Physics & Astronomy Sample Diagnostic & Review Exam

These problems should serve as a tool to give both you and me an idea of where you are and what you remember. They range from very easy to very hard; don't expect to do them all. If a whole section makes no sense, then just ignore it - though maybe it will give you a taste of things to come.

I urge you to try the problems first without any notes or texts, even the ones that require constants - just guesstimate as best you can. If that doesn't work, I don't mind if you use old notes or textbooks, as long as you indicate which sources you used.

Good luck,

Jim Mahoney

Sept. `96

Math

Algebra

  1. Solve for x : .
  2. Write down two equations in two unknowns, x and y. Solve them both algebraically and graphically.
  3. A chicken-and-a-half can lay an egg-and-a-half in a day-and-a-half. How many chickens will lay ten eggs in three days?
Vectors
  1. A woman walks 10 paces east, then 5 paces north. How far from her starting point is she, and in what direction?
  2. What is a "vector dot product"? Give an example.
Calculus
  1. Given , find and . Explain what they mean.
  2. Find the average of .
Beyond
  1. What is the "curl" of a vector field? Give an example of a calculation that uses one.
  2. Write down a second order differential equation and solve it.
  3. Give a non-trivial example of a 3x3 orthogonal matrix. Invert it.

Physics

  1. What is an atom? How big are they? What are they made of?
  2. Convert g = 9.8 m/sec2 to mm/millenium2.
Mechanics (1st term Gen. Phys. I)
  1. What is "Force"? "Energy"? Momentum? "Angular Momentum"? What are their units in MKS (meter, kilogram, sec) terms? Under what conditions are which ones conserved?
  2. A projectile is fired at a 30deg. angle with a velocity of 100 m/sec. How high does it rise, and where does it land? What happens on the earth's surface if the velocity is much higher? And how fast is "much"?
  3. I heard someone on a children's television show say something like this: "astronauts float around in the shuttle as it orbits the earth because there is no gravity in space." Would you agree? Explain.
  4. Describe an experiment to measure the forces vs velocity relationship for an object whirling at the end of a rope. What do you expect this relationship to look like?
  5. A motionless flatbed train car on a frictionless track has 10 men standing on it. As they jump off, the train moves in the opposite direction. Does it go faster if they jump all at once, or one at a time?

    Astronomy

    1. Explain what solar and lunar eclipses are, roughly how often they take place, and roughly how much of the earth is affected.
    2. For each of the following describe briefly what it is, how far from it is, how big it appears from earth, and what sorts of instruments are commonly used to study it.
      • the Moon
      • the Sun
      • Jupiter
      • Sirius
      • the Crab Nebula
      • the Milky Way
      • the Andromeda Galaxy
    3. What kinds of magnification would you expect from a telescope with a 1.5m focal length and a 26mm eyepiece? What are the limits on this instruments resolving power? (On earth? In space?)
    4. Discuss briefly why the "Big Bang" theory is in vogue.
    5. What is "dark matter?" What is the evidence for it?
    6. Astronomers measure the brightness of objects by "magnitudes." What are they? Give some examples.
    7. Explain the basic phyics behind the birth and death of stars.
    8. Suppose you see Mars, the Moon, and a star all align at exactly 10pm on a certain night, due south of you. Where are each of these objects in the night sky the next night at precisely the same time? To the east? West? How far?