Answer: 2352 N
Explanation:
The gravitational force exerted by the Earth on an object is given by
[tex]F=G\frac{mM}{r^2}[/tex] (1)
where
[tex]G=6.67\cdot 10^{-11} m^3 kg^{-1} s^{-2}[/tex] is the gravitational constant
m is the mass of the object
[tex]M=5.98\cdot 10^{24} kg[/tex] is the Earth's mass
r is the distance between the object and the Earth's center
In this problem, we have an object of mass [tex]m=6.50 \cdot 10^2 kg[/tex]. Its distance from the Earth's center is given by its distance above the surface plus the Earth's radius, R:
[tex]r=h+R=4.15\cdot 10^6 m+6.37\cdot 10^6 m=1.05\cdot 10^7 m[/tex]
Substituting into equation (1), we find
[tex]F=(6.67\cdot 10^{-11}) \frac{(6.5\cdot 10^2 )(5.98\cdot 10^{24})}{(1.05 \cdot 10^7)^2}=2352 N[/tex]
