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.
- 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?)
- 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.
- 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.