Question

Three odd-shaped blocks of chocolate have the following masses and center-of-mass coordinates: (1) 0.310kg , ( 0.200 m, 0.320m )(2) 0.410kg , ( 0.110m , -0.380m ) (3) 0.210kg , ( -0.300m , 0.630m )Find the x-coordinate of the center of mass of the system of three chocolate blocksFind the y-coordinate of the center of mass of the system of three chocolate blocks

Answer 1

Answer:

The x coordinate is 0.047m while y coordinate is 0.081 m

Step-by-step explanation:

The coordinates of the center of the mass of the system are given as follows

$x_c=\dfrac{\sum_{i=1}x_im_i}{\sum_{i=1}m_i}\\y_c=\dfrac{\sum_{i=1}y_im_i}{\sum_{i=1}m_i}$

So from the data

m1=0.310, x1=0.20,y1=0.320

m2=0.410,x2=0.110,y2=-0.380

m3=0.210,x3=-0.300,y3=0.630

Now by substitution of the values in the above equation

$x_c=\dfrac{\sum_{i=1}x_im_i}{\sum_{i=1}m_i}\\x_c=\dfrac{x_1m_1+x_2m_2+x_3m_3}{m_1+m_2+m_3}\\x_c=\dfrac{0.310*0.2+0.410*.110+0.210*-0.3}{0.310+0.410+0.210}\\x_c=0.047m\\\\\\y_c=\dfrac{\sum_{i=1}y_im_i}{\sum_{i=1}m_i}\\y_c=\dfrac{y_1m_1+y_2m_2+y_3m_3}{m_1+m_2+m_3}\\y_c=\dfrac{0.310*0.320+0.410*-0.380+0.210*.630}{0.310+0.410+0.210}\\y_c=0.081m$

So the x coordinate is 0.047m while y coordinate is 0.081 m