Question

The masses of three dices are 12.70 g, 13.10 g, and 17.50 g . their respective coordinates after one particular throw are (0.1710 m, -0.2090 m), (-0.1770 m, 0.2810 m), and (-0.4350 m, -0.2810). what are the resulting coordinates of the center of mass of the dice, Xcm, and Ycm?

O Xcm=0.1327 m, and Ycm=-0.3217 m
O Xcm=0 m, and Ycm=0 m
O Xcm=0.1734 m, and Ycm= -0.2315 m
O Xcm=-0.1792 m, and Ycm=-0.08985 m
O Xcm=-0.2864 m, and Ycm=-0.1243 m

Answer 1

The center of mass for the three dice is at coordinates (Xcm, Ycm) = (-0.1792 m, -0.08985 m), which is calculated by taking the mass-weighted average of the x and y coordinates of each die.

The center of mass (Xcm, Ycm) of a system can be found by taking the mass-weighted average of the coordinates of each mass in the system. To do this, we must calculate the sum of the mass times the coordinate (both x and y) for each die and then divide by the total mass of the system.

We can use the following equations:

Xcm = (m1 × x1 + m2 × x2 + m3 × x3) / (m1 + m2 + m3)

Ycm = (m1 × y1 + m2 × y2 + m3 × y3) / (m1 + m2 + m3)

Calculations for Xcm:

Xcm = (12.70 × 0.1710 + 13.10 × -0.1770 + 17.50 × -0.4350) / (12.70 + 13.10 + 17.50) = -0.1792 m

Calculations for Ycm:

Ycm = (12.70 × -0.2090 + 13.10 × 0.2810 + 17.50 × -0.2810) / (12.70 + 13.10 + 17.50) = -0.08985 m

Therefore, the center of mass for the dice is at the coordinates (Xcm, Ycm) = (-0.1792 m, -0.08985 m).