A ball with weight of 1000 pounds is held 1000 above the earth. What is the ball's potential energy in kip-feet? one-kip=1000 pounds

I assume the ball weighs 10000 pounds force at that altitude.?

Can't use PE = mgh as the value of g changes with altitude. At that heigh, it is significantly lower.

First we need the mass.

10000 lb force = 44452 newtons

1000 miles = 1.61e6 m

g value at that altitude is

g = Gm/r²

g is acceleration from mass attraction in m/s²

m is mass of earth or other body generating the a

r is radius of body in meters.

G = 6.67e-11 m³/kgs²

earth radius 6,371 km = 6.37e6 meters

earth mass M 5.974e24 kg

earth GM = 3.987e14

g = (3.987e14) / (6.37e6 + 1.61e6) ² = 6.26 m/s²

mass = 44452/6.26 = 7098 kg

Gravitational potential energy (to surface)

from height h

E = [GmM / (R+h) ] - [GmM/R]

E = GmM[ (1 / (R+h)) - (1/R) ]

E = (3.987e14) (7098) [ (1 / (6.37e6 + 1.61e6)) - (1/6.37e6) ]

you can do the rest.

edit:

E = (3.987e14) (7098) [ (1 / (6.37e6 + 1.61e6)) - (1/6.37e6) ]

E = (3.987e14) (7098) [ (3.17e-8] = 8.97e10 J

for curiosity, use E = mgh so see the difference.

E = (4336) (9.8) (1.61e6) = 7.16e10 J (false