem with an identity of force and the change of motion. But that's not what Newton had in mind.

 

[pixel]

Newton's laws involve the effect of an unbalanced (net) force on rest or motion. I don't think they define force. If I have a spring attached to a wall at one end and some kind of gauge at the other end and I pull on the spring, I can measure the force.

 

[olgerm]

According to the first law force is the reason for changes of motion. This causality doesn't follow from the second law.

$a=\frac{F}{m} \to \frac{\partial v}{\partial t}=\frac{F}{m}$⇒change of velocity(motion) is proportional to force.

 

[DrStupid]

$a=\frac{F}{m} \to \frac{\partial v}{\partial t}=\frac{F}{m}$⇒change of velocity(motion) is proportional to force.

That just means that force is a measure for the change of motion. It doesn't mean that force is the reason for the change of motion as the first law says.

PS: Motion means momentum and not velocity. Newtons term for momentum is "motus" and his term for velocity is "velocitate". In the second law he used the term "motus". That means that force is proportional to the change of momentum but not necessarily to the change of velocity.

 

[morrobay]

∫ F dt = Δ mv.
∫ F dx = Δ K D' Alembert

 

[olgerm]

Newton's laws involve the effect of an unbalanced (net) force on rest or motion. I don't think they define force.

I agree. Newton's II law only defines netforce.

 

[yrjosmiel]

Force is basically the change of momentum per second.

 

[olgerm]

Force is basically the change of momentum per second.

Netforce is change of momentum per timeunit.

 

[yrjosmiel]

Net force is change of momentum per time unit.

Or to be more exact, that.

 

[DrStupid]

Netforce is change of momentum per timeunit.

Force is equal to the corresponding change of momentum and netforce is equal to the total change of momentum per time unit.

 

[morrobay]

That just means that force is a measure for the change of motion. It doesn't mean that force is the reason for the change of motion as the first law says.

PS: Motion means momentum and not velocity. Newtons term for momentum is "motus" and his term for velocity is "velocitate". In the second law he used the term "motus". That means that force is proportional to the change of momentum but not necessarily to the change of velocity.

It seems that force is proportional to velocity with : ∫ F dx = ∫^x_xo mv dv/dx (dx) = ∫^v_v0 mvdv = 1/2mv² - 1/2mv₀² , Δ KE ≅ v - v₀
As opposed to ∫^t_t0 F dt = ^t∫_t0 m dv/dt = ∫_t0^t d/dt mv = dp/dt
F ≅ t - t₀

 

[DrStupid]

It seems that force is proportional to velocity with : ∫ F dx = ∫^x_xo mv dv/dx (dx) = ∫^v_v0 mvdv = 1/2mv² - 1/2mv₀² , Δ KE ≅ v - v₀
As opposed to ∫^t_t0 F dt = ^t∫_t0 m dv/dt = ∫_t0^t d/dt mv = dp/dt
F ≅ t - t₀

I don't know what you are talking about.

 

[olgerm]

force is the reason for the change of motion as the first law says.

Does this statement contain any information, that equation $\frac{\partial^2 x}{\partial t^2}=\frac{F_x}{m}$ doesn't?

 

[Mister T]

Law I establishes the equivalence of inertial reference frames. It is not, as many textbooks report in error, a special case of Law II. In modern physics it's the Principle of Relativity

Law II defines force. For a particle acted upon by a single force, it equals by definition the rate of change of the particle's momentum. A definition that remains valid in modern physics.

Law III, taken together with Law II implies conservation of momentum. In modern physics Law III is not valid, but that conservation law is.

 

[morrobay]

It seems that force is proportional to velocity with : ∫ F dx = ∫^x_xo mv dv/dx (dx) = ∫^v_v0 mvdv = 1/2mv² - 1/2mv₀² , Δ KE ≅ v - v₀

And also with ∫ F dt
Edit: ∫ F dt = ∫^t_t0 dp/dt dt = Δp = mv₂ - mv₁

 

[DrStupid]

Does this statement contain any information, that equation $\frac{\partial^2 x}{\partial t^2}=\frac{F_x}{m}$ doesn't?

Yes, it contains information about causality: According to the first law F is the cause for the effect d²x/dt². The second law just tells you that F and d²x/dt² are proportional if m is constant.

 

[olgerm]

it contains information about causality: According to the first law F is the cause for the effect d²x/dt².

I doubt that this statement is even meaningful. Could any experiment prove that? Newton's 1st law as worded in Wikipedia ("In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.") does not say anything about causality.
Are you using uncommon definition of causality

Causality should not be confused with Newton's second law, which is related to the conservation of momentum, and is a consequence of the spatial homogeneity of physical laws. The name causality suggests that all effects must have specific causes, which is a concept unrelated to the common use of causality in physics, and is violated in some mainstream interpretations of quantum mechanics.

?

 

[DrStupid]

Could any experiment prove that?

It can't be proved and it doesn't need to be proved because it is a definition.

Newton's 1st law as worded in Wikipedia ("In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.") does not say anything about causality.

That's a modern replacement for the first law. The original wording can also be find in Wikipedia:

"Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare."

"Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed."

That means that force (and only force) causes the change of the state motion of a body (which can be read as "closed system" in this case) - no less, no more. As this has no practical relevance, the original first law is often replaced by some kind of definition for inertial frames (like in the wording you posted above). The original version doesn't even mention inertial frames or frames of reference at all. Newton already introduced them in a previous chapter of the Principia.

 

[Mister T]

Can we say that the First law of Newton defines the force whereas the Second law gives the magnitude of force?

Yeah, think of Law I as providing a qualitative definition of force, it's the thing that causes an object to depart from a state of uniform motion or (equivalently) a state of rest.

Law II provides a quantitative definition.

This is by no means the only approach to understanding, but it is in my opinion the best.

Once you go beyond that and refine your knowledge you appreciate the claim that a state of rest is equivalent to a state of uniform motion. This is the Principle of Relativity. There's no experiment that can distinguish between the two states so any distinction is purely artificial.