The mass and coordinates of three objects are given below: m1 = 6.0 kg at (0.0, 0.0) m, m2 = 1.5 kg at (0.0, 4.1) m, and m3 = 4.0 kg at (1.9, 0.0) m. Determine where we should place a fourth object with a mass m4 = 7.9 kg so that the center of gravity of the four-object arrangement will be at (0.0, 0.0) m
Answers: 3
.
), measured in meters, is defined by the following formula:
(1)
, 
, 
, 
- Masses of the objects, measured in kilograms. 
, 
, 
, 
- Location of the center of mass of each object with respect to origin, measured in meters. ![\vec r_{cg} = (0,0)\,[m]](/tpl/images/0960/5046/c8901.png)
, ![\vec r_{1} = (0,0)\,[m]](/tpl/images/0960/5046/cbbd8.png)
, ![\vec r_{2} = (0, 4.1)\,[m]](/tpl/images/0960/5046/cecf7.png)
, ![\vec r_{3} = (1.9,0.0)\,[m]](/tpl/images/0960/5046/37339.png)
, 
, 
, 
and 
, then the equation is reduced into this:![(0,0) = \frac{(6\,kg)\cdot (0,0)\,[m]+(1.5\,kg)\cdot (0,4.1)\,[m]+(4.0\,kg)\cdot (1.9,0)\,[m]+(7.9\,kg)\cdot \vec r_{4}}{6\,kg+1.5\,kg+4\,kg+7.9\,kg}](/tpl/images/0960/5046/ad51c.png)
![(6\,kg)\cdot (0,0)\,[m]+(1.5\,kg)\cdot (0,4.1)\,[m]+(4\,kg)\cdot (1.9,0)\,[m]+(7.9\,kg)\cdot \vec r_{4} = (0,0)\,[kg\cdot m]](/tpl/images/0960/5046/7f69d.png)
![(7.9\,kg)\cdot \vec r_{4} = -(6\,kg)\cdot (0,0)\,[m]-(1.5\,kg)\cdot (0,4.1)\,[m]-(4\,kg)\cdot (1.9,0)\,[m]](/tpl/images/0960/5046/166d4.png)
![\vec r_{4} = -0.759\cdot (0,0)\,[m]-0.190\cdot (0,4.1)\,[m]-0.506\cdot (1.9,0)\,[m]](/tpl/images/0960/5046/26091.png)
![\vec r_{4} = (0, 0)\,[m] -(0, 0.779)\,[m]-(0.961,0)\,[m]](/tpl/images/0960/5046/7eda4.png)
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The mass and coordinates of three objects are given below: m1 = 6.0 kg at (0.0, 0.0) m, m2 = 1.5 kg...
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