Reinforced Tripod

MediumPractice Problems

16.Reinforced Tripod

+10

A three-legged stool has a massless equilateral triangular top of side length

s

, supported by vertical legs at its corners

A

B

C

. Legs

B

and

C

are identical and each fail when the compressive force in them exceeds

F_0

. Leg

A

is reinforced and fails only when its compressive force exceeds

2F_0

. A point mass

m = 2F_0/g

is placed on the top. Which of the following shaded regions correctly shows the area within which the mass can be placed without breaking any leg?

AThe medial triangle (the inverted equilateral triangle formed by joining the midpoints of the three sides).

BA rhombus with one vertex at

A

and the opposite vertex at the midpoint of side

BC

, with its remaining two vertices at the midpoints of sides

AB

and

AC

CA regular hexagonal region centered at the centroid of the top.

DThe entire stool top — any placement is safe.

EA small equilateral triangular region adjacent to vertex

A

, with side length

s/2

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