Exercise 4.26

Consider $ n$ particles in a plane, with position vectors $ r_1, r_2, \ldots,r_n$ and masses $ m_1, m_2,\ldots,m_n$ . The position vector of the center of mass is given by:

$\displaystyle r_{CM}=\frac{r_1 m_1+ r_2m_2+\ldots+r_nm_n}{m_1+m_2+\ldots m_n}

Consider a triangular plate with corner points $ (1,2)$ , $ (5,1)$ and $ (4,4)$ , whose mass is concentrated at the three corner points. How should we distribute a total mass of 1kg over the corner points, such that the center of mass is positioned at $ (3,3)$ ?
Now, consider a plate with four corner points. Hereto, use the previous positions for three of the points, choose a fourth position yourself. What mass distributions are possible?

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Esteur 2010-03-22