A tabletop gamer has designed a game that requires three dice to be thrown onto

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 mases of the three dice are 10.30 g, 13.90 g, and 17.50 g, and their respective coordinates after one particular throw are (0.3690 m, -0.2350 m), (-0.2590 m, 0.4550 m), and (-0.4730 m, -0.1450 m). What are the resulting coordinates of the center of mass of the dice, x_cm and y_cm?

Explanation / Answer

m1 = 10.3 g       (x1 , y1 ) = ( 0.3690 , -0.2350 )

m2 = 13.9 g       ( x2 , y2 ) = ( -0.2590 , 0.4550 )

m3 = 17.5 g      ( x3 , y3 ) = ( -0.4730 , -0.1450 )

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

Xcm = ((10.3*0.3690) - (13.9*0.2590)-(17.9*0.4730))/(10.3+13.9+17.5)

Xcm = -0.198 m

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

Ycm = (-(10.3*0.2350) + (13.9*0.4550)-(17.9*0.1450))/(10.3+13.9+17.5)

Ycm = 0.0314 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.