Question

You have three identical, uniform, square pieces of wood, each with side length L. You stack the three pieces of wood at the edge of the horizontal top of a table. The first block extends a distance L/4 past the edge of the table. The next block extends a distance L/4 past the edge of the first block, so a distance L/2 past the edge of the table. The third block extends a distance L/4 past the edge of the block beneath it, so 3L/4 past the edge of the table. The stack is unstable if the center of mass of the stack extends beyond the edge of the table.

Calculate the horizontal location of the center of mass of the three-block stack. Suppose that the origin of the horizontal x-axis is at the edge of the table, and the x-axis points toward the table's center.

Answer 1

Explanation:

of wood, each with side length L. You stack the three pieces of wood at the edge of the horizontal top of a table. The first block extends a distance L/4 past the edge of the table. The next block extends a distance L/4 past the edge of the first block, so a distance L/2 past the edge of the table. The third block extends a distance L/4 past the edge of the block beneath it, so 3L/4 past the edge of the table. The stack is unstable if the center of mass of the stack extends beyond the edge of the table.

Calculate the horizontal location of the center of mass of the three-block stack. Suppose that the origin of the horizontal x-axis is at the edge of the table, and the x-axis points toward the table's center.

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Answer 2

Answer:

Explanation:

Concept:

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Given:

Three identical, uniform, square pieces of wood, each with side length $L$.

The first block extends a distance $L/4$ past the edge of the table.

The next block extends a distance $L/4$ past the edge of the first block.

The third block extends a distance $L/4$ past the edge of the block beneath it

So $3L/4$ past the edge of the table.

Find:

To find the horizontal location of the center of the mass of the three-block stack. Suppose that the origin of the horizontal x-axis is at the edge of the table, and the x-axis points toward the table's center.

Solution:

$X com =$ ∑$m ix i /$∑$mi$

$X com = m (+L/4) + m(0) + m(-L/4) / m+m+m$

$X com = 0$

The center of mass of the system lies at the origin , that is at the edge of the table.

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