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A brave (or foolish) $55.0\text{ kg}$ teacher demonstrates static equilibrium by placing a $13.0\text{ kg}$ wooden board on her desk. The length of the board is $3.66\text{ m}$ and she makes sure that $50.0\text{ cm}$ of the board extends beyond the desk to the right.

The teacher climbs onto her desk, stands on the board and then slowly moves until her center of gravity is $28\text{ cm}$ from the right end of the board as shown below. Note that the picture is not drawn to scale.

Which of the following statements about the teacher-board system are correct? Select ALL that apply.

A

The foolish teacher cannot balance on any part of the board that is not supported by the desk so she flips the board and falls to the floor.

B

The brave teacher is able to balance even though her center of gravity is $22\text{ cm}$ beyond the edge of of the desk.

C

The foolish teacher first had to stack twenty $2.0\text{ kg}$ physics books on the other end of the board (with their centers of gravity $15\text{ cm}$ from that end) to balance when her center of gravity is $22\text{ cm}$ beyond the edge of the desk.

D

The brave teacher can balance a distance of $22\text{ cm}$ beyond the edge of the table even if she is holding two $2.0\text{ kg}$ physics books.

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