Well I don’t want you guys to lose all of your brain power and still remember some formulas for the school year, which isn’t really that far away. So I decided to do a pretty complex problem for you guys but you guys should be able to follow it.
It is how to calculate the mass of the Earth and then take that and figure out how much gravity per kilogram that is imposed on an object. don’t worry we will take this a step at a time.
Alright first things first, how to calculate the volume of a sphere is 4 *(times) PI * R. R = radius squared.
So now that you have the formula you will now be asking what is the radius of the earth? Well if I remember correctly it was 4000 miles. So now we punch that into our formula.
4 * PI * 16,000 (4000 squared remember) MI = 201,061.9 Cubic Miles
Alright is everybody following me? Well good. So now we need to convert this into square feet so we can accurately measure the mass of the earth. 1 mile is approximately 5,000 feet so we just multiply this by five thousand
201,061.9 Miles Cubed * 5,000 = 1,005,309,500 Cubic feet
SO we got that now what. Well remember that the earth is covered with two third of water but that doesn’t mean that it mass is made up of two thirds of water. So let just say that the earth’s mass is made up of two fifths of water. So multiply two fifths by 1,005,309,500.
2 / 5 (two fifths) * 1,005,309,500 = 402,123,800
So let me break this up for you
Water mass of the Earth is approximately 402,123,800 Cubic feet
Mass of dirt in the earth is approximately 603,185,700 Cubic feet
So now with these two number we can get closer two out answer. Alright how much weight do you think that a cubic foot of dirt weighs? Well a sandbag is about a cubic foot and it weighs about twenty pounds. So here we go.
603,185,700 * 20 = 12,063,714,000 pounds of dirt
We do the same with water. I think that 1 cubic foot of water will weigh about 30 pounds.
402,123,800 * 30 = 12,063,714,000 pounds of water, isn’t that funny they weigh exactly the same amount!
Okay to calculate force the formula is
mass * acceleration
Mass is measured in kilograms, so we multiply a pound by 2.2 to get a kilogram. So let’s combine the numbers and get cookin.
24,127,428,000 pounds of mass * 2.2 = 33,080,341,600 kilograms
So now we just need to multiply our answer by the acceleration of the earth to get the amount of force the earth imposes on an object. The acceleration of the earth is 9.8 meters per second by the way!
33,080,341,600 * 9.8 = 324,187,347,680 Newtons of force imposed by the earth!
Pretty cool isn’t it! Also, I had too do some of these problems by my self without a calculator because the numbers were to big. If anybody has any suggestions or other answers please let me know by leaving a comment.