Answer:
To raise the mass to an altitude of 12,000 Km 2E joules are required.
Explanation:
Gravitational Potential Energy
It's the energy stored in an object because of its vertical position or height in a gravitational field.
It can be calculated with the equation:
U=m.g.h
Where:
m = mass of the object
h = height with respect to a fixed reference
g = acceleration of gravity, or [tex]9.8 m/s^2[/tex].
If a mass has a height h1, its potential energy is
[tex]U_1=m.g.h_1[/tex]
If a mass has a height h2, its potential energy is
[tex]U_2=m.g.h_2[/tex]
The ratio of both potential energies is:
[tex]\displaystyle \frac{U_2}{U_1}=\frac{m.g.h_2}{m.g.h_1}[/tex]
Simplifying:
[tex]\displaystyle \frac{U_2}{U_1}=\frac{h_2}{h_1}[/tex]
Solving for U2:
[tex]\displaystyle U_2=U_1.\frac{h_2}{h_1}[/tex]
Since U1=E:
[tex]\displaystyle U_2=E.\frac{12,000~Km}{6,000~Km}[/tex]
[tex]U_2 = 2E[/tex]
To raise the mass to an altitude of 12,000 Km 2E joules are required.
