SUPPLEMENTARY PROBLEMS - PHYSICS 244

• S1. From the center-of-mass coordinate system two objects of masses m and 3m are moving toward one another at velocities +v and -v/3, respectively. They make a completely inelastic collision.
  • (a) Calculate the total ordered kinetic energy before and after the collision and the increase in thermal energy resulting from the collision.
  • (b) Do part (a) from the point of view of an observer moving at velocity +v with respect to the center of mass.
• S2. Assume that in the Michelson-Morley experiment the length of the cylinders is 10.0 m and the wavelength of the light is 5000 Angstroms. a) If the speed of the earth through the ether is 3 X 10⁴ m/s, what fraction of a wavelength shift will there be between the two beams when they recombine? b) At what speed must the apparatus move through the ether to have the two beams recombine 180^o out of phase with one another?
• S3. Protons leave a particle accelerator at a speed of 0.8c to enter and travel through an evacuated tube 1.0 m long, as measured by an observer at rest in the laboratory, and finally reach a detecting device. a) How long does it take for a proton to travel from one end of the tube to the other according to an observer traveling with a proton? b) What is the tube's length as measured by an observer traveling with a proton?
• S4. Two spaceships moving toward one another on a head-on collision course are separated by a distance of 4 X 10¹⁰ m according to an observer on earth. At this time, according to the observer, one of the spaceships is coincident with the earth. Relative to the earth system both ships are traveling at the same speed, 0.98c. a) How much later do the two ships, collide, according to the observer on earth? b) How much later do they collide according to an observer on the spaceship coincident with the earth at the initial separation?
• S5. Distant galaxies have been found to be moving away from earth with speed as high as 0.81c. If the lifetime of a star, as measured by an observer at rest with respect to the star, is 10 billion years, how long would the star live, according to an earth observer, if it were moving at 0.81c relative to earth?
• S6. In a recent experimental test of the time-dilation phenomenon an atomic clock carried on a jet plane flying on a coast-to-coast round trip was compared with the time interval registered on an atomic clock which the traveling clock is behind the stationary clock for a one-way distance of 4,000 km for a plane traveling at a constant speed of 1,000 km/hr.
  Find out the time difference between these two clocks.
  (In actuality the computation is more complex by virtue of the fact that the earth is in orbital motion about the sun and in rotational motion about its axis.)
• S7. A rigid rod is oriented at an angle theta of with respect to the X-axis of S system. What is the rod's orientation as measured by an observer S' traveling at a speed v along the positive X-axis?
• S8. Train A travels east at 0.80c relative to a station; train B travels north at 0.80c relative to the same station. Find the velocity of train A relative to train B.
• S9. A rod 1.25 m long is to pass through a window 1.00 m wide. More precisely, the rod of rest length 1.25 m, in motion as shown in figure, passes through an opening that is 1.00 m between edges when measured by an observer at rest with respect to the window. The rod's speed is such that the two ends of the rod coincide simultaneously with the two window edges, according to an observer in the reference frame in which the window is at rest.
  • (a) What is the speed of the rod?
  • (b) Now consider events from the point of view of an observer traveling with the rod. What is the width of the window opening relative to this observer?
  • (c) From the point of view of an observer traveling with the rod, do the two rod ends coincide simultaneously with the two window edges and, if not, which rod end, the leading or the trailing one, first coincides with a window edge?
  • (d) What is the time interval between the two coincidences as measured by an observer traveling with the rod?
• S10. A fast train traveling at a speed of 0.8c passes two posts fixed to the ground and adjoining the train tracks. The posts are separated by a distance of 125m, measured by an observer on the ground. Observers on the ground find that the front and back ends of the train coincide simultaneously with the two posts as the train passes.
  • (a) What is the length of the train according to an observer traveling in the train?
  • (b) How long does it take, according to an observer on the ground, for the train to pass one post?
  • (c) What is the time interval, measured by an observer standing at one point in the train, between the passing of the first and second posts?
  • (d) What is the distance between the posts according to observers riding in the train?
  • (e) The coincidence of the ends of the train with the two posts was simultaneous from the viewpoint of an observer fixed on the ground. What end of the train, front or back, first coincided with a post, as according to an observer on the train?
• S11. The pion is an unstable elementary particle with a rest energy of 140 MeV and a mean life of 2.55 X 10^-8 s. The mean life is the average time interval, measured in the reference frame in which the particle is at rest, between the creation of a pion and its decay into other particles. A track in a bubble-chamber photograph, showing the life history of a pion decaying in its mean life, has a length of 5.0m. The pion moves at essentially constant speed in producing the track.
  • (a) What is the kinetic energy of the pion?
  • (b) What is the pion's speed?
• S12. What is the fractional difference in mass between a 1.0g piece of copper at 0.0 ^oC and the same piece of copper at 100 ^o specific heat of copper is 0.093 cal/g^oC .