Practice problems for the midterm

  1. Problems are easier if you choose the appropriate units -- so that the numerical values lie between 1 and 1000, without any big or small exponents. Can you pick a good set of units for the following situations? Try to choose one unit which has a name based on a distance (such as "meter" or "nanometer") and a unit which is based on a time measurement (such as "second" or "year").
    1. Joe measures the lengths of snakes at the zoo.
    2. JPL plans their communications with the Cassini space probe.
    3. Control Center in Houston talks to astronauts on the Moon.

    Answers to Problem 1

  2. Alpha Centauri is the star closest to the Sun. Let's consider a future space mission to this star.
    1. How far is Alpha Centauri from the solar system? (choose a good unit)
    2. Major Tom, the commander of the mission, is 25 years old. He wants to reach Alpha Centauri before he dies. What is the minimum speed the ship must have on its journey? (Yes, it depends on how old he lives to be. Make a good estimate and go with it).
    3. What is the highest speed of any current space mission?

    Answers to Problem 2 (part i) with mistake fixed Answers to Problem 2 (part ii) with mistake fixed

  3. Let's make a space-time diagram! Mark all the following actors and events on your diagram, and use it to help you answer the questions.
    1. Joe drives from Rochester (x = 0) to Buffalo (x = 150 km) at v = 0.3c. He leaves Rochester at t = 0 km.
    2. At t = 100 km, Joe's mother realizes that her son has left his lunch at home. She gets into her Maserati and chases after him at v = 0.4c. Does she reach him before he arrives in Buffalo? If so, where and when?
    3. At t = 150 km, a dumptruck leaves Buffalo and heads towards Rochester at v = -0.2c When and where does it meet Joe?

    Answers to Problem 3 (part i) Answers to Problem 3 (part ii) Answers to Problem 3 (part iii)

  4. Dr. Smith shoots a bunch of electrons out of his particle accelerator in the lab. He measures the bunch as they fly through particle detector A and particle detector B. 
                 particle detector A      x = 3 m       t = 1 m

             particle detector B      x = 8 m       t = 12 m

    Dr. Ogqlaf of Planet Q flies through the lab in his tiny spacecraft at w = 0.5c to the right. By a nice coincidence, as Dr. Ogqlaf passes Dr. Smith, he notes that both his watch and Dr. Smith's watch both read t = 0 m.

    1. Compute the time and location of both events according to Dr. Ogqlaf.
    2. What is the apparent speed of the electrons, according to Dr. Ogqlaf?

    Answers to Problem 4 (part i) Answers to Problem 4 (part ii)