The figure below shows three uniform objects: a rod with m1 = 4.75 kg, a right t

Question

The figure below shows three uniform objects: a rod with m1 = 4.75 kg, a right triangle with m2 = 3.10 kg, and a square with m3 = 3.85 kg. Their coordinates in meters are given. Determine the center of gravity for the three-object system. x coordinate 2.915 Ix Your response is within 10% of the correct value. This may be due to round off error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize round off error. m y coordinate m

Explanation / Answer

the cneter of mass of the rod is

m1 = ( 2+ 9/2) , ( 7+7/2 ) = ( 5.5, 7)

The center of m2 ( 6.6667 , 2.333) (the center of mass of a right triangle is 1/3 the height of the triangle, and is closer to the base not the point)

The center of m3 = ( -3.5 , 3.5)

Now we find the x-coordinate of the center of gravity by adding each mass times its x-coordinate.

the center of gravity of the three objetcs is

XCM = m1 x1 + m2 x2 + m3 x3/ m1+ m2 + m3

    =(4.75 kg)(5.50)+(3.1 kg)(6.66667)+(3.85kg)(-3.50)/ ( 4.75 + 3.1 + 3.85 ) kg

   = 2.84 m

YCm = m1 y1 + m2 y2 + m3 y3/ m1+ m2 + m3

((4.75 kg)(7 )+(3.1 kg)(2.333)+(3.85kg)(3.50))/( 4.75 + 3.1 + 3.85 ) kg

= 4.61 m

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