Answer:
E = 1.77*10^11 [J]
Explanation:
We can solve this problem by using the definition of potential energy which tells us that potential energy is equal to the product of mass by gravity by height.
E_{p}=m*g*h
where:
m = mass = 1450[kg]
g = gravity = 9.81[m/s^2]
h = elevation = 2.38 * (6.37 × 10^6) = 15.16*10^6 [m]
[tex]E_{p}=1450*9.81*(15.16*10^6)\\E_{p}=2.156*10^{11}[J][/tex]
The total energy will be equal to that potential energy minus the energy exerted by the force of gravity.
[tex]F_{G}=6.67*10^{-11} *\frac{1450*5.98*10^{24} }{(15.16*10^{6})x^{2} } \\F_{G}= 2516.5 [N]\\[/tex]
The work done by the gravity force:
W =FG * d
W = 2516.5 * (15.16*10^6)
W = 3.815*10^10 [J]
The energy will be:
E = (2.156*10^11 ) - (3.815*10^10)
E = 1.77*10^11 [J]
The required amount of energy would be "4.01 × 10¹⁰ J".
According to the question,
Mass of earth, M = 5.98 × 10²⁴ kg
Radius of earth, [tex]R_E[/tex] = 6.37 × 10⁶ m
Acceleration due to gravity, g = 9.8 m/s
At surface,
→ [tex]E_i[/tex] = [tex]-\frac{GMm}{R_E}[/tex]
Now, at the altitude when h = 1.84 [tex]R_E[/tex]
→ [tex]E_f[/tex] = [tex]- \frac{GMm}{h+R_E}[/tex]
By substituting the values,
= [tex]- \frac{GMm}{1.84 \ R_E+R_E}[/tex]
= [tex]- \frac{GMm}{R_E}[/tex]
hence,
The required energy be:
→ ΔE = [tex]E_f[/tex] - [tex]E_i[/tex]
= [tex]- \frac{GMm}{2.84 \ R_E} -(- \frac{GMm}{R_E} )[/tex]
= [tex]\frac{GMm}{R_E}[1-\frac{1}{2.84} ][/tex]
= [tex]\frac{G(5.98\times 10^{24})(989)}{6.37\times 10^6} [1-\frac{1}{2.84} ][/tex]
= 4.01 × 10¹⁰ J
Thus the above approach is correct.
Find out more information about gravitational force here:
https://brainly.com/question/19050897
