###
Physics 105 Problem Set 4

Due: THURSDAY, October 11, 2007, by 4:30 pm in 208 Jadwin.

### Review:

If you have not already done so, please review the sections of
Kleppner and Kolenkow listed below. Those following ``especially''
are sections where we think the K&K treatment is a notable addition to
the 103 material.

- K&K 1.1-1.8; especially example 1.8. Note 1.1 is worth reviewing as well.
- K&K all of Chapter 2; especially 2.1, 2.2, and the examples
in sections 2.4 and 2.5.
- K&K 4.1-4.9, 4.11-4.13; especially 4.4, 4.8, 4.9.

Note: K&K makes early reference to several topics that we won't cover
till later, notably Newtonian gravitation and the differential equation
for the harmonic oscillator (mass on a spring). Until we do cover them,
when these come up in K&K's examples, don't worry about them.

### Reading for this week (by Monday):

- K&K all of Chapter 3. (Don't worry about example 3.8.)
- K&K 4.14

It is a good idea to warm up by doing all the
problems in 103 Learning Guide 4 after you've done the required reading.

### Problems to turn in:

- K&K 3.1
- K&K 3.4
- K&K 3.11
- K&K 4.23
- K&K 4.29 (Hint: compute v(x))

- The slingshot maneuver. A spacecraft of mass
*m*
approaches
a planet of mass *M* (*M>>m*, of course) with velocity **v**,
antiparallel to the planet's velocity **v**_{p}.
The spacecraft comes pretty close to
the planet, and it is observed that after the encounter it is moving at
90 degrees to its original line of motion with a new velocity
*v*_{f}. What is the energy gained by the spacecraft
from the planet? Use
*M>>m* to keep your expressions simple and ignore the Sun's
gravitational influence.
Links to sites related to the slingshot problem:

Galileo to Jupiter: