Three odd-shaped blocks of chocolate have the following masses and center-of-mass coordinates: (1) 0.300kg , (0.300m , 0.400m ); (2) 0.400kg , (0.200m , -0.400m ); (3) 0.200kg , (-0.300m , 0.700m ).
Find the x-coordinate of the center of mass of the system of three chocolate blocks.
Find the y-coordinate of the center of mass of the system of three chocolate blocks.
use the center of mass formula to solve for the x and y
coordinates separately:
x = (m1x1 + m2x2 + m3x3)/(m1 + m2 +m3) =
[(.300)(.300)+(.4)(.2)+(.2)(-.3)]/(.0.3 + 0.4+0.2)
=0.122
y = (m1y1 + m2y2 + m3y3)/(m1 + m2 +m3) =
[(.3)(.4)+(.4)(-.4)+(.2)(.7)]/(.0.3 + 0.4+0.2)
= .111
so the coordinate is: (.122, .111)
ANSWER :
Let the x-coordinate of the mass centre be x.
Total mass at mass centre = 0.400 + 0.300 + 0.200 = 0.900 kg
So,
0.900 * x = 0.300 * 0.300 + 0.400 * 0.200 - 0.200 * 0.300
=> x = (0.300 * 0.300 + 0.400 * 0.200 - 0.200 * 0.300) / 0.900 = 0.122 m
So, x-coordinate of mass centre is 0.122 m (ANSWER).
Let the y-coordinate of the mass centre be y.
Total mass at mass centre = 0.400 + 0.300 + 0.200 = 0.900 kg
So,
0.900 * y = 0.300 * 0.400 - 0.400 * 0.400 + 0.200 * 0.700
=> y = (0.300 * 0.400 - 0.400 * 0.400 + 0.200 * 0.700) / 0.900 = 0.111 m
So, y-coordinate of mass centre is 0.111 m (ANSWER).
Three odd-shaped blocks of chocolate have the following masses and center-of-mass coordinates: (1) 0.300kg , (0.300m...
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