Simple Nature - Light and Matter

∆m = 0, where m is the total mass of any closed system.a / The two pendulum bobsare constructed with equal gravitationalmasses. If their inertialmasses are also equal, then eachpendulum should take exactly thesame amount of time per swing.b / If the cylinders have slightlyunequal ratios of inertial to gravitationalmass, their trajectorieswill be a little different.c / A simplified drawing of anEötvös-style experiment. Ifthe two masses, made out oftwo different substances, haveslightly different ratios of inertialto gravitational mass, then theapparatus will twist slightly as theearth spins.self-check BIf x represents the location of an object moving in one dimension, thenhow would positive and negative signs of ∆x be interpreted? ⊲Answer, p. 921Discussion QuestionsA If an object had a straight-line x − t graph with ∆x = 0 and ∆t ≠ 0,what would be true about its velocity? What would this look like on agraph? What about ∆t = 0 and ∆x ≠ 0?1.2 Equivalence of Gravitational and Inertial MassWe find experimentally that both gravitational and inertial massare conserved to a high degree of precision for a great number ofprocesses, including chemical reactions, melting, boiling, soaking upwater with a sponge, and rotting of meat and vegetables. Now it’slogically possible that both gravitational and inertial mass are conserved,but that there is no particular relationship between them, inwhich case we would say that they are separately conserved. On theother hand, the two conservation laws may be redundant, like havingone law against murder and another law against killing people!Here’s an experiment that gets at the issue: stand up now anddrop a coin and one of your shoes side by side. I used a 400-gramshoe and a 2-gram penny, and they hit the floor at the same timeas far as I could tell by eye. This is an interesting result, but aphysicist and an ordinary person will find it interesting for differentreasons.The layperson is surprised, since it would seem logical thatheaver objects would always fall faster than light ones. However,it’s fairly easy to prove that if air friction is negligible, any two objectsmade of the same substance must have identical motion whenthey fall. For instance, a 2-kg copper mass must exhibit the samefalling motion as a 1-kg copper mass, because nothing would bechanged by physically joining together two 1-kg copper masses tomake a single 2-kg copper mass. Suppose, for example, that theyare joined with a dab of glue; the glue isn’t under any strain, becausethe two masses are doing the same thing side by side. Sincethe glue isn’t really doing anything, it makes no difference whetherthe masses fall separately or side by side. 2What a physicist finds remarkable about the shoe-and-penny experimentis that it came out the way it did even though the shoeand the penny are made of different substances. There is absolutelyno theoretical reason why this should be true. We could say that it2 The argument only fails for objects light enough to be affected appreciablyby air friction: a bunch of feathers falls differently if you wad them up becausethe pattern of air flow is altered by putting them together.60 Chapter 1 Conservation of Mass