What if the actual force for a Newton was different?

[Jason DiCaprio]

ince f=ma, and we derive whatever the force it takes to accelerate a specific mass at a specific acceleration as a unit of force. I understand this ratio of actual force will always be the same in the entire universe but is there a reason why for example 1kg accelerated a 1m/s^2=1 N which is equivalent to .225 pound force. (don't focus so much that I am using pound force my main question is why is the actual force what it is, why not more why not less) This is a such a light force, but what if we didn't know any better and 1 N was equivalent to 100 pounds of force(instead of .225),(could you imagine if it took 100 pounds to accelerate 1kg mass at 1 ms^2) this would mean it would be very hard to accelerate objects and approx 400 x the force we are currently use to would be required to accelerate matter throughout the universe. This would then mean to accelerate a 10 kg object at 10 m/s ^2 would still be 100 N but since we are hypothetically pretending 1 N = 100 pounds this would then mean a 10 kg mass on Earth would be 9,800 pounds. Now I know this is all hypothetical but my only question is why is any unit of force what it is for example 1 N is a very light amount of pressure why is the amount of force to accelerate 1 kg 1 m/s^2 not a heavier force or even a much lighter force. Is this just a constant value we "accept" or is there a reason why to break inertia at a specific acceleration equals what it does. Why isn't the force to accelerate 1 kg 1 m/s^2 not more or less then we are currently use to in this universe?. Why is the "actual force" what it is? Why not more why not less?? What if 1 N was very light like 1/100th the actual force it is now this would mean that using the f=ma everything would be 1/100th. But again why is "the actual for what it is". Maybe there is no reason and it is what it is. But that is an answer as well.

 

[Dale]

The Newton is the amount of force that it is because the BIPM (international bureau of weights and measures) held a committee meeting, had a vote, and decided that is how they wanted to define it. There is no physical reason for the size of the unit.

You may be interested more in a question like why is the inertial mass the same as the gravitational mass, but I am not sure.

 

[Nugatory]

why is any unit of force what it is for example 1 N is a very light amount of pressure why is the amount of force to accelerate 1 kg 1 m/s^2 not a heavier force or even a much lighter force?

First we decide how much time a second is. For reasons that are somewhat obscure but very convincing when you dig into the details, we've decided that one second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

Then we decide how long a meter is. Again, the reasons are obscure but very convincing when you dig into the details (and we have many many threads about this already) and we've decided that one meter is the length of the path traveled by light in vacuum during a time interval of 1/299792458 of a second.

Finally, we decide how much mass a kilogram is. Decades ago we defined it to be the mass of a special piece of metal stored in a lab in France. (This is a somewhat unsatisfactory definition because random molecules randomly stick to the object or fall off it, so as our measurement technology gets better we start to notice that the definition of the kilogram randomly varies over time. This problem will be fixed next year by a new definition of the kilogram based on Planck's constant).

Once we've been through all of that, we know how much force a Newton represents: It's the amount of force that accelerates a one Kg mass at one meter per second per second. It can't be anything different, because if it were different it wouldn't be a Newton.

And as for why the Newton is equal to .225 pounds? Because that's how we defined the Newton and the pound. That number .225 tells us nothing about physics or whether $F=ma$ is a good law of physics. It just tells us that we've defined our units in such a way that the ratio came out to be .225; and if we had defined the units differently the ratio would come out differently.

 

[Dale]

This problem will be fixed next year by a new definition of the kilogram based on Planck's constant

If the BIPM does the major overhaul of the SI system that they have discussed then it will be very interesting and will change the validity of many threads on the forum. I am very interested to see how it goes

 

[Jason DiCaprio]

So what if the force of a Newton equaled double the force we are use to. Suppose from day 1 of the universe 1kg accelerated at 1m/s^2 was equal to .448 pounds instead of .224. Would this just be accepted as the force of a Newton if we knew nothing different?

 

[Nugatory]

So what if the force of a Newton equaled double the force we are use to. Suppose from day 1 of the universe 1kg accelerated at 1m/s^2 was equal to .448 pounds instead of .224. Would this just be accepted as the force of a Newton if we knew nothing different?

You have it backwards. The force of the Newton would be the same; it's still the force that accelerates that piece of metal in France at one meter per second per second, and that's a fact about the universe completely independent of the numbers that we've printed on the dials of our force-measuring devices. What would be different is the amount of force that we call "one pound"; we'd say that one pound is defined to be 1/.448 Newtons instead of 1/.224 Newtons.

What's really going on here is that the particular values of numbers that have units attached to them (such as "33 Newtons" or "8 pounds" or "12 inches" ) have no physical significance. Change the units and the number changes, and that just tells us how we've chosen to define the units. .224 isn't any more special than .448, it's just that we used one instead of the other to define the pound.

It's the numbers that don't have units attached to them that have real meaning. For example, the ratio of the circumference of a circle to the diameter is 3.14159...; this is a fact about circles that is true whether you measure distances in meters, feet, miles, furlongs, leagues, inches, microns, whatever.

 

[Dale]

So what if the force of a Newton equaled double the force we are use to. Suppose from day 1 of the universe 1kg accelerated at 1m/s^2 was equal to .448 pounds instead of .224. Would this just be accepted as the force of a Newton if we knew nothing different?

About the only thing that would be different would be the labeling for food packages. The pair of numbers that gives the weight of the contents in pounds and kilograms would be different by a factor of two. Nothing physical would change, just the labels and similar things.

 

[CWatters]

Most units have arbitrary size. The important thing is not how big they are, it's that you have a set that are consistent with each other. F=ma works in both metric and imperial units...

1N = 1kg * 1m/s²

1 lbf = 1 slug * 1 ft/s²

 

[russ_watters]

I think all of you are misinterpreting the OP's question. The question isn't about units, it is about the real physical relationship between force and acceleration. If it were twice what we know now, we'd still call it one Newton, but, for example, we wouldn't be able to jump as high...but we'd also re-define that distance to be the same. The math would still work out, but there'd be no skyscrapers, airplanes or space travel. Similar to if we were on a planet with twice the mass (and same diameter).

 

[Dale]

The question isn't about units, it is about the real physical relationship between force and acceleration. If it were twice what we know now, we'd still call it one Newton, but, for example, we wouldn't be able to jump as high...but we'd also re-define that distance to be the same. The math would still work out, but there'd be no skyscrapers, airplanes or space travel.

I don't think so. A world where the ONLY difference is f=2ma would be physically identical to this one in every way. We would still have skyscrapers and airplanes. All that would be different is that we would label things differently according to a different set of units.

What you are describing (changes to buildings and airplanes) would be due to a change in the fine structure constant.