Answer to Question #98183 in Classical Mechanics for emma

Question

im trying to find where the center of mass of a rectangular table made up from a thin homogeneous plate of 1.2m by 2.3m weighing 8.5kg. It has 4 thin rod shaped legs on its corners. They are homogeneous and have a height of 58cm and weigh 1,7kg each.

Answer 1

From symmetry, center of mass situated on vertical axis which parallel to rods, and cross center of plate.

Center of mass is beneath plate. Denote mass of plate $M=8.5\text{ kg}$ , mass of rod $m=1.7\text{ kg}$ and its height $H=0.58 \text{ m}$.

Find distance from center of plate to center of mass:

$$h = \frac{M\cdot 0 + 4m\cdot H}{M+4m} = \frac{4m\cdot H}{M+4m}=0.26\text{ m} = 36 \text{ cm}$$

Finally, the center of mass is 26 cm under of the center of plate.