The right concept to solve this problem is the conservation of gravitational, kinetic and friction energy made by the body.
Recall that by conservation of energy, potential energy and energy released by friction (heat) must be equal to those given in the initial state. In other words:
[tex]PE_1 +KE_1 = PE_2 +KE_2 +Q_f[/tex]
Where
[tex]PE_i[/tex]= Potential energy at each state
[tex]KE_i[/tex]= Kinetic energy at each state
[tex]Q_f[/tex]= Heat energy
There is not Kinetic Energy at the beginning therefore:
[tex]PE_1 = PE_2 +KE_2 +Q_f[/tex]
[tex]-(\frac{GMm}{R+h}) = -(\frac{GMm}{R})+\frac{1}{2}m(v)^2+Q_f[/tex]
Where
[tex]G = 6.673*10^{-11} m^3kg^{-1}s^{-2} \rightarrow[/tex] Gravitational universal constant
[tex]M = 5.98*10^{24} Kg \rightarrow [/tex] Mass of earth
[tex]m = 500Kg[/tex] mass of object
[tex]R = 6.371*10^6km[/tex] Radius of earth
[tex]h = 500*10^3m[/tex] Orbit from earth surface
[tex]v = 2000m/s[/tex] Velocity
Solving to find the Heat energy friction we have
[tex]Q_f = GMm (\frac{1}{R}-\frac{1}{R+h})-\frac{1}{2}mv^2[/tex]
[tex]Q_f = (6.673*10^{-11})(5.98*10^{24})(500Kg)(\frac{1}{6.371*10^6}-\frac{1}{6.371*10^6+500*10^3})-\frac{1}{2}(500)(2000)^2[/tex]
[tex]Q_f = 1.2789*10^9J[/tex]
The quantity of energy that will be transformed into internal energy by means of air friction is [tex]1.2789*10^9J[/tex]
