Having trouble finding the center of mass for multiple objects

AI Thread Summary
The discussion focuses on calculating the x-coordinate of the center of mass for a composite object consisting of a sphere, cylinder, and rectangular solid, with given masses and dimensions. The formula used is M \bar{x}=m_1x_1+m_2x_2+m_3x_3 divided by the total mass, but the user is confused about the placement of the centroids for each shape. The user calculates a value of 12.0346 but questions the accuracy of their approach, particularly regarding the centroid of the sphere. It is clarified that the centroid of a sphere is indeed at its geometric center, not at the end of its diameter. Proper identification of centroids is crucial for accurate center of mass calculations.
kavamo
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Homework Statement



Find the x-coordinate of the center of mass of the composite object shown in the figure. The sphere, cylinder, and rectangular solid all have a uniform composition. Their masses and dimensions are: sphere: 200 g, diameter = 10 cm; cylinder: 450 g, length = 11 cm, radius = 5.0 cm; rectangular solid: m = 220 g, length in x-direction = 16 cm, height = 10 cm, depth = 12 cm.

Homework Equations



using the formula: x1m1+x2m2+x3m3 / Total mass of objects


The Attempt at a Solution



200(10) + 11(450) + 16(220) / 870 = 12.0346

what am I missing/doing wrong?
 
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In the formula

M \bar{x}=m_1x_1+m_2x_2+m_3x_3

x1,x2 and x3 are the centroids of the masses m1, m2 and m3 respectively.

I don't think the centroid of a sphere is at the end of its diameter.
 

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