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Phy 3221 Due: January 12, 2011
Homework set # 1
You are encouraged and welcome to work together on the homework assignments. But your homework must be in your own handwriting.
Show enough of your work so that I (a reasonably experienced physicist) can understand your thought process.
In applications of dimensional analysis, accuracy is not the goal. Rather, understanding is. Try hard to understand why the answer is as simple as it appears to be. For these dimensional analysis problems, it is always a good idea to give your answer using units that are meaningful to you.
Reading:
Sections 1.1–1.3 and 1.14–1.17
Sections 2.1–2.3
Problem 1: Use dimensional analysis to estimate the speed of the Space Station. Hint: In this problem and the next, the variables of interest might (or might not) include the mass, radius or average density of the Earth, Newton’s gravitational constant G , acceleration of gravity at the Earth’s surface g or the mass of the Space Station. If you think that it would help to know the radius of the Earth, for example, try googling “radius of Earth.” In fact,
Google will even do some arithmetic for you: see what happens with “10 x radius of the earth.”
Problem 2: Use dimensional analysis to estimate the period of one orbit of the Space
Station.
Problem 3: Imagine a small mote of dust gravitationally bound to and orbiting a marble, of radius 1 cm, somewhere far from any galaxy. Use dimensional analysis to estimate the period of one orbit of the mote of dust. Hint: You might (or might not) wish to know the density of the marble. As a rule of thumb, a liquid or any solid object that floats has a density of about 1 g / cm 3 , and any solid object that sinks has a density of about 5 g / cm 3 .
In fact the density of a marble is comparable to the average density of the Earth.
Problem 4: Edwin Hubble, in the 1920’s, made the astronomical observation that all observed galaxies were receding directly away from our own Milky Way galaxy at a rate given by ~ = H ~ , where ~ is the velocity of recession,
~ is the vector from the Milky Way to the observed galaxy, and H = 75( km / s) / mpc is today’s best value of Hubble’s constant . From this single fact, estimate the age of the Universe. Hint: 1 mpc = 10 6 pc, 1 pc = 1 parsec, a unit of distance that astronomers use. Also, 1 parsec ≈ 3 .
3 light years ≈ 3 × 10 13 km.
Problem 5: Estimate the value of 1 −
√
1 − 2 × 10 − 32 . The correct answer is not zero. You might wish to take a good look at the mathematics self-assessment for some help.

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Problem
6: An object is moving in the x y plane according to the following formulae: x ( t ) = x
1
+ A cos( ωt ) and y ( t ) = A sin( ωt ), for some constant distance A and some constant angular velocity ω . Assume that x
1 is positive.
a. Describe the shape of the motion.
b. What is the maximum speed of the object?
c. What is the minimum speed of the object?
d. What is the maximum distance of the object away from the origin?
Problem 7: An object is moving in the x y plane according to the following formulae: x ( t ) = x
1
+ A cos( ωt ) and y ( t ) = A cos( ωt ), for some constant distance A and some constant angular velocity ω . Assume that x
1 is positive.
a. Describe the shape of the motion.
b. What is the maximum speed of the object?
c. What is the minimum speed of the object?
d. What is the maximum distance of the object away from the origin?