Simple Nature - Light and Matter

d / Two magnets exert forceson each other.e / It doesn’t make sense forthe man to talk about thewoman’s money canceling out hisbar tab, because there is no goodreason to combine his debts andher assets.f / Newton’s third law doesnot mean that forces always cancelout so that nothing can evermove. If these two ice skaters,initially at rest, push against eachother, they will both move.Changing frames of reference example 24Suppose we change from one frame reference into another, whichis moving relative to the first one at a constant velocity u. If anobject of mass m is moving at velocity v (which need not be constant),then the effect is to change its momentum from mv in oneframe to mv +mu in the other. Force is defined as the derivative ofmomentum with respect to time, and the derivative of a constantis zero, so adding the constant mu has no effect on the result.We therefore conclude that observers in different inertial framesof reference agree on forces.Using the third law correctlyIf you’ve already accepted Galilean relativity in your heart, thenthere is nothing really difficult about the first and second laws. Thethird law, however, is more of a conceptual challenge. The firsthurdle is that it is counterintuitive. Is it really true that if a fighterjet collides with a mosquito, the mosquito’s force on the jet is justas strong as the jet’s force on the mosquito? Yes, it is true, but itis hard to believe at first. That amount of force simply has more ofan effect on the mosquito, because it has less mass.A more humane and practical experiment is shown in figure d. Alarge magnet and a small magnet are weighed separately, and thenone magnet is hung from the pan of the top balance so that it isdirectly above the other magnet. There is an attraction between thetwo magnets, causing the reading on the top scale to increase and thereading on the bottom scale to decrease. The large magnet is more“powerful” in the sense that it can pick up a heavier paperclip fromthe same distance, so many people have a strong expectation thatone scale’s reading will change by a far different amount than theother. Instead, we find that the two changes are equal in magnitudebut opposite in direction, so the upward force of the top magnet onthe bottom magnet is of the same magnitude as the downward forceof the bottom magnet on the top magnet.To students, it often sounds as though Newton’s third law impliesnothing could ever change its motion, since the two equal andopposite forces would always cancel. As illustrated in figure e, thefallacy arises from assuming that we can add things that it doesn’tmake sense to add. It only makes sense to add up forces that areacting on the same object, whereas two forces related to each otherby Newton’s third law are always acting on two different objects.If two objects are interacting via a force and no other forces areinvolved, then both objects will accelerate — in opposite directions,as shown in figure f!Here are some suggestions for avoiding misapplication of Newton’sthird law:148 Chapter 3 Conservation of Momentum