sparknotes
Gravitation: Potential
Problems for Newton's Theorem
Problem : If the Universal Law of Gravitation was a 1/r 3 force instead of a 1/r 2 force, would it still be possible to treat the mass of a sphere as concentrated at its center?
Problem : Show that the gravitational force is independent of the path taken by evaluating some line integrals explicitly. Take a 10 kilogram mass at (1, 0) and calculate the work done to move a one kilogram mass from (2, 0) to the origin. Take one path as being directly along the x -axis and the other taking a quarter-circle path from (2, 0) to (1, 1) , and then a straight path from (1, 1) to (1, 0) .
Problem :
Problem : Determine the magnitude and direction of the force for the set-up described in the previous problem.
Problem : Show that the gravitational force on a point P inside a spherical shell is zero by the following method: 1) pick a point P; 2) draw two lines through P which intersect the edges of a circle representing the spherical shell--in fact, in three dimensions these lines will makes two cones with their base as pieces of the shell; 3)show that the force from each piece of mass at the ends of the cones cancels.


.dr
dx =
=
10G = - 5G
= - 100G
ln(x +
)
= - 100G(2.781.82) = - 96.2G
= - 100G
ln(x +
)
= - 100G(ln(5 +
)ln(- 5 +


