# I Is true force just "accepted" if it satisfies Newton law?

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1. Jun 7, 2017

### Physics is awesome

So I understand the relationship between mass x acceleration=force but all that relationship tells me is "Whatever the force is to accelerate a given mass at a specific unit of acceleration = units of force, and we just accept whatever the unit of force is. example 1/ms² x 1 kg mass = 1 N force.
So my question here the unit of force "accepted" as to whatever it is based on satisfying the force equation?
So basically here is a simple question, "How much force is needed to accelerate a 50 kg mass @ 14 m/s². Simple equation 50 x 14= 700 N
Now what is 700 N? 700 N is the force applied to the 50 kg mass to accelerate it at 14 m/s². So we are back to just stating its the force that accelerates an object at a specified acceleration with a specified mass.

Now, We can take 700 N / 9.8/ms² to get the equivalent force on a mass being pulled in by gravity on the surface of the earth which equals =71.42 kg and we can covert kg to pounds by dividing by .4535 = 157.49 pounds of force.

So now back to my question is what actually really determines true net force. What if gravity was 2x the force so everything that weighs 100 pounds is now equal 200 pounds of force. What if gravity was still 9.8/ms² but outputted double the gravitational pull on matter. This wouldn't throw off our equation to determine force based on acceleration x mass. We would still have units of acceleration and mass and force , but for example to satisfy newtons law that would mean if 9.8/ms² doubled force it would also apply for the force of any acceleration , so for example 4 m/s² would have double the amount of net force on an mass if our constant gravity was doubled from what we currently know it as(in order to satisfy newtons law), a but it still remained at 9.8. So basically what I am asking is if everything with force is based off newtons law and a newton is defined as 1 kg accelerating a 1 m/s² do we just accept whatever this net force is? Which then brings me to the next question as why is the net force what it is? SO if we ask why is 1 newton = .22 pounds of force. The only way we have to answer this question is base it off newtons formula and comparing it to the current force of gravity on matter on earth. So is this just accepted? If gravity was putting out double the force at the same acceleration speed would this be the new norm for physics? Would we just accept it as long as it satisfies Newtons law?
Just pretend it took100 pounds of force to accelerate the mass of a spec of dust at 1 m/s². This then according to Newtons law of force would mean a spec of dust would weigh 5.06 pounds assuming gravitiy acceleration was still 9.8 ms². Would these numbers just be "accepted" because it satisfies the equation (and assume we as humans were put on the planet like this not knowing of gravity being any other way).

2. Jun 7, 2017

### Staff: Mentor

You're basically right, but over thinking. The Newton is defined to be the unit of force proportional to ma in SI units. Sure, we could arbitrarily add a factor of 2 to the definition, but since is adds no value, changes nothing and adds unnecessary complexity, we don't.

3. Jun 7, 2017

### Staff: Mentor

You are essentially correct. If you use SI units then you are accepting the definition that 1 N = 1 kg m/s^2. The newton is a derived unit, not a base unit, so it has no independent value.

You might choose to use some other system of units besides SI. If you chose to do so, then you would write Newtons 2nd law as: $F_{net}=k m a$ where k is a unit conversion factor converting units of mass times acceleration to units of force.

In SI k=1 and is dimensionless, so it is usually dropped.

4. Jun 8, 2017

5. Jun 8, 2017

### Domullus

You are totally correct. The same thing applies to many different physical quantities and laws. Just take for example vacuum permittivity and permeability. They are just unit conversion coefficients (k) like Dale pointed out. Once there was a discussion how to choose these coefficients wisely to make them practical and physics community changed them in 1950's. It was called rationalization of units. Due to rationalization you have 4π appearing in Coulombs constant. This 4π has nothing to do with physics - just people agreed to scale these constants to make math easier and cleanlier.

6. Jun 8, 2017

### Stephen Tashi

As the others have stated, a Newton of a force is a defined quantity. However, its worthwhile to point out that we must check that definitions are useful.

For example, if 1 Newton is defined to be the force needed to give a 1 kg mass an accleration of 1 meter per sec^2 , this definition does not require that two forces, each of 1 Newton applied to a 1 kg mass will give it an acceleration of 2 meters per sec^2. The fact that 2 forces, each of 1 Newton have that effect must be an experimental result. As you indicated, the behavior of a 2 Newton force is consequence of the "force law" F = MA, not a consequence of the definition of a Newton. The empirical support for F = MA is what assures us that the definition of a Newton is useful.

By contrast, suppose we define 1 "velkin" to be the amount of velocity ( in meters per sec) needed to give a 1 kg mass an kinetic energy of 1 joule. It is not empirically true that 2 velkins would give a 1 kg mass a kinetic energy of 2 joules. So the definition isn't very useful because we can't calculate with it by using simple addition.

7. Jun 9, 2017