Physics 281: Homework #1: due April 11
By the end of the week, there will be seven problems (two from each lecture, plus a bonus).
- How many people must UCSD employ to keep parking spaces painted
with various designations (reserved, A/B/S/V spaces, handicapped, etc.)?
A useful expression would be how many hours per day of effort must go into
the enterprise.
- Some roadside billboard convinces you to participate in a program to
shine your laser pointer at the center of the Moon at a particular time,
the goal being to illuminate the Moon enough to be seen by the naked eye
from the Earth. How many people/laser pointers would this take? Put the
number in context/perspective. Is there any way to make it easier? What
are the minimum requirements?
- The observed vacuum energy (i.e., "Dark Energy")
density is (2.3 meV)4 (here meV =
"milli-electron-volts"). This presumably pervades all of
space—an energy proportional to physical volume. Consider all the
vacuum energy inside of the earth's orbit around the sun. What is the size
(mass and dimension) of an asteroid (a rock) with an equivalent
mass-energy? This is a good opportunity to familiarize yourself with natural
units.
- How large would an asteroid need to be to vaporize the earth upon
impact (provide context)? By contrast, the "dinosaur killer" asteroid was
supposedly only 10 km across. How much stuff (water vapor/rock
vapor/etc.) did it throw into the atmosphere?
- Pick a familiar plant or tree and estimate its photosynthetic efficiency
(by doing more than guessing the final answer!).
- Ethanol from corn is optimistically 20% over break-even, meaning that
1.2 J of energy is derived from 1.0 J of input energy (mechanized
agriculture, harvest, processing to ethanol). If corn were used to
completely supplant oil—including the energy input needed to run the
enterprise—how much land area would this take for the U.S.? It is
instructive to draw this on a map of the U.S. for scale.
- Invent a problem of your own in the spirit of this week's class topics.
You do not need to provide a complete solution, though you might outline
how it may go. The art is to strike a balance between trivial and hopelessly
complex.