Question

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

• A. 175 lb
• B. 100 lb
• C. 70 lb
• D. 150 lb

Answer 1

The correct option is C

70 lb

Since the system is in equilibrium therefore $\sum F_x=0and\sum F_y=0\therefore F=R_{2}andW=R_1$ Now by taking the moment of forces about point B.

$F.\left(BC\right)+W.\left(EC\right)=R_1$ (AC) [from the figure EC = 4 cos 60

$F.\left(20sin60\right)+W\left(4cos60\right)=R_1\left(20cos60\right)$

$10\sqrt{3}F+2W=10R_1[As{R}_1=W]\therefore F=\frac{8W}{10\sqrt{3}}=\frac{8\times 150}{10\sqrt{3}}=701b$