Cascading Disadvantage

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69.Cascading Disadvantage

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Two massless rods rest on frictionless pivots in a vertical plane. Rod A is horizontal, of length

3\text{ m}

, pivoted

2\text{ m}

from its left end. Rod B is straight and inclined at

60°

to the horizontal, of length

4\text{ m}

, pivoted at its upper end. Rod A's right end touches the underside of rod B at a point

2\text{ m}

along rod B from rod B's pivot; the contact between the rods is frictionless. A vertical force

F

is applied downward at the left end of rod A. What vertical force

F'

applied downward at the lower (free) end of rod B keeps the system in equilibrium?

$A two-rod lever cascade in a vertical plane. Rod A is horizontal, drawn as a thin segment of length $3\text{ m}$, with a frictionless pivot (small triangle) beneath rod A at a point $2\text{ m}$ from its left end (so $1\text{ m}$ from its right end). A downward arrow labeled $F$ originates at rod A's left end. Rod B is drawn as a segment of length $4\text{ m}$ sloping downward to the right at $60°$ below horizontal (upper end at upper-left, lower end at lower-right). A frictionless pivot (small triangle) at rod B's upper end. Rod A's right end touches rod B from below at a point $2\text{ m}$ along rod B from its upper pivot (so $2\text{ m}$ from rod B's lower end as well). A downward arrow labeled $F'$ originates at rod B's lower (free) end. Label the $60°$ angle between rod B and the horizontal. Label segment lengths: $2\text{ m}$ and $1\text{ m}$ on rod A, and $2\text{ m}$ and $2\text{ m}$ on rod B.$

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