Question

Determine the center of mass of three plates filled with food on a table. The plates have the following masses, correspond to by their arbitrary coordinates; m1 = 2 kg; (-3, -1) m2 = 3 kg; ( 2, 2) m3 = 5 kg; ( 3, -3) draw the diagram locate the points show complete solutions

Answer 1

Explanations & Calculations

• Equaling the torque of the total mass about the Y-axis to that of each individual mass, the x-distance to the centre of mass can be found.

$\qquad\qquad \begin{aligned} \small (2+3+5)kg\times \bar{X}&=\small 5kg\times3+3kg\times2+2kg\times(-3)\\ \small \bar{X}&=\small 1.5 \end{aligned}$

• Taking that about X axis,

$\qquad\qquad \begin{aligned} \small (2+3+5)kg\times \bar{Y}&=\small 2kg\times(-1)+3kg\times2+5kg\times(-3)\\ \small \bar{Y}&=\small -1.1 \end{aligned}$

• Therefore, the centre of mass is located at $\small (1.5, -1.1)$