Understanding arithmetic and the Newton

[Jacobim]

A Newton is: ( (one kilogram times one meter) per second) per second)

I am trying to get at the basic logic of how we can apply numbers to reality.

I have a good understanding of how we use a ratio to express things. A ratio separates one quantity into the amount of another quantity. In fact that kind of makes sense of the word numerator and the word denominator. Denominator kind of sounds like the dominant unit; the fraction gives one quantity in terms of the quantity in the denominator.

But I don't have a clear notion of how multiplication makes sense. One kilogram is moved one meter: A mass quantity, multiplied by a distance quantity. I suppose this just gives you a definite value that can be compared in the same types of situations involving a mass moving a distance. Hmm I think I answered my own question.

Any suggestions on understanding the basics meanings of mathematics?

I have thought that a good way to get a grasp of physics is to understand all of the units and how they are arithematically related to each other.

I have completed up through Calc 3 and will start differential equations next semester, and there are a lot of simple things I have taken for granted about mathematics and do not really understand.

 

[rashi]

What are the things that you do not undersatnd?

Mathametics is logical and practical subject.

 

[jedishrfu]

The Newton is a basic measure of force and force is defined as F=m*a

So units of measure follow from the equation with m in kilograms and a in m/sec/sec

The acceleration follows from changing velocity or a = v(t) / sec so a is in m /sec/sec

and velocity from changing distance v = d(t) / sec so v is in m/sec

so while the Newton units of measure look strange they aren't any stranger than acceleration or velocity.

 

[rashi]

It means if you apply a force of mass 1 Kg and that body traveled a disatnce of of one meter and takes two seconds, it means the applied force is one Newton.
i.e 1N= 1Kgm/s^2

 

[jbriggs444]

A Newton is: ( (one kilogram times one meter) per second) per second)
I have a good understanding of how we use a ratio to express things. A ratio separates one quantity into the amount of another quantity. In fact that kind of makes sense of the word numerator and the word denominator. Denominator kind of sounds like the dominant unit; the fraction gives one quantity in terms of the quantity in the denominator.

But I don't have a clear notion of how multiplication makes sense. One kilogram is moved one meter: A mass quantity, multiplied by a distance quantity. I suppose this just gives you a definite value that can be compared in the same types of situations involving a mass moving a distance. Hmm I think I answered my own question.

You may be over-thinking things.

A Newton is the force required to accelerate an object whose mass is one kilogram at an acceleration rate of one meter per second per second.

An acceleration rate of one meter per second per second means that an object increases its velocity by one meter per second in an elapsed time of one second.

A velocity of one meter per second means that an object moves at one meter in an elapsed time of one second. Or one tenth of a meter in one tenth of a second. Or one hundredth of a meter on one hundredth of a second... But you say you have already taken CALC 1 and 2, so this may not be news to you.

If you had to accelerate two kilograms at one meter per second per second it would take twice as much force, right? And three kilograms would take three times the force. So the force is _proportional_ to the number of kilograms.

If you had to accelerate one kilogram at twice the acceleration rate it would take twice the force, right? And at three times the rate it would take three times the force. So the force is _proportional_ to the acceleration rate.

So force is proportional to mass multiplied by acceleration rate.

Once you decide upon units for mass, force and acceleration rate, this proportionality becomes an actual equation:

F = k * m * a

The k depends on the units of measurement you have chosen. The units that we conventionally use (the kilogram, the Newton, the meter and the second) make the numeric value of the constant k work out to one.

 

[Jacobim]

Thanks Jbriggs and everyone else. I just have these concepts and I get them confused, but actually they are simple concepts, so the trick is to not get them confused.