Jon P. answered • 04/22/15
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There are two ways to do this:
1) "F is inversely proportional to the square of the distance" means that F = k/d2. Since you know F at the surface (184 pounds) and d (4000 miles), you can compute the constant of proportionality k. Then you can use it to calculate the force when d = 4300 miles.
184 = k / 40002
184 * 40002 = k
2944000000 = k
F' = k / 43002
F' = 2944000000 / 43002 = 159.2 pounds.
2) "F is inversely proportional to the square of the distance" means that multiplying the distance by some ratio results in dividing F by the square of the ratio. The ratio of the new distance to the original is 4300/4000 = 1.075. So to calculate the weight at the new height, divide the original weight by 1.0752. So 184 / 1.0752 = 159.2 pounds
They're really the same thing, just two ways to get there.
Jon P.
tutor
Ugh, I'm sorry! I totally misread the problem. It's 4300 miles above the earth, not 4300 miles from the center.
So that's 8300 miles from the center.
Go to the second method I described, and use the ratio 8300/4000 instead of 4300/4000. That's 2.075. The square of that is 4.306. So if you divide 184 by 4.306, you get 42.7 pounds.
Again, my apologies!!
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04/22/15
Lexi A.
Thank you! Could you help With this one too?
The he volume of a gas in a container varies inversely as the pressure of the gas. If a gas has a volume of 97 cubic inches under a pressure of 2 pounds per square inch, what will be its volume of the pressure is increased to 5 pounds per square inch? (Round to nearest integer)....would you use the same formula?
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04/22/15
Jon P.
tutor
Sorry, I wasn't able to get to this yesterday.
Not quite, but close. In this case the volume varies inversely with the pressure, not the SQUARE of the pressure. So if the pressure is increased from 2 to 5, it's multiplied by 2.5. Therefore the volume would be DIVIDED by 2.5. 97 / 2.5 = 38.8. So the volume would be 38.8 cubic inches.
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04/23/15
Patriot R.
Weight is inversely related to the square of the distance between an object and the center of the Earth. If the distance between an object and the center of the Earth is increased by a factor of three, the weight will _______ by a factor of _______. A. increase, three B. decrease, three C. increase, four D. decrease, six E. decrease, nine Would this be E? because we are squaring it?
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02/07/22
Jessica L.
The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object and the center of the Earth. If an astronaut weighs 209 pounds on the surface of the Earth, what will this astronaut weigh 200 miles above the Earth? Assume that the radius of the Earth is 4000 miles. Round your answer to one decimal place if necessary.
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03/29/22
Jessica L.
The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object and the center of the Earth. If an astronaut weighs 209 pounds on the surface of the Earth, what will this astronaut weigh 200 miles above the Earth? Assume that the radius of the Earth is 4000 miles. Round your answer to one decimal place if necessary.
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03/29/22
Jessica L.
The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object and the center of the Earth. If an astronaut weighs 209 pounds on the surface of the Earth, what will this astronaut weigh 200 miles above the Earth? Assume that the radius of the Earth is 4000 miles. Round your answer to one decimal place if necessary.
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03/29/22
Lexi A.
04/22/15