You occupy a one-dimensional world in which beads— of mass m0 when isolated—attract each other if and only if in contact. Were the beads to interact solely by this attraction, it would take energy H to break the contact. Consequently, we could extract this much energy by sticking two together. However, they also share a repulsive force, no matter what their separation, for which the potential energy is U(r) = 0.%5Ha/r, where a is a bead's radius and r- is ccnter-to-center separation, The closer the beads, the higher is this energy, (a) For one stationary bead, by how much does the energy differ from m0c2? (b) For two stationary beads in contact, by how much does the energy differ from 2m0c2? (c) For three beads in contact (in a line, of course, since this world is one-dimensional), by how much does the energy differ from 3m0c2? (d) For four beads in contact, by how much docs the energy differ from 4m0c2? (e) If you had 12 isolated beads and wished to extract the most energy by sticking them together (in linear groupings), into sets of what number would you group them? (f) Sets of what number would be suitable fuel for the release of fusion energy? Of fission energy?
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