Archimedes is supposed to have said, “Give me a place to stand on and I will move the Earth.” While in principle the claim is valid, the prob-
lems of testing it are vast. Consider the following, highly unrealistic
conditions. Suppose you had a mass equal to that of the Earth—5.98 X
1024 kg—and that it rests on one end of a lever that is balanced on a
fulcrum. The fulcrum is placed on a vast, flat surface in a gravitational
field equal to that at Earth's surface. Let Earth be placed 1.00 m from
the fulcrum, while the distance from the fulcrum to the applied force is
3.8 x 1016 m, or the approximate distance from the sun to the next
closest star. How large must the applied force be to balance the Earth's
weight? How large is the upward force exerted by the fulcrum on the
lever? Assume the lever to be massless.