Answer:
∆U = 2.296×10^10Joules
Explanation:
Gravitational potential energy is defined as the energy possessed by an object under the influence of gravity due to its virtue of position.
Potential energy U = Fr where;
F is the force of attraction between the masses of the moon and the rocket.
r is the radius or height of the object.
From Newton's law of universal gravitation, F = GMm/r²
Potential energy U = (-GMm/r²)×r
Potential energy U = -GMm/r
The force is negative because the objects act upward.
M is the mass of the rocket
m is the mass of the moon
Gravitational potential energy possessed by the rocket
U1 = -GMm/r1
r1 is the altitude covered by the rocket
Gravitational potential energy possessed by the Moon
U2 = -GMm/(r2+r1)
r2 is the radius of the moon
Change in gravitational potential energy ∆U = U2-U1
∆U = -GMm/(r2+r1)-(-GMm/r1)
∆U = -GMm/(r2+r1) + GMm/r1
∆U = -GMm{1/(r2+r1)-1/r1}
Given
G = 6.67×10^-11m³/kgs²
M = 1130kg
m = 7.36×10²²kg
r1 = 215km = 215,000m
r2 = 1740km = 1,740,000m
∆U = -6.67×10^-11× 7.36×10²² × 1130{1/(215,000+1,740,000)-1/215000}
∆U= -55.47×10¹⁴{1/1955000-1/215000}
∆U = -55.47×10¹⁴{5.12×10^-7 - 4.65×10^-6}
∆U = -284×10^7 + 257.94×10^8
∆U = 22,954,000,000Joules
∆U = 2.296×10^10Joules
