Respuesta :
Answer:
a)[tex]w=5,101.2N[/tex]
b) [tex]F=169.13N[/tex]
Explanation:
The weight of an object on the surface of the earth is calculated as follows
[tex]w=mg[/tex]
where [tex]w[/tex] is the weight, [tex]m[/tex] is the mass and [tex]g[/tex] is the acceleration of gravity, wich is equal to [tex]g=9.81m/s^2[/tex], and for this case: [tex]m=520kg[/tex]
Therefore the weight of the satellite will be:
[tex]w=(520kg)(9.81m/s^2)\\w=5,101.2N[/tex]
The gravitational force is calculated with the following formula:
[tex]F=\frac{Gm_{1}m_{2}}{r^2}[/tex]
Where [tex]G[/tex] is the universal gravitational constant: [tex]G=6.6738x10^{-11}Nm^2/kg^2[/tex]
m1 is the mass of earth: [tex]m_{1}=5.97x10^{24}kg[/tex]
m2 is the satellite mass: [tex]m_{2}=520kg[/tex]
and r is the radius of the satellite orbit from the center of the earth: [tex]r=35,000 km=35x10^6m[/tex]
Thus, the gravitational force excerted on the satellite by the Earth:
[tex]F=\frac{(6.6738x10^{-11}Nm^2/kg^2)(5.97x10^{24}kg)(520kg)}{(35x10^6m)^2}\\F=169.13N[/tex]
- The weight of the satellite on the surface of the Earth is 5101.2N
- The gravitational force exerted on the orbiting satellite by the Earth is 169.13N.
How to calculate force?
The weight of an object on the surface of the earth can be calculated as follows
W = mg
Where;
- w = weight
- m = mass = 520kg
- g = acceleration of gravity = 9.81m/s²
The weight of the satellite will be:
W = 520 × 9.81
W = 5101.2N
The gravitational force can be calculated with the following formula:
F = Gm1m2/r²
Where;
- G = universal gravitational constant = 6.67 × 10-¹¹
- m1 = mass of earth = 5.97 × 10²⁴ kg
- m2 = satellite mass = 520kg
- r = radius of the satellite orbit from the center of the earth = 3.5 × 10⁴m
F = 6.67 × 10-¹¹ × 5.97 × 10²⁴ × 520/(3.5 × 10⁴)²
F = 169.13N
Therefore;
- The weight of the satellite on the surface of the Earth is 5101.2N
- The gravitational force exerted on the orbiting satellite by the Earth is 169.13N.
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