Question

When you arrive at Duke's Dude Ranch, you are greeted by the large wooden sign shown in the figure(Figure 1). The left end of the sign is held in place by a bolt, the right end is tied to a rope that makes an angle of 20.0 ∘ with the horizontal. The sign is uniform, 3.20 m long, and has a mass of 12.0 kg .

Part A What is the tension in the rope?

Part B What is the horizontal and vertical components of the force, F⃗ , exerted by the bolt?

Answer 1

A)

Tension, T = [mg (L/2) sin(90)]/(L sin(20)

T = (12 x 9.8)/(2 x sin(20)) = 171.92 N

B)

Horizontal component, Fx = 171.92 cos(20) = 161.55 N

Vertical component, Fy = (12 x 9.8) - (171.92 sin(20)) = 58.80 N

Comment in case any doubt please rate my answer....