- Date:09 Apr 2020
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462 C APTER 9 CENtER OF GRAV I TY ANQ CENTRO IQ, Determine Ihe mass and Ihe location of the ce nt er of. i j of the uniform parabolic sh lp d rod The mass,p r unit length of Ihe rod i 2 glm. 9 3 Delennine the d ista nce x to the center of mass of Ihe. homogeneous rod bent into the shape shown if the rod has. a mass per un t length of 0 5 kgfm detcnn ne the react ions. u the fixed support O, 9 2 The uniform rod is bent inlo the shap IIf a parabola 9 4 Determine the mass and locate the center of mass. and has a weight p r unit length of n Ihj f Determine the i J of the uniform rod The mass per unit length of the. r 1ctions 3t the fixed support A rod is 3 kg Ill, 9 1 CENTER OF GRA TY CENTER OF MASS ANO TliE CENTROIO OF A Booy 463. 1 5 Determine the mass and the 100ation of the cent r of 0 41 tenninc the area and the ce ntroid i Y of the area. mass x of the rod if its mass peT unit length is,II 1110 1 xI L.

IXterminc the locatioo f of the centroid of the wire. 9 Detcmlinc the area and tbe centroid x y of hc area. 1 7 Locate the ntroid i of the circular rod Express the. answer in terms of the radius and scmiarc angle R I rub 9 9. 9 10 Detemlinc the area and the centroid x y of the area. Prob J 7 Proh 9 l ll,464 CHAPfE 9 CEN TER Of G RAVITY AND CENlRO ID. 9 11 I clcrmi lll the area and lhe cenlroid l oflhe area 9 14 I ctermine Ihe area and the cenlroid x y oflhe area. Prllb 9 14, J 9 15 o lennine the are a and the centroid t f oflhe area. 9 12 Locale Ihe cenlroid j of Ihe area,0 9 13 Locale the centroid y of Ihe area. f rob J IS,16 Locale the ce ntroid x jl of the area. Prob 9 IZlI3 Prob 1 16, 9 1 CENTER Of GRAVITY CENTEII Of MASS ANO IltE CENT1 OCI Of A 800Y 465.

9 17 Dctcmunc the 3rea md The cenTroid I j oithe area 9 20 Thc plalc has a thICkness of 0 5 in and IS made of. Iel l hal lng a speClrtC clght of 490 lb ft Dctl mme the. horizontal and cnkal componenTs of rC3cllon allhc pm A. and The force m 11M cord 318, 9 11l lhe plate is made of steel ha ng a dcnsity of. 7850 kgfm 1f the Thlclness of the platt IS 10 mm dc Tcrmine. the horizontal and erlical components of rcacllon 3TThe pin. A and the Tension in c blc He,Prob 9 2il,20 9 21 Locale the centroid x of the adcd area. r a 2t r l J, 9 19 DeTcnninc Ihe locaTion t to the cenlrold C of The. opper ponTOn of the cardioid r utI OS 8,PrOO 9 2 1. 466 C APTER 9 CENtER OF GRAV I TY ANO CENTRO IO, 9 22 Loca le Ille C Clll roid i of Ihe area 09 25 Xlcrmine Ille area and tile centroid X 1 of tile.

9 l3 Locale tile ce ntroid y of tile area,Probs 9 l lB l rob 9 25. 9 2 1 Locate the ce ntroid 1 y of the art a 9 26 Locale the cc nnoid X of the area. 9 27 Locate the centroid y of the area,Prol 9 24 I robs 9 26127. 9 1 CENTER OF GRA TY CENTER OF MASS ANO TliE CENTROIO OF A Booy 467. 1 28 Locate tbe centroid of tbc ar a 9 3 1 Locate tbe centroid of the area Hill ChO l C. clements of thickness I and length 2 y il,9 29 Locate tbe centroid y ortbe area. Prob 1 3 1, 9 30 The steel platc is 0 3 m tbick and bas a density of 9 32 Locate the centroid x of the area. 7850 kg m Determine the location of its center of mass. so determine the bori7 onwl and vertical reactions at the 9 13 Locate the centroid yof the area. pin and the reaction attbe roller suppor lIim The nomlal. force at 8 is perpendicular to the tangent 3t lJ wbicb is. found fTonltan if dy d l,Pmb 1 30 Prllhs 1 32 33,468 C APTER 9 CENtER OF GRAV I TY ANO CENTRO IO.

