Intro to Center of Mass Video Lessons

Concept

# Problem: 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 , (0.100m , -0.400m ); (3) 0.200kg , (-0.300m , 0.600m ).Part A: Find the x-coordinate of the center of mass of the system of three chocolate blocks.Part B: Find the y-coordinate of the center of mass of the system of three chocolate blocks.

###### FREE Expert Solution

X-coordinate of the center of mass:

$\overline{){{\mathbf{x}}}_{\mathbf{c}\mathbf{m}}{\mathbf{=}}\frac{{\mathbf{m}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{1}}\mathbf{+}{\mathbf{m}}_{\mathbf{2}}{\mathbf{x}}_{\mathbf{2}}\mathbf{+}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{+}{\mathbf{m}}_{\mathbf{n}}{\mathbf{x}}_{\mathbf{n}}}{{\mathbf{m}}_{\mathbf{1}}\mathbf{+}{\mathbf{m}}_{\mathbf{2}}\mathbf{+}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{+}{\mathbf{m}}_{\mathbf{n}}}}$

Y-coordinate of the center of mass:

$\overline{){{\mathbf{Y}}}_{{\mathbf{cm}}}{\mathbf{=}}\frac{{\mathbf{m}}_{\mathbf{1}}{\mathbf{y}}_{\mathbf{1}}\mathbf{+}{\mathbf{m}}_{\mathbf{2}}{\mathbf{y}}_{\mathbf{2}}\mathbf{+}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{+}{\mathbf{m}}_{\mathbf{n}}{\mathbf{y}}_{\mathbf{n}}}{{\mathbf{m}}_{\mathbf{1}}\mathbf{+}{\mathbf{m}}_{\mathbf{2}}\mathbf{+}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{+}{\mathbf{m}}_{\mathbf{n}}}}$

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###### Problem Details

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 , (0.100m , -0.400m ); (3) 0.200kg , (-0.300m , 0.600m ).

Part A: Find the x-coordinate of the center of mass of the system of three chocolate blocks.

Part B: Find the y-coordinate of the center of mass of the system of three chocolate blocks.