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Exercise 4.26

Consider
particles in a plane, with position vectors
and masses
. The position vector of the center of mass is given by:

Consider a triangular plate with corner points
,
and
, 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
?

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?

Esteur
2010-03-22