E6    Problems and Suggestions

  1. How much mass does a radio station radiate daily, if it broadcasts around the clock with an output of 12 kW?
  2. How much mass is supplied daily to the earth through its exposure to the sun? Assume a ‘solar constant’ of 1400 W/m2. What pressure does this radiation exert on the earth (→ E5 )
  3. In 2005 the total energy consumption of Switzerland according to the Federal Bureau of Statistics amounted to 890' 440 TJ. How many m3 of granite does this correspond to?
  4. Calculate in general the v / c for electrons, which have passed through a given accelerating voltage U
    a) classically    and     b) relativistically
  5. For a few years now HighCap condensers have offered capacities of several Farads. However they can not be used with high voltages. A HighCap condenser of 4.7 Farad has a mass of 4 gram when uncharged. What mass does it have, after it is subjected to 12 volts?
  6. Chemists always suppose the conservation of mass. Is it not possible however that so much energy is set free with violent reactions that a small mass deficit becomes measurable? Examine the following gas reaction (called an oxyhydrogen reaction): 2 mol of H2 and 1 mol of O2 yield 2 mol of H2O, and thereby an energy of 2 • 240 kJ is released. What % of the original mass ‘disappears’ in this reaction?
  7. Which velocity (as % of c) results in mv = 3 • m0? Solve the problem with both a diagram and a calculation!
  8. The ratio mv / m0 can be taken as a measure for velocities reached in a particle accelerator. Another measure is the difference to the speed of light, and yet another is the energy input into the particles. At the Super Proton Synchrotron in CERN one can accelerate since 1976 protons in such a manner that mv is 427 times as large as m0. Compute v / c, the difference c – v, as well as the necessary acceleration energy in GeV.
  9. Continuation of problem 8: The CERN circular tunnel, in which the protons race around, has a radius of 1200 meters. How strong does the magnetic field have to be, in order to hold the protons with assistance of the Lorentz force on the circular path, given that they only have a rest mass m0? What mass mv do they have, given that an effective magnetic field of 1.11 Tesla is required?
  10. The energy, which is in the electrical field of a charged sphere, amounts to q2 / (2 • 4 • π • ε0 • r). What radius results for the electron if one assumes that its rest mass is nothing more than the mass which corresponds to the energy of its electrical field? (Note: there are no experiments, which prove a spatial expansion of the electron)
  11. We know from E1 that momentum is invariant perpendicular to v: py' = py. If one defines force as temporal change in momentum (F = dp / dt), then it is easy to show how forces perpendicular to v are transformed. From this one can derive that the pressure is an invariant. Use the general gas equation p • V = n • R • T to think about the transformation of temperature and the other thermodynamic state variables ...
  12. Try to show: In 'classic mechanics' as in STR we get the kinetic energy if we multiply the momentum p with 'half of the speed' w

This is a so-called 'autostereogram': Fix your gaze at a point some 40 cm behind the picture, while letting your eyes adapt to the picture itself. Some never succeed while for others the 3-D effect precipitates almost immediately as they ‘sink into the picture’. With some effort most eventually succeed and subsequent success usually comes more easily…