A weightless ladder, 20 ft long rests against a frictionless wall at an angle of

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A weightless ladder, 20 ft long rests against a frictionless wall at an angle of 60⁰ with the horizontal. A 150 pound main is 4 ft from the top of the ladder. A horizontal force is needed to prevent it from slipping choose the correct magnitude from the following

Options:

A . 175 lb

B . 100 lb

C . 70 lb

D . 150 lb

Answer: Option C
:
C
Since the system is in equilibrium therefore

\sum F_{x} = 0 a n d \sum F_{y} = 0 ∴ F = R_{2} a n d W = R_{1}

Now by taking the moment of forces about point B.

F . (B C) + W . (E C) = R_{1}

(AC) [from the figure EC = 4 cos 60

F . (20 s i n 60) + W (4 c o s 60) = R_{1} (20 c o s 60)

10 \sqrt{3} F + 2 W = 10 R_{1} [A s R_{1} = W] ∴ F = \frac{8 W}{10 \sqrt{3}} = \frac{8 \times 150}{10 \sqrt{3}} = 701 b

A Weightless Ladder, 20 Ft Long Rests Against A Frictionless...

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