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Phy 3031 Modern physics, Spring 2008
Homework set #1.
Due at the start of class on Monday, January 7, 2008.
This is the first homework assignment of the semester and it is complete. It is also
due at the beginning of the first class meeting on Monday, January 7. I know that this is a
bit unusual, but I like to start the course at full speed talking about physics — I won’t be
talking much about the syllabus, because I assume that you will read it before the first class.
1. Carefully read the course syllabus — there is a link to it on the course home page.
On the homework to be handed in, state whether you carefully read it (2pts) or not
(1pt).
2. Carefully read the Math self-assessment—there is a link to it on the course home page.
On the homework to be handed in, state whether you carefully read it (2pts) or not
(1pt).
3. What is the ratio of the electric force to the gravitational force between an electron and
a proton? Give your answer to within a factor of 10. Hint: Don’t use your calculator.
4. With v = 1 × 10−16 c, evaluate
1−
q
1 − v 2 /c2 = ?
to two significant figures. Hint: don’t use your calculator.
5. Find the values of µ0 and 0 on the inside, back cover of your textbook, and evaluate
√
1/ µ0 0 to two significant figures. Show clearly and carefully how the units simplify.
Hint: Don’t use your calculator.
6. To within a factor of 100 how many protons and neutrons, together, are in a penny?
I am assuming that you have had some chemistry. Hint: Don’t use your calculator.
7. Assume that you and I are each a height h = 6 ft tall, and that we are on the shore
of a very large lake on a planet which might not be the Earth. The shore line is
quite straight. You walk along the shore and keep track of the distance covered, while
we both look at each other through good binoculars. You find that after you have
traveled a distance d = 10,000 ft, you can no longer see the top of my head. What is
the radius R of the planet, to one significant figure? Hints: This involves some tricky,
but elementary, trigonometry and geometry. Draw a careful picture. Use letters and
not numbers. Don’t use your calculator. Recall what the definition of an angle is in
units of radians. Finally, you ought to use the approximation that for small angles θ
measured in radians,
sin θ ≈ tan θ ≈ θ + O(θ3 ).
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8. (a) You flip a penny and a nickel into the air simultaneously. If the penny comes up
heads what is the probability that the nickel also comes up heads?
(b) You flip two pennies into the air. If at least one of them comes up heads, then
what is the probability that the other penny also comes up heads?
(c) You have 10 different numbers on pieces of paper in a hat. You randomly take
a number out and write the number down, and then you replace the number in
the hat. You do this a total of 4 times. What is the probability that no single
number was taken out more than once?
(d) In a classroom of 50 students, what is the probability that no birthday is repeated?
Assume that no one was born on February 29, and that the likelihood of being
born on a specific day is the same for all days.