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Phy 3031 Modern physics, Spring 2007
Homework set #1. Due at the start of class on Wednesday, January 10, 2007.
1. 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 actually looked at it (2pts) or not
(1pt).
2. 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.
3. With v = 1 × 10−12 c, evaluate
q
1−
1 − v 2 /c2 = ?
to two significant figures. Hint: don’t use your calculator.
4. Find the values of µ0 and ²0 on the inside, back cover of your textbook, and evaluate
√
1/ µ0 ²0 to two significant figures. Show clearly and carefully how the units simplify.
Hint: Don’t use your calculator.
5. 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.
6. 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 ).
7. This problem is really an experiment. You should do just one of the these two procedures.
Either:
(a) Flip a coin 100 times and record, in the actual order, whether the coin comes up
heads or tails. Your answer might start something like “THHTHTTTH. . . ”
or:
(b) Choose the letters T and H randomly, to mimic flipping a coin randomly 100
times. Your answer might start something like “THHTHTTTH. . . ”
This is important: On your homework that you hand in, DO NOT indicate whether
you actually flipped the coin, or just mimicked flipping the coin.