Simple Nature - Light and Matter

this to the x component of the acceleration, we find∫ (∫ )x = a x dt dt∫= (a x t + v xo ) dt ,where v xo is a constant of integration, andx = 1 2 a xt 2 + v xo t + x o .Similarly, y=(1/2)a y t 2 +v yo t +y o and z = (1/2)a z t 2 +v zo t +z o . Onceone has gained a little confidence, it becomes natural to do thewhole thing as a single vector integral,∫ (∫ )r = a dt dt∫= (at + v o ) dt= 1 2 at2 + v o t + r o ,where now the constants of integration are vectors.Discussion QuestionsA In the game of crack the whip, a line of people stand holding hands,and then they start sweeping out a circle. One person is at the center, androtates without changing location. At the opposite end is the person whois running the fastest, in a wide circle. In this game, someone always endsup losing their grip and flying off. Suppose the person on the end losesher grip. What path does she follow as she goes flying off? (Assume sheis going so fast that she is really just trying to put one foot in front of theother fast enough to keep from falling; she is not able to get any significanthorizontal force between her feet and the ground.)B Suppose the person on the outside is still holding on, but feels thatshe may loose her grip at any moment. What force or forces are actingon her, and in what directions are they? (We are not interested in thevertical forces, which are the earth’s gravitational force pulling down, andthe ground’s normal force pushing up.) Make a table in the format shownin subsection 3.2.6.C Suppose the person on the outside is still holding on, but feels thatshe may loose her grip at any moment. What is wrong with the followinganalysis of the situation? “The person whose hand she’s holding exertsan inward force on her, and because of Newton’s third law, there’s anequal and opposite force acting outward. That outward force is the oneshe feels throwing her outward, and the outward force is what might makeher go flying off, if it’s strong enough.”D If the only force felt by the person on the outside is an inward force,why doesn’t she go straight in?E In the amusement park ride shown in the figure, the cylinder spinsfaster and faster until the customer can pick her feet up off the floor withoutfalling. In the old Coney Island version of the ride, the floor actuallyac / Discussion question A.ad / Discussion question E.Section 3.4 Motion In Three Dimensions 211