32. two cyclists who weigh the same and have identical bicycles ride up the same mountain, both starting at the same time. joe rides straight up the mountain, and bob rides up the longer road that has a lower grade. joe gets to the top before bob. ignoring friction and wind resistance, which one of the following statements is true? a) the amount of work done by joe is equal to the amount of work done by bob, but the average power exerted by joe is greater than that of bob. b) the amount of work done by joe is greater than the amount of work done by bob, and the average power exerted by joe is greater than that of bob. c) bob and joe exerted the same amount of work, and the average power of each cyclist was also the same. d) the average power exerted by bob and joe was the same, but joe exerted more work in getting there.

Some material consisting of a collection of microscopic objects is kept at a high temperature. a photon detector capable of detecting photon energies from infrared through ultraviolet observes photons emitted with energies of 0.3 ev, 0.5 ev, 0.8 ev, 2.0ev, 2.5ev, and 2.8ev. these are the only photon energies observed. (a) draw and label a possible energy-level diagram for one of the microscopic objects, which has four bound states. on the diagram, indicate the transitions corresponding to the emitted photons. explain briefly. (b) would a spring–mass model be a good model for these microscopic objects? why or why not? (c) the material is now cooled down to a very low temperature, and the photon detector stops detecting photon emissions. next, a beam of light with a continuous range of energies from infrared through ultraviolet shines on the material, and the photon detector observes the beam of light after it passes through the material. what photon energies in this beam of light are observed to be significantly reduced in intensity (“dark absorption lines”)? explain briefly.