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:

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

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.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Intro to Center of Mass concept. You can view video lessons to learn Intro to Center of Mass. Or if you need more Intro to Center of Mass practice, you can also practice Intro to Center of Mass practice problems.