Chapter 9267*P9.42(a)Represent the height of a particle of mass dmwithin the object as y. Its contribution to thegravitational energy of the object-Earth system is dm gyaf. The total gravitational energy isUgydm g ydmg==zzall mass. For the center of mass we have yMydmCM=z1, so UgMyg=CM.(b)The volume of the ramp is 1236157648183 103....m mm3af=×. Its mass isρV=×3 8001 83 106 96 10kg mmkg33ej... Its center of mass is above its base by one-third of its height, yCMm1315 75 23... ThenUMgyg×=×CM2kgm smJ696 1098523357 1068.....P9.43(a)Mdxxdx+λ00300050 020 0m2mgmMxx=+=50 010 015 920..g2m(b)xxdmMMxdxMxxdxCMall massm2m=+z1150 020 0020xCM2mgmLNMMOQPP=115 925 02030153230..*P9.44Take the origin at the center of curvature. We have Lr=142π,rL=2. An incremental bit of the rod at angle θfrom the xaxis has
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .