A statistician has designed a random number generator that requires three dice t

Question

A statistician has designed a random number generator that requires three dice to be thrown onto a tray with a measurement grid. To add an extra degree of randomness, the coordinates of the center of mass of the three dice are used as well. The mases of the three dice are 10.3 g, 14.3 g, and 17.1 g, and their respective coordinates after one particular throw are (0.123 m. -0.409 m), (-0.433 m, 0.299 m), and (-0.279 m, -0.129 m). What are the resulting coordinates of the center of mass of the dice, xcm and ycm?

Explanation / Answer

Total mass = 10.3 + 14.3 + 17.1 = 41.7 g

Then the center of mass Xcm= mixi / mi

Xcm = [(10.3)0.123 - (14.3)0.433 - (17.1)0.279] / 41.7

            = [(1.2669-6.1919-4.7709)]/41.7

Xcm = -0.232 m

Ycm = [(10.3)(-0.409) +(14.3)0.299 - (17.1)0.129] / 41.7

            = [(-4.2127+4.2757-2.2054)]/41.7

Ycm=-0.0513 m

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