## Challenge Problems for PHYS104

Do any of these problems at your leisure. Hand in your solution and get
extra marks!

1. A 10.0 mile long caravan is moving across the desert at constant speed.
A rider takes a message from the rear of the caravan to the leader in the
front and immediately returns, also moving at a constant speed. He notes
that the caravan has travelled 15 miles while he was away. How far did he
ride?

2. A small 1 kg mass is placed on the inside of a frictionless pipe half way
up one side
(say at the 9:00 position). It slides to the bottom of the pipe. How much
work was done on the mass? How much was done if it slides around to the 3:00
position? Don't use conservation of energy to solve this (its too easy).

3. Derive an expression for the acceleration of a particle moving at uniform
speed along a spiral. Give your answer in terms of theta, r, v_{r}, and
v_{t}. Here v_{r} is the particle's speed in the radial direction
and v_{t} is the particle's speed in the tangential direction. Define these
concepts carefully in your derivation. Sketch the acceleration vector at some point
on the spiral.

4. The astronauts on the space station have decided to colonize Mars. They have also
decided to get there by ejecting 10 percent of their mass. However, they are arguing
over whether it is better to eject it all at once or to emit it in a constant stream.
Which method is better? Assume that the speed with which they can eject mass
is independent of the size of the mass.

5. If a chicken and a half lays an egg and a half in a day and a half, how many eggs
do 4 chickens lay in 6 days?