Lexi A.

asked • 04/22/15

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.

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 184 pounds on the surface of the earth, what will this astronaut weigh 4300 miles above the earth? Assume that the radius of the earth is 4000 miles. (Round to 1 decimal place) 

1 Expert Answer

By:

Lexi A.

The answer was 42.7 pounds 
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04/22/15

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

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