Heidi T. answered • 03/06/22
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MS in Mathematics, PhD in Physics, 7+ years teaching experience
The law of universal gravitation is
F = (G M m )/ r2 ==> r = √(G M m )/F
G = 6.67408 × 10-11 m3 kg-1 s-2
r = √(6.67408 × 10-11 m3 kg-1 s-2)(5.97 X 10 ²⁴ kg)(10 kg) / (1,030 kg m s-2)
= √(3.868 × 1012 m2)
r = 1.967 × 106 m
Heidi T.
Yes. The person is closer to the center of the earth than the "average" radius. You can tell this by the fact that the gravitational force given in the problem is greater than (10kg)(9.81m/s^2) = 98.1N
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03/06/22
Heidi T.
Of course, if the force between the person and the Earth was mis-written and should have been 1.030N instead of 1030(1,030)N, then the radius would be 6.22X10^7m and the person would be above the surface of the earth.
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03/06/22
Anthony T.
Hi,Heidi I would have done the problem your way, but when I Googled the radius of the earth, it was 6.37 x 10^6meters. Am I missing something?03/06/22