Answers:
a) [tex]8.009(10)^{-7} N[/tex]
b) [tex]1.8(10)^{-8} [/tex]
Explanation:
a) Accoding to the Universal Law of Gravitation we have:
[tex]F_{g}=G\frac{Mm}{d^2}[/tex] (1)
Where:
[tex]F_{g}[/tex] is the gravitational force between the eagle and the throng
[tex]G=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}[/tex] is the Universal Gravitational constant
[tex]M=4.5 kg[/tex] is the mass of the eagle
[tex]m=(80 kg)(3(10)^{6} people/kg)=240(10)^{6} kg[/tex] is the mass of the throng
[tex]d=300 m[/tex] is the distance between the throng and the eagle
[tex]F_{g}=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}} \frac{(4.5 kg)(240(10)^{6} kg)}{(300 m)^{2}}[/tex] (2)
[tex]F_{g}=8.009 (10)^{-7} N[/tex] (3) As we can see the gravitational force between the eagle and the throng is quite small.
b) The attraction force between the eagle and Earth is the weight [tex]W[/tex] of the eagle, which is given by:
[tex]W=Mg[/tex] (4)
Where [tex]g=9.8 m/s^{2}[/tex] is the acceleration due gravity on Earth
[tex]W=(4.5 kg)(9.8 m/s^{2})[/tex] (5)
[tex]W=44.1 N[/tex] (6)
Now we can find the ratio between [tex]F_{g}[/tex] and [tex]W[/tex]:
[tex]\frac{F_{g}}{W}=\frac{8.009 (10)^{-7} N}{44.1N}[/tex]
[tex]\frac{F_{g}}{W}=1.8(^{-8})[/tex] As we can see this ratio is also quite small
