Physics 321 -- Spring 2006

Homework #9, due at beginning
of class Wednesday April 5.

1. [4pts] A long thin straight wire
with uniform mass per unit length rho extends along the positive x axis from 0
to infinity.

(a) Calculate the gravitational field at an arbitrary point on the negative
x axis.

(b) Calculate the gravitational potential at an arbitrary point on the negative
x axis. (Hint: You can start by assuming the wire has a finite length L. Add an
appropriate constant before taking the limit L --> infinity, in order to obtain
a finite answer.)

(c) Calculate the gravitational field using part (b) and check that it agrees
with your result for (a).

2. [4pts] Marion & Thornton: problem 8-3 (Same in Edition 4).

3. [4pts] Marion & Thornton: problem 8-6
(Same in Edition 4). Hint:
Use conservation of momentum and energy.

4. [4pts] Marion & Thornton, problem 8-10 (Same in Edition 4).
Hint:
Calculate the total energy of the Earth’s orbit (algebraically, not with
numbers) both before and after the sun (hypothetically!) loses half its mass.
You do not need to
include "reduced mass" corrections, since the mass of the earth is so small
compared to that of the sun. Note that the first half of this problem is identical
to problem 2, so you can begin with your results from there.

5. [4pts] Marion & Thornton, problem 8-9 part (a)
(Same in Edition 4). Assume the rocket fires in the radial direction for an
extremely short time, so its effect is to instantaneously add a radial component
to the velocity.

6. [4pts]
Marion & Thornton, problem 8-21 (Same in Edition 4).