Consider some particles in the plane with position vectors rj, 2,..., rn and masses m j

Chapter 1, Problem 40

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Consider some particles in the plane with position vectors rj, ?2,..., rn and masses m j, m2.......mn.The position vector of the center of mass of this system is1 = T7^wlrl + m2'*2 + -----\~mnrn), Mwhere M = m\ + m2 H-----+ mn. Consider the triangular plate shown in the accompanying sketch. How must a total mass of 1 kg be distributed among the three vertices of the plate so that r 2l the plate can be supported at the point ^ ; that is,r cm ? Assume that the mass of the plate itselfis negligible.

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