The work done against a force F(r) in moving an object from r = r1 to r = r2 is integral F(r) dr limits R2 at top and r1 at bottom. The gravitational attraction between two masses m1 and m2 at distance d is given be F=GMM/d2, G = 6.67 x 10-11. Find the work done in lifting a 4000 kg payload from the surface on the moon to a height of 25000m above its surface. The mass of the moon can be taken as 7.3 x 1022 and its radius at 1.7 x 106.

Question

The work done against a force F(r) in moving an object from r = r1 to r = r2 is integral F(r) dr limits R2 at top and r1 at bottom. The gravitational attraction between two masses m1 and m2 at distance d is given be F=GMM/d2,  G = 6.67 x 10-11. Find the work done in lifting a 4000 kg payload from the surface on the moon to a height of 25000m above its surface. The mass of the moon can be taken as 7.3 x 1022 and its radius at 1.7 x 106.

drwls · Answer

The work done would be

G m1*m2[1/r1 - 1/r2]

r1 = 1.7*10^6 m
r2 = 1.7*10^6 + 2.5*10^4 = 1.725 *10^6 m

Make sure mass is in kg and use the value of G that they provided. The answer should be in Joules.

Be more careful to show units with your numbers.