Answer to Question #172541 in Physics for Kenneth

Question #172541

Locate the center of mass of three particles m1=5kg, m2=7kg and m3=8kg located at ( -1,2,3),(2,4,6) and ( 3,-2,5) respectively coordinates in metres.


1
Expert's answer
2021-03-21T11:36:52-0400

By definition, the radius-vector of the center of mass is given by the formula:


R=rimimi\mathbf{R} = \dfrac{\sum\mathbf{r}_im_i}{\sum m_i}

where

r1m1=(1,2,3)5kg=(5,10,15) (kg)\mathbf{r}_1m_1 = (-1,2,3)\cdot 5kg = (-5,10,15)\space (kg) is the product of the radius-vector and the mass of the first particle, and

r2m2=(2,4,6)7kg=(14,28,42) (kg)\mathbf{r}_2m_2 = (2,4,6)\cdot 7kg = (14,28,42)\space (kg) - the same for the second mass

r3m3=(3,2,5)8kg=(24,16,40) (kg)\mathbf{r}_3m_3 = (3,-2,5)\cdot 8kg = (24,-16,40)\space (kg) - the same for the third mass.

The summation is over all particles, thus, obtain:

R=(5,10,15)+(14,28,42)+(24,16,40)5+7+8=120(33,22,97)=(1.65,1.1,4.85)\mathbf{R} = \dfrac{(-5,10,15) + (14,28,42) + (24,-16,40)}{5 + 7+8} = \dfrac{1}{20}(33, 22, 97) = (1.65,1.1,4.85)

Answer. (1.65,1.1,4.85)(1.65,1.1,4.85)


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