265_Physics ProblemsTechnical Physics

265_Physics ProblemsTechnical Physics - Chapter 9 *P9.42...

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Chapter 9 267 *P9.42 (a) Represent the height of a particle of mass dm within the object as y . Its contribution to the gravitational energy of the object-Earth system is dm gy af . The total gravitational energy is U gydm g ydm g == zz all mass . For the center of mass we have y M ydm CM = z 1 , so Ug M y g = CM . (b) The volume of the ramp is 1 2 36 157 648 183 10 3 .... m m m 3 a f . Its mass is ρ V = × 3 800 1 83 10 6 96 10 kg m m kg 33 ej . . . Its center of mass is above its base by one- third of its height, y CM m 1 3 15 7 5 23 . . . Then UM g y g × = × CM 2 kg m s m J 696 10 98 523 357 10 68 .. . . . P9.43 (a) Md x xd x + λ 0 0300 0 50 0 20 0 m 2 m gm Mx x =+ = 50 0 10 0 15 9 2 0 . . g 2 m (b) x xdm MM xdx M xx d x CM all mass m 2 m = + z 11 50 0 20 0 0 2 0 x CM 2 m g m L N M M O Q P P = 1 15 9 25 0 20 3 0153 2 3 0 . . *P9.44 Take the origin at the center of curvature. We have Lr = 1 4 2 π , r L = 2 . An incremental bit of the rod at angle θ from the x axis 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 .

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