Take-Home Exam
I'll be out of town this weekend at a friend's wedding, so here's something to work on while I'm gone. This is a closed-book test, and you may not discuss your answers with other students. Show all work for full credit. Exam papers are due at the beginning of class on Monday.
Fall 2003, Exam 1
1) A clever physics student decides that we need better demonstrations of Special Relativity, and sets out to provide one. He takes a cheap digital alarm clock (without a seconds display), and hops a convenient rocket ship into a frame that is stationary with respect to the Sun.
(Helpful facts: The Earth orbits the Sun at a radius of approximately 1.5 1011 m, taking 365.25 days to complete a single orbit. For the purposes of this exam, we can assume that the orbit is circular and that the Earth and the Sun are each in inertial frames.)
(Hint: The binomial expansion is your friend.)
a) Approximately how long does he need to wait for his clock and an identical clock left on Earth to end up one minute out of synch?
b) To pass the time, he carefully observes the Earth. If the Earth in its own rest frame is a perfect sphere, what shape would our hapless colleague see as the Earth passes (ignore the rotation of the Earth), and why?
c) If the radius of the Earth in its own rest frame is 6.37 106 m, what is the difference (in meters) between the maximum and minimum radii he measures?
2) A badly underpaid professor of English drives a 1975 Oldsmobuick, with a rest length of 6 m. Unfortunately, his garage is only 5 m deep. Overhearing a conversation between two Physics 19 students, though, he decides that he can use Relativity to make the car fit. He tells his wife to close the garage door at the instant when the car is completely within the garage, and then stomps on the gas.
a) How fast would he need to go for his (stationary) wife to see the car fit in the garage?
b) At this speed, does he see the car fitting in the garage? If not, how much of the car does he see sticking out of the garage at the instant when the front bumper first touches the back wall?
c) At this speed, how much force is required to accelerate the 1000-kg car at 1 m/s2?
Short Answer:
1) The Sun delivers energy to the Earth at an average rate of 1.7 1017 W. How much mass (in kg) must be converted to energy each second in order to supply energy to the Earth?
2) A muon (mass 105.66 MeV/c2) with a kinetic energy of 70.44 MeV collides with a second particle of unknown mass, initially at rest. The two particles stick together after the collision.
a) What is the initial speed of the muon?
b) If the final speed of the two particles is v = 0.6 c, what is the mass of the unknown particle?
3) As in one of the homework problems, a spaceship of rest length LR is flying alongside a very long stick floating in space, at a speed of 0.8 c. Two space cadets, Alice and Bob, want to cut a piece of the stick that is exactly the length of the ship as seen in the stick frame. If Alice is in the front of the ship, and Bob in the back, how should they time the firing of their lasers to make their cuts simultaneous in the stick frame? (That is, who fires first, and how long does the second person wait before firing?)
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