A human with mass “m” lives at the flat end
of a huge cylinder of mass “M”,
diameter “D” and length “L”
An asteroid collides with this cylinder
destroying one half of its length.
Does the human weigh less or more
after the asteroid impact? How much?
sorry about set up of question I had to copy from a bad .pdf file
The Attempt at a Solution
Assume the following:
1) The cylinder has an even distribution of mass M
2) The asteroid causes enough damage to thoroughly destroy and scatter the matter that the second half of the cylinder comprised of.
3) The system is far enough away from any other body that any force of gravity is essentially 0.
4) As in the diagram the human lives on the flat end of the cylinder
F = (GmM)/(0.5L)^2
f = [Gm(0.5M)]/[0.5 * (0.5L)]^2
2f = (GmM)/[0.25 * (0.5L)^2]
2f = 4 * (GmM)/(0.5L)^2
0.5f = F
f = 2F
The force acting on the person or his weight is doubled because the both the length L and the mass M are halved if the distance from the center of gravity was not squared in the universal gravitation equation this would result in no change however since the change due to the halving of the distance is squared the result is that the force doubles.