The drawing shows a human figure approximately in a sitting position. For the pu

Question

The drawing shows a human figure approximately in a sitting position. For the purposes of this problem, there are three parts to the figure, and the center of mass of each one is shown in the drawing. These parts are: (1) the torso, neck, and head (total mass = 42.2 kg) with a center of mass located on the y axis at a point 0.434 m above the origin, (2) the upper legs (mass = 18.2 kg) with a center of mass located on the x axis at a point 0.173 m to the right of the origin, and (3) the lower legs and feet (total mass = 9.57 kg) with a center of mass located 0.448 to the right of and 0.272 m below the origin. Find the (a) x coordinate and (b) the y coordinate of the center of mass of the human figure. Note that the mass of the arms and hands (approximately 12% of the whole-body mass) has been ignored to simplify the drawing.

Explanation / Answer

Given that mass of torso, neck, and head is m1=41.1 kg coordinates oftorso, neck, and head is(x1 ,y1) = (0,0.395m) mass of upper legs is m2 = 17.3 kg coordinates ofupper legs is (x2 ,y2) =(0.165m,0) mass of lowerlegs is m3 = 10.2 kg coordinates oflower legs is (x3 ,y3) =(0.485m,-0.294m) a ) Then x -cordinate of centre of mass is Xcm = (m1x1 + m2x2+m3x3)/m1+m2+m3 Xcm=(41.1*0 + 17.3kg*0.165m + 10.2kg*0.485m)/41.1kg +17.3kg +10.2kg Xcm = 0.1137 m b) Theny -cordinate of centre of mass is Ycm = (m1y1 +m2y2 +m3y3)/m1+m2+m3 Xcm=(41.1*0.395 + 17.3kg*0m- 10.2kg*0.294m)/41.1kg +17.3kg +10.2kg Ycm = 0.1029 m Xcm=(41.1*0.395 + 17.3kg*0m- 10.2kg*0.294m)/41.1kg +17.3kg +10.2kg Ycm = 0.1029 m

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