Question
A coordinate system (in meters) is constructed on the surfaceof a pool table , and three objects are placed on the coordinatesystem as follows: a 2 kg object at the origin, a 3.5 kg object at(0m,2m), and a 4.4 kg object at (3.9m,0m). At what angle does it act with respect to the positive x axis?Let counterclockwise be positive, within the limits of -180 degreesto 180 degress. Ans in units of degrees. A coordinate system (in meters) is constructed on the surfaceof a pool table , and three objects are placed on the coordinatesystem as follows: a 2 kg object at the origin, a 3.5 kg object at(0m,2m), and a 4.4 kg object at (3.9m,0m). At what angle does it act with respect to the positive x axis?Let counterclockwise be positive, within the limits of -180 degreesto 180 degress. Ans in units of degrees.
Explanation / Answer
Giventhat the masse are m1 = 2kg ,m2 = 3.5 kg and m3 = 4.4kg Thecoardinates are (x1,y1) = (0 , 0) , (x2,y2) = (0 , 2m) and(x3,y3) = (3.9m , 0) ------------------------------------------------------------------------------------------------ X-coardinate of the center of mass is Xcm = ( m1*x1 + m2*x2 +m3*x3) / ( m1 +m2 +m3 ) =( 0 + 0 + 4.4kg*3.9m) / ( 2kg + 3.5kg+ 4.4kg) = 1.733 m Y-coardinateof the center of mass is Ycm = ( m1*y1 + m2*y2 + m3*y3) / ( m1 +m2+m3 ) =( 0 + 3.5kg*2m + 0) / ( 2kg + 3.5kg+ 4.4kg) = 0.70m Theangle with positive x-axis is tan = Ycm / Xcm = tan-1 (Ycm / Xcm) =tan-1 ( 0.70m / 1.733m ) =21.990 =( 0 + 3.5kg*2m + 0) / ( 2kg + 3.5kg+ 4.4kg) = 0.70m Theangle with positive x-axis is tan = Ycm / Xcm = tan-1 (Ycm / Xcm) =tan-1 ( 0.70m / 1.733m ) =21.990