a8 - 3 In frame S particle 1 is at rest and particle 2 is...

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Phys 263/Amath 261 Assignment 8 Due: Wednesday, July 30, 2008 (in class) 1. Two spaceships, each of proper length 100m, pass near each other heading in opposite directions. If an astronaut at the front of one ship measures a time interval of 2 . 50 × 10 - 6 s for the second ship to pass him, then (a) What is the relative velocity of the spaceships? (b) What time interval is measured on the ﬁrst ship for the front of the second ship to pass from back to front of the ﬁrst ship? 2. A spacecraft in outbound ﬂight to a distant star communicates with earth by sending radio signals back and forth. (a) Derive the shift in frequency of a signal that the ship receives when it is sent by the earth. What is the frequency shift experienced on earth when the signal is sent by the ship? (b) During the ﬁght, signals are sent back and forth at annual intervals. If the ship is moving at u = 0 . 8 c , what is the frequency that each receives a message from the other? What would the frequency be during the return ﬂight at the same speed?
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Unformatted text preview: 3. In frame S , particle 1 is at rest and particle 2 is moving to the right with velocity v . Consider frame S , moving relative to S , with speed u . Find the value of u such that the two particles appear in S to be approaching each other with equal but opposite velocities. 4. Deuterium (or heavy hydrogen) is placed in a particle accelerator where it is ionized. (a) The electrons emerge from the accelerator with m/m = 40 , 000. What is their laboratory speed, both in m/s and in terms of c 2 ? (b) Examining the atomic masses of the neutron and proton compared to the mass of the deuteron (the remaining nucleus), what is the binding energy of the duteron (in MeV)? 5. Calculate the range of speeds for a particle of mass m in which the classical relation for kinetic energy is within 1% of the correct relativistic value. 1...
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