Question

An object of mass m = 1.6 kg is initially held in place at radial distance r = 2.2R_E from the center of Earth, where R_E is the radius of Earth. Let M_E be the mass of Earth. A force is applied to the object to move it to a radial distance r = 4.2R_E, where it again is held in place. Calculate the work done by the applied force during the move.

Answer 1

given that

m = 1.6 kg

r1 = 2.2*R_E

r2 = 4.2*R_E

Work done is difference in the total energies of the object at these two locations given by

E = ( (m*v2^2)/2 - G*M*m/r2) - (m*v1^2/2 - G*M*m/r1) )

E = (m*v2^2)/2 - G*M*m/r2 - m*v1^2/2 + G*M*m/r1

E = G*M/r2 - G*M*m/r2 - G*M/r1 + GMm/r1

E = G*M*(1/r2 - 1/r1) + G*M*m*(1/r1 - 1/r2)

E = G*M*(1/4.2R_E - 1/2.2R_E) + G*M*m*(1/2.2R_E - 1/4.2R_E)

E = G*M/R_E [ -0.22 +m*0.22]

E = G*M/R_E [-0.22 +0.35]

E = G*M/R_E (0.132)

put G = 6.67*10^(-11) Nm^2/kg^2

R_E = radius of earth = 6400km

M = mass of earth = 6*10^24 kg

E = W = 6.67*10^(-11) *6*10^24 *0.132 / 6400*10^3

W = 8.25*10^7 J