The drawing shows a human figure approximately in a sitting position. For the pu
ID: 2207301 • Letter: T
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 = 44.4 kg) with a center of mass located on the y axis at a point 0.449 m above the origin, (2) the upper legs (mass = 16.4 kg) with a center of mass located on the x axis at a point 0.152 m to the right of the origin, and (3) the lower legs and feet (total mass = 10.7 kg) with a center of mass located 0.421 to the right of and 0.218 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.
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 = 44.4 kg) with a center of mass located on the y axis at a point 0.449 m above the origin, (2) the upper legs (mass = 16.4 kg) with a center of mass located on the x axis at a point 0.152 m to the right of the origin, and (3) the lower legs and feet (total mass = 10.7 kg) with a center of mass located 0.421 to the right of and 0.218 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
Center of mass is the sum of the moments over the sum of the masses
x cm = (m1 * x1 + m2 x2 + m3 x3) / (m1 + m2 + m3)
y cm = (m1 * y1 + m2 y2 + m3 y3) / (m1 + m2 + m3)
They give you all the masses and all the positions. Note that some of the coordinates aren't given explicitly because they're zero.
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