A thinrectangular plate of uniform areal density s = 2.86 kg/m 2 has length of 4

Question

A thinrectangular plate of uniform areal density s = 2.86 kg/m2 has length of 40.0 cm andwidth of 25.0 cm. The lower left hand corner is located at theorigin, (x,y)= (0,0) and the length is along the x-axis. There is a circular hole of radius 7.00cm with center at (x,y) = (14.00,10.50) cm in the plate. Calculatethe mass of plate. Calculate the x-coordinateof CM of the plate. Calculate the distance ofthe plate's CM from the origin. A thinrectangular plate of uniform areal density s = 2.86 kg/m2 has length of 40.0 cm andwidth of 25.0 cm. The lower left hand corner is located at theorigin, (x,y)= (0,0) and the length is along the x-axis. There is a circular hole of radius 7.00cm with center at (x,y) = (14.00,10.50) cm in the plate. Calculatethe mass of plate. Calculate the x-coordinateof CM of the plate. Calculate the distance ofthe plate's CM from the origin. There is a circular hole of radius 7.00cm with center at (x,y) = (14.00,10.50) cm in the plate. Calculatethe mass of plate. Calculate the x-coordinateof CM of the plate. Calculate the distance ofthe plate's CM from the origin.

Explanation / Answer

the easiest way to deal with this problem is to take advantage ofsuperposition: If A and B are two masses with centers of gravity at positions(vectors) P and Q, the center of mass of the system containing bothA and B is just: http://en.wikipedia.org/wiki/Center_of_m… R = [(Ma P) + (Mb Q) / (Ma + Mb) In this case, take A as the plate without the hole, and take B asthe hole with negative mass (mass density = -2.86 kg/m^2) You can then compute R and answer parts 2 and 3.

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