Review: Center of Mass Video Lessons

Concept

# Problem: The center of gravity of an irregular object of mass 5.10 g is shown in the figure.You need to move the center of gravity 2.30 cm to the left by gluing on a tiny 1.60-g mass, which will then be considered as part of the object.Where should you attach this additional mass?

###### FREE Expert Solution

X-coordinate of the center of mass:

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

Let x be the distance between the object mass and the tiny mass.

###### Problem Details

The center of gravity of an irregular object of mass 5.10 g is shown in the figure.

You need to move the center of gravity 2.30 cm to the left by gluing on a tiny 1.60-g mass, which will then be considered as part of the object.

Where should you attach this additional mass?