Physics 341: Homework Questions Due October 15th

You may find referring to: http://xray.rutgers.edu/matilsky/gravity/gravity2.htm helpful for some of the problems below.

1
Is the potential given by U=k/(r*r)=k/r**2 (where k is a positive constant) attractive or repulsive? What about U=k*r*r=kr**2? How can you turn them into their opposite counterpart, and still maintain the same functional dependence? (By opposite counterpart is meant: if it's attractive, what would make it repulsive? If it's repulsive, how can you make it attractive?)

2
Derive the potential for any point interior to a uniform spherical shell that obeys a 1/r**2 repulsive potential for any point mass. (I.e. derive the equation for phi(iM) as given in the gravity paper). You may have to look up a definite integral in a table of integrals.

3
From your answer to 2 (or by looking up the result for the potential in the paper!), find the field g~(r). I.e. derive the next equation in the paper. Note that the field g~ is given by the force divided by the mass.