This is a general question regarding force (mass x acceleration). I understand 1N =1kg mass x 1 m per second sq) all this basically tells me is that the force is proportionally increased and decreased when i increased or decrease the mass or force or both. However my question that I have been wondering is why is the actual force of a newton what it is. I know 1 newton equals .225 pounds because .1020 kg of mass accelerated at 9.8 m/s sq equals a newton and I can easily convert the force of kg mass into pound force since 1kg mass= 1kg mass force at gravity on earth . So why is it .225 pounds of force per newton. Why not any other number? I know it would change the force proportionally to the force of accelerating any matter in the universe, but I am just wondering why it is that amount of force .225 for 1 newton. Is this just an "ACCEPTED CONSTANT" that doesn't change with no reason?
3 Answers
They're just different units of force. If you hold a one kilogram object in your hand, its weight is $1\ \mathrm{kg}\times9.8\ \mathrm{m/s^2} = 9.8\ \mathrm N$. If you choose to measure the weight of that object in imperial units, you will find that it weighs about $2.2\ \mathrm{lbs}$.
Therefore, $$9.8\ \mathrm N = 2.2\ \mathrm{lbs}$$ so $$ 1\ \mathrm N = \frac{2.2}{9.8}\ \mathrm{lbs} \approx 0.224\ \mathrm{lbs}$$
It's just like inches vs. centimeters – they are two different units for measuring length, and 1 inch equals 2.54 centimeters.
It's important to remember that all units, like "Newtons", "Joules", "Power", are all derived from a few basic units. In this case, the only basic units involved are:
time (measured in seconds). distance (measured in meters). mass (measured in kilograms).
For the above three, the units (seconds, meters, and kilograms) are entirely arbitrary. They are completely made up by humans.
Now let's derive from these basic units:
velocity = distance / time. So, unit of velocity is: meters/seconds
acceleration = velocity / time. So, unit of acceleration is: meters/seconds/seconds, or just meters/seconds^2
Newton = mass * acceleration. So, unit of Newton is: kg * meters/seconds^2
Here we find that:
N = kg*meters/seconds^2
So, a "Newton" is just equal to a combination of our three basic (arbitrary) units (kilograms, meters, and seconds). The value of a Newton was not determined based on 0.225 pounds. A Newton just happens to be equal to 0.225 pounds ("Newton" and "Pounds" are just different units that measure force).
That number most likely comes from the most commonly used factors for converting the types of weight from kgs... For N it would be acceleration due to gravity which is 9.80665 or more commonly 9.8 and for lbs it is about 2.205 the decimal is actually much longer but approximately that... 2.205/9.8=.225 i just really dont like that because they are rounded to different decimal places so its really more like either 2.2/9.8=.224480796 ...... Or 2.205/9.807 =.2248394...... Which is also bad because mathematically you shouldn't round until your final answer but it ends up rounding to .225 reason for that specific decimal is probably either what i said at first or because in math we love rounding to the thousandths place
