Question

A uniform yardstick, 3 feet, weighing 1.00 pound is hung vertically from a nail through a hole in one end. The lower end is pulled aside by horizontal force F, of such magnitude that the stick makes an angle of 37 ° with the vertical. Find:The horizontal component of the force exerted by the nail on the stick."

Answer 1

Answer:

F = 0.3766[lb]

Explanation:

In order to solve this problem, we must perform a static analysis, draw a free body diagram and analyze the forces acting on the yardstick.

In the attached free body diagram we can see these forces, then we can perform a sum of moments at point A of the yardstick.

The horizontal distance can be found using the distance and the angle:

x = 3*sin(37)

x = 1.805[ft] and the middle distance will be 0.902[ft]

For the vertical distance we have:

y = 3*cos(37)

y = 2.395[ft]

$SM_{A} =0\\0=-(1*0.902)+(F*2.395)\\F = 0.3766[lb]$