A 26.1-cm-by-26.1-cm checkerboard has a mass of 128.3 g. There are four 27.1-g c
ID: 2143357 • Letter: A
Question
A 26.1-cm-by-26.1-cm checkerboard has a mass of 128.3 g. There are four 27.1-g checkers located on the checkerboard, as shown in the figure. Relative to the origin located at the bottom left corner of the checkerboard, where is the center of mass of the checkerboard-checkers system?
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A 26.1-cm-by-26.1-cm checkerboard has a mass of 128.3 g. There are four 27.1-g checkers located on the checkerboard, as shown in the figure. Relative to the origin located at the bottom left corner of the checkerboard, where is the center of mass of the checkerboard-checkers system?Explanation / Answer
From Pythagoras theorem you can calculate X and Y separately.
The checkers are at (6, 14), (14, 22), (22, 10), (30, 30)
COM board = 13.05 cm
X = (13.05cm * 128.3g + (6cm + 14cm + 22cm + 30 cm) * 27.1g) / (128.3g + 4*27.1g)
X = (1674.3 + 72*27.1) / (128.3 + 108.4)
= (1674.3 + 1951.2) / 236.7
= 3625.5/236.7
X = 15.31 cm
Y = (13.05cm * 128.3g + (14cm + 22cm + 10cm + 30 cm) * 27.1g) / (128.3g + 4*27.1g)
= (1674.3 + 76*27.1) / 236.7
= (1674.3 + 2059.6) / 236.7
= 3733.9 / 236.7
Y = 15.77 cm
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