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# Suppose the moon has a radius of R miles and a payload weighs P pounds at the surface of the moon (at a distance of R miles from the center of the...

Suppose the moon has a radius of R miles and a payload weighs P pounds at the surface of the moon (at a distance of R miles from the center of the moon). When the payload is x miles from the center of the moon (x ≥ R), the force required to overcome the gravitational attraction between the moon and the payload is given by the following relation:

required force = f(x) = R2P

x2

pounds

For example, the amount of work done raising the payload from the surface of the moon (i.e., x = R) to an altitude of R miles above the surface of the moon (i.e., x = 2R) is

work = b

f(xdxa

= 2R

R2P

x2

dxR

= RP

2

mile-pounds

How much work would be needed to raise the payload from the surface of the moon (i.e., x = R) to the "end of the universe"?

work =   mile-pounds

Suppose the moon has a radius of R miles and a payload weighs P pounds at the surface of the moon (at a distance of R miles from the center of the moon). When the payload is x miles from the
center of the moon (x 2 R), the force required to overcome the gravitational attraction between the moon and the payload is given by the following relation: . _ _ R213
requlred force 7 f(x) 7 7 pounds For example, the amount of work done raising the payload from the surface of the moon (i.e., x = R) to an altitude of R miles above the surface of the moon (i.e., x 2 2R) is
b 2
work =f ﬁx} dx 7 ﬂ dX = % mile—pounds
a How much work would be needed to raise the payload from the surface of the moon (Le.r x : R) to the &quot;end of the universe&quot;? work = x mile-pounds

The solution is... View the full answer

1 comment
• Thank you very much!
• zby1998221
• May 15, 2018 at 11:42pm

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