166 Circular Motion and Other Applications of Newton’s LawsP6.20(a)avrc=2rvac===2213 02980862...ms±msm2bgej(b)Let nbe the force exerted by the rail.Newton’s law givesFIG. P6.20MgnMvr+=2nMvrgMggMg=−FHGIKJ=22, downward(c)avrc=2ac13 020 08452...m2If the force exerted by the rail is n1thengMvrMac12=agc1which is <0 since ac=. ms2Thus, the normal force would have to point away from the center of the curve. Unless theyhave belts, the riders will fall from the cars. To be safe we must require n1to be positive.Then c>. We needvrg2>or vrg>=20 09 80..m ms2af, v>14 0. ms.Section 6.3Motion in Accelerated Frames
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