a) Calculate the mass of plate. b) Calculate the x-coordinate of CM of the plate

Question

a)Calculate the mass of plate.

b)Calculate the x-coordinate of CM of the plate.

c) Calculate the distance of the plate's CM from the origin


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A thin rectangular plate of uniform areal density ? = 3.09 kg/m2 has length of 35.0 cm and width of 25.0 cm. The lower left hand corner is located at the origin, (x,y)= (0,0) and the length is along the x-axis. There is a circular hole of radius 8.00 cm with center at (x,y) = (11.50,10.50) cm in the plate. a)Calculate the mass of plate. b)Calculate the x-coordinate of CM of the plate. c) Calculate the distance of the plate's CM from the origin

Explanation / Answer

a)Mass of the plate =(area of rectangular sheet-area of circular hole)*density

[(0.35*0.25) -(pi*0.008^2)}]*2.93

=(0.0875-0.0002)*2.93

=0.255Kg

b) Calculate the x-coordinate of CM of the plate.

  The area of the plate is 25.0cm * 35.0 cm = 875cm^2

The xCM of the plate is 17.5cm and the y CM is 12.5cm

The area of the hole is -(?*r^2) = -(?*8.00^2) = -200cm^2

and x CM of the hole is 11.5cm and y CM is 10.5cm

Now sum the xCM*A for each body => 17.5*875+ (11.5*(-200)

=15312.5-2300

= 13012.5cm^3

and yCM*A = 875*12.5 + 10.5*(-200)

=10937.5-2100

= 8837.5cm^3

Now divide each of the by the total area to find the CM of the composite figure

So A = 875 - 200 = 675cm^2

So x CM = 13012.5cm^3 /675cm^2 = 19.2cm

and y CM = = 8837.5/675 = 13.09cm

c)And the distance to the origin is sqrt(19.2^2 + 13.09^2)

=sqrt(368.64+171.34)

=sqrt(539.9)

= 23.2cm

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