Answer:
the energy transformed into internal energy is E fr = 1.57*10¹⁰ J
Explanation:
From energy conservation , the internal energy gained by friction should be equal to the loss of total energy of the satellite
Since the total energy of the satellite can be decomposed into kinetic and potential energy
E fr = ΔE = E₂-E₁
E₁= K₁+V₁ = 1/2*m*v₁² + m*g*h₁
E₂ = K₂+V₂= 1/2*m*v₂² + m*g*h₂
first, we can choose our reference state so that h₂=0 and h₁=h=500 km
second , we can calculate the approximate the inicial velocity as the velocity required for a stable circular orbit
g = v₁²/(h+R) → v₁² = g*(h+R)
as the velocity diminishes, h diminishes, falling into the earth
assuming the radius of the Earth as R= 6371 km , then
v₁² = g*(h+R) = 9.8 m/s² * (500 km+ 6371 km) *1000 m/km = 6.73 * 10⁷ (m/s)²
replacing values
E₁ = 1/2*m*v₁² + m*g*h₁ = 1/2* 500kg *6.73 * 10⁷ (m/s)² + 500kg* 9.8m/s² * 500 km = 1.67*10¹⁰ J
E₂= 1/2*m*v₂² + m*g*h₂ = 1/2* 500kg *(2000 m/s)² + 0 = 1*10⁹ J
therefore
E fr = ΔE = E₂-E₁ = 1.67*10¹⁰ J - 1*10⁹ J = 1.57*10¹⁰ J
