Neglecting air resistance and the weight of the propellant, determine the work done in propelling a six-ton satellite to a height of 200 miles above earth. Assume that Earth has a radius of 4000 miles.
A) ft-lb
B) ft-lb
C) ft-lb
D) ft-lb
E) ft-lb

Question

Neglecting air resistance and the weight of the propellant, determine the work done in propelling a six-ton satellite to a height of 200 miles above earth. Assume that Earth has a radius of 4000 miles.
A) ft-lb 
B) ft-lb 
C) ft-lb 
D) ft-lb 
E) ft-lb

Quizplus · Accepted Answer

The work done in propelling the satellite is equal to the change in its potential energy. 
Potential Energy = mgh 
where m = 6 tons = 12000 pounds (since 1 ton = 2000 pounds) 
h = 200 miles + radius of the earth (since the height is measured from the earth's surface) 
= 200 + 4000 miles = 4200 miles 
g = acceleration due to gravity at the earth's surface = 32.2 ft/s^2 
Conversion factor: 1 mile = 5280 feet 
Therefore, Potential Energy = (12000 x 32.2 x 5280 x 4200) ft-lb 
= 11eaa595_64fa_59ed_a696_b532cdebb95d_TB4584_11_TB4584_11 ft-lb.

Neglecting Air Resistance and the Weight of the Propellant, Determine