AP® Physics C: Mechanics

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Center of Mass of Two Stacked Boxes

APPHMC-U98PYR

TOMIHIRO ONO. Created for Albert.io. Copyright 2016. All rights reserved.

Consider a system of $2$ boxes, each with mass $M$, which are stacked as shown in the diagram. The top box has height $a$ and the bottom height $b$.

At what y-coordinate is the system's center of mass located, if the bottom of the lower box is at $y = 0$? Assume both boxes have uniform density (the center of mass of each box is located at its center).

A

$\cfrac {1} {4} (a + 4 b)$

B

$\cfrac {1} {2} a$

C

$\cfrac {1} {2} (a + 3 b)$

D

$\cfrac {1} {2} (a + b)$

E

$\cfrac {1} {4} (a + 3 b)$