Ch 16 Special Relativity - Length, Momentum, & Energy

Assignment Answers:

Ch 16 Review Answers:

  1. Lengths in the moving reference frame would appear shorter.
  2.  L = 10 cm
  3.  If the meter stick were traveling at 99.5% of the speed of light with its length perpendicular to the direction of motion, its length would still be 1 meter. Length contraction only occurs in the direction of motion, so the meter stick would be one-tenth of its thickness in this situation
  4. No. Everything would seem normal to you, since they do not have a high speed relative to you.
  5. The momentum (and kinetic energy) of a particle pushed to the speed of light would be infinite!
  6. Rest mass is the mass of a particle at rest relative to you.
  7. The high speed particles don't bend as readily - they have more inertia (mass).
  8. Mass and energy are actually the same thing - mass is a form of energy.
  9. Since E = mc2, E/m = c2 = (3 x 108 m/s)2 = 9 x 1016 m2/s2 = 9 x 1016 J/kg
  10. No, the equation E = mc2 applies to all matter.
  11. Evidence for the equivalence of mass and energy include:
    (1) The Sun's energy output is much too great to be accounted for by any other process.
    (2) Energy is produced by nuclear fission and fusion reactions. 
  12. As the Sun releases energy, its mass decreases. 
  13. An object at rest has total energy mc2, plus any other potential energies that it might have. When the object is in motion, it has additional energy in the form of kinetic energy. 
  14. Yes, for low speeds, the relativistic and Newtonian equations for kinetic energy (and everything else) agree, as they must. 
  15. If an object were to travel at the speed of light it would have infinite kinetic energy - which is more energy than the Universe contains!  This is why no object can move at or faster than the speed of light.
  16. The Correspondence Principle says that new laws of nature and well-tested old laws of nature must agree in any areas of overlap. 
  17. When low, everyday speeds are used in the relativistic equations, you get the same results as you would from the Newtonian equations. 
  18. The equations of Newton and Einstein overlap in regions where the Newtonian equations apply - that is, where speeds are small compared to the speed of light. 

Ch 16 Think and Explain Answers:

  1. If your space ship passes Earth at nearly the speed of light and observers on Earth tell you that the length of your space ship is contracted, checking your ship's length yourself would tell you that it was still its normal length! Since your space ship is at rest relative to you, it looks normal. You would say that it is the observers on Earth whose lengths are contracted!
  2. From the frame of reference of a photon of light (whatever that is...) the distance to the center of our galaxy, 24 000 light-years to us, is zero! Since light travels at the speed of light:
  3. Special Relativity provides several reasons for the inability of an object to be accelerated to (or beyond) the speed of light. Among them are:
    * The time dilation equation says that as an object's speed increases, its time slows down. As the object's speed approaches the speed of light, its time moves infinitely slowly. At the speed of light, time would not pass at all.
    * The length contraction equation says that as an object's speed increases, its length decreases. As the object's speed approaches the speed of light, its length becomes infinitely small. At the speed of light, its length would be zero.
    * As the book suggests, it requires an impulse to increase the momentum of an object, in fact, impulse exerted on the object by the net force on it equals the change in the object's momentum. Special Relativity says that as the object's speed increases, its momentum increases because both its speed and mass (p = mv) increase. At the speed of light, the object's momentum would be infinite, so it would require an infinite impulse to get it there. Since impulse is force times time, an infinite impulse would require either an infinite force or an infinite time (our time - not the object's time).
    * Impulse is not linked directly to acceleration as the book suggests in this problem (see the previous point) - force is linked to acceleration by Newton's Second Law which says that acceleration = Fnet/mass. Special Relativity says that as a net force accelerates the object its mass increases. As the mass increases, the net force will produce less and less acceleration. As the object's speed approaches the speed of light, its mass approaches infinity, and any finite net force will be ineffective in accelerating the object.
  4. Since the electrons in the accelerator have a high velocity relative to the accelerator, the accelerator has a high velocity relative to the electrons. From the electron's point of view, the accelerator's length is contracted in the direction of motion. (Challenge: How fast are these electrons moving?)
  5. (a) Since you are moving with the electron, its velocity relative to you is zero, so its momentum (= mv) is also zero. The kinetic energy of the electron (= mv2/2) would also be zero. The electron would have reset energy equal to mc2, though.
  9. No. This is the rest energy of the mass, and simply a statement of the equivalence of mass and energy. It applies to all mass, everywhere.
last update May 4, 2009 by JL Stanbrough