3

I usually hear explanation of the second law like this: If you apply twice as much force, it doubles the acceleration. When the same force is applied, if the mass is doubled, the acceleration becomes half. so we get $a=\frac{F}m × k$ with such proportional relationship and the unit "newton, N" makes $k$ 1.

I think this explanation has some problems. How we know the applied force is double of original force? if the question was "The speed is proportional to the volume" , we can know the speed or volume without any Circular argument. if someone say "the double of force means "the force that accelerate double". it becomes Circular argument. Can we know "this force is double of that force" sensuously, like length or volume? Can we define force without $F=\frac{dp}{dt}$?

Furthermore, how we define mass? If we define mass as $\frac Fa$, how we provide the circular argument? How should i understand force?

i thought, we defined force as $\frac{dp}{dt}$. and experimentally, we can know force mathmatically. So we know the $\frac{dp}{dt}$ and the motion of object. What is wrong in this statement?

Qmechanic
  • 201,751
dogum
  • 39
  • 1
    Does this answer answer your question? – md2perpe Oct 13 '21 at 13:52
  • Possible duplicates: https://physics.stackexchange.com/q/70186/2451 and links therein. – Qmechanic Oct 13 '21 at 16:07
  • There's no any $k$ in Newton formula. If you substitute $F=2F_0$ into acceleration you'll get $a= \frac {2F_0}{m}$. But then why you have chosen such $F$ expression ? In general there's no limit on how force can act in nature. That is, force can be any form of function, i.e. $F=F(F_0, t, x,y,z, \ldots)$. Newton second law is rather experimental thing, because it was concluded from Kepler's laws of planetary motion. And lastly science is applied math methods to nature phenomenon. With only boolean logic you can't do any useful stuff in science. It's not philosophy. – Agnius Vasiliauskas Oct 13 '21 at 16:13

1 Answers1

1

If you want to work with momentum, you still need to define mass. I would prefer to say that force is what you measure with a spring scale, and Newton's equation experimentally defines inertial mass (but the Newton is currently defined in terms of kilograms).

R.W. Bird
  • 12,139