Question

A tabletop gamer has designed a game 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 masses of the three dice are 11.30 g, 14.50 g, and 18.90 g, and their respective coordinates after one particular throw are (0.3810 m,−0.4390 m), (−0.1730 m,0.2810 m), and (−0.1390 m,−0.4090 m). What are the resulting coordinates of the center of mass of the dice, ?cm and ?cm ?

Answer 1

Suppose the center of mass of system is (Xcm, Ycm)

then we know that

Xcm = (m1x1 + m2x2 + m3x3)/(m1 + m2 + m3)

Using givne values:

Xcm = (11.30*0.3810 + 14.50*(-0.1730) + 18.90*(-0.1390))/(11.30 + 14.50 + 18.90)

Xcm = -0.0186 m

Similarly

Ycm = (m1y1 + m2y2 + m3y3)/(m1 + m2 + m3)

Using givne values:

Ycm = (11.30*(-0.4390) + 14.50*0.2810 + 18.90*(-0.4090))/(11.30 + 14.50 + 18.90)

Ycm = -0.1928 m

So, Coordinates of center of mass = (-0.0186 m, -0.1928 m)

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