posted by jess .
A 715 kg object is lifted from the surface of the earth to a height of 880 kg above the surface of the earth.
Calculate the increase in gravitational potential energy using the exact expression and compare it with the approximate expression using g=9.81. Give the magnitude of the difference between the two expressions divided by the exact result (that is the relative error) as your answer. Use 6.0x10^24 kg, 6.4x10^6 m and 6.67x10^-11 for the earth mass, earth radius and the Gravitational Constant G, respectively.
The exact PE is:
PE= GMe*m/r where r is the distance from the center of the Earth.
So compute it for both r, then subtract.
What bothers me about this question, is that you are asking for a comparision to 9.81, a three digit expression, but then using "exact" constants to two significant (three in the case of G) digits. That of course, is sheer nonsense.