What are the coordinates of the center of mass for the combination of the three

Question

What are the coordinates of the center of mass for the combination of the three objects shown in figure below? The uniform rod has a mass of 8.0 kg, has a length of 26.0 cm, and is located at x = 45.0 cm. The oval football has a mass of 2.00 kg, a semimajor axis of 15.0 cm, a semiminor axis of 8.00 cm, and is centered at x = -45.0 cm. The spherical volleyball has a mass of 1.00 kg, a radius of 10.0 cm, and is centered at y = -26.0 cm. Determine the x coordinate of the center of mass for the combination of the three objects. (Express your answer to three significant figures.) Determine the y coordinate of the center of mass for the combination of the three objects. (Express your answer to three significant figures.)

Explanation / Answer

centre of rod (x,y) = (45cm, 0)

centre of football (x,y) = (-45, 0)

centre of vollyball (x,y) = (0 , -26)

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

Xcm = (8*0.45 - 2*0.45 + 1 * 0)/(8+2+1)

Xcm = 24.52 cm

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

Ycm = (8* 0 + 2*0 -1*0.26)/( 8+2+1)

Ycm = - 2.36 cm

Centre of mass (x.y) = (24.52. 2.36 ) cm

1. answer is 24.52 cm

2. nswer is 2.36 cm

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