9 l4 If the density 31 any point in the rcClangular plate is 0 1 37 Locate the centroid of the homogeneous solid. defined by p Joil fl u where is a constant formed hy re oh n the shaded arca about the y axis. dt lerminc the nla5S and locale Ihe cenler of mass j of tl c. plale l he plate It Is a Ihiclme S I, 9 35 Loca le Ihe centroid y of the homogeneous solid. formed by revoh ng the shaded area about the y axis. Ao j 11 38 Locate Ihe centroid of Ihe homogeneous solid. frustum of the paraboloid formed by revolving the shaded. area aboul the axis,9 36 Locate Ihe centroid of 1he solid. J rob 1 38, 9 1 CENTER OF GRA TY CENTER OF MASS ANO TliE CENTROIO OF A Booy 46 9. J9 Locate the centroid y of the homogeoeous solid 09 41 Delermine the mass aod locate the cc nter of mass y. formcd by rcvoh IIlS thc shadcd area about the axis of Ihe Ilcmisphere formed by revolving Ihe shaded arCH. about the 3Kis The density at any poiru in the hemisphere. can 1M defi ned by p p 1 y a where PI is a constant. 9 42 Determi ne Ihe volume and locate the cen troid y. of the homogeneous conical edge,Locate the eeruer of mass y of the circular cone. fomled by re ol ing the shaded area about the axis The. density 8t nny point in Ihe cone is defined by I p j ll. where 1 0 is a consta nt,I rob 9 42, 9 43 The hemisphere of radius r is made from a slack of.

cry thin plates such that the densi ty varies with height. p kz where k is a constant Determi ne its mass and the. distance z to Ihe ce nter of mass G,t ro h Prob U,9 2 COMPOSln BOOES 475. shape shown,FUNDAMENTAL PROBLEMS, Locale the centroid x Z of the wire bi nl in the FY 1I1 Loc llc the centroid X fJ of th e cJ OS i seclional area. 400mm 0 5 no, t s l X lc th cen troid y of the beam s crosHcclional tll lI Locale the center of ma5S t y of Ihe. homogeneous solid block, PJ 9 Locale the centroid of the beam s cross P I l De termine the center of mass x y fJ of Ihe. sectional area homogeneollS solid block,476 C APTER 9 CENtER OF GRAV ITY ANO CENTRO IO.

9 44 Locate the centroid x y of the uniform wire b n. in Ihc shape shown,46 Locale th C ntroid t y of the wire. Yroh 9 44 l rob 9 16, 9 15 Locate the centroid I y of the ire 9 17 Locale the centroid x y Z of the wire which s bent. in the shape sho n,Proh 9 I5 Prob II I7,9 2 COMPOSln BODIES 477. 9 48 The truss is made from 5C en m mbers each having J 541 Eac h of Ihe Ihree memb rs of th frame h s a mass. a mass per unit length of 6 kg m Locate the position r y per unit lenglh of 6 kg m Locale Ihe position I y of Ihe. of the center of mass Neglect Ihe mass of Ihe gussel plales cenler of mass Neglectlhe size of Ihe pins al Ihe joints and. allhe join ts Ihe Ihickness of Ihe members Also ca leul 31e Ihe reaclions. allhe pin A and roller E,l I tiilooo m c,I rob rob 9 50. 0 1 49 Locate Ihe cemroid x y of Ihe wire If Ihe wire is J SI Locale Ihe cen foid i n of Ihe er05s 5Cclionalarea. suspended from A determine Ihe angle segment AU m tes oflhe channel. wilh Ihe venical when the wire is in equi librium,Il lOOmm 2 X n m c.

tin r 9 n I n,Prob H9 l rob 1 5 1,4 78 C APTER 9 CENtER OF GRAV I TY ANO CENTRO IO. 9 52 L o alc the centroid y of the crOS Cl ional area of 9 54 Lo alc the centroid y of tbe channel s cross. the concrele beam sectional arCR, 9 53 Locate the cenlroid y or the cross sectional area of 9 55 Locate he distancc y 10 the cenlroid of he. the buih op beam member s cross sectional area,0 5 111 in. J ill ri r,l n in Jill 1 3in j,rob 9 53 Prob 9 55,9 2 COMPOSln BOOES 479. I Locale the centroid y of he eross sc ional area of l SII Locate the ce ntroid of the composite area. lhe buill UP beam,I rob 1 58, 1 59 Locate the centroid IX YJ of the composite area.

I rob 9 56, 09 57 The gmvi t walt is made or concrete Determine the. locadon t y of lhe cenler ofmass G for lh wall,1 I roo 9 59. Locate the centroid t y of th composit e area,311 t 3 ft. I rob l S7 I rob 9 60,480 CHAPfE 9 CENTER Of GRAVITY AND CENlROID. J 61 Divide th plate into parts and using the grid for J 6J Locate the centroid of the cfoss sectional area of. mcasur men1 det rmin pproximatel the location t y the built up beam. of the ntroid of the plate,Prob J 6 1 rob 9 6J, J 62 To det rmin the location of the center of gr3lojt of Locale the cenlroid y of the cross sectional arca of.

the automohile it is first placed in a Inri pomiQu with the the built up beam. twO wheels on one side resting on the scale platform I In. th is position the scale records 3 reading of II t Then one. side is clcl ntcd LO a ronl cn ent height as shown The new. readtng on the scale is IV If the automohile has a total. weight of 11 dctennine the location of its center of gm it. 9 1 CENTER Of GRAVITY CENTEII Of MASS ANO IltE CENT1 OCI Of A 800Y 465 9 17 Dctcmunc the 3rea md The cenTroid I j oithe area rob 9 17 9 11l lhe plate is made of steel ha ng a dcnsity of 7850 kgfm 1f the Thlclness of the platt IS 10 mm dc Tcrmine the horizontal and erlical components of rcacllon 3TThe pin

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