Answer:
T= 8793 .04 N
Explanation:
We calculate the angle (β) formed by the rope with the horizontal after hanging the weight:
tan (β ) = V / H Formula (1)
Where :
tan (β) : β angle tangent
H : horizontal distance from a support to the center
V : vertical displacement of the rope when the weight is hung
Data
H = 3.23 m / 2 = 1.615 m = 161.5 cm
V = 32.5 cm
β angle calculation
We replace data in the formula (1)
tan (β) = 32.5 cm /161.5 = 0.20124
[tex]\beta = tan^{-1} (0.20124)[/tex]
β = 11.38°
Forces acting in the center of the rope
W: Weight of the object : In vertical direction (y) and downwards
T₁ : Rope tension to the left and upwards
T₂ : Rope tension to the right and upwards
x-y components of the T₁ and T₂
T₁ = T₂ = T because it is the same rope
T₁x = T₂x = T*cos( 11.38°)
T₁y = T₂y = T*sin( 11.38°)
Equilibrium equation of forces in vertical direction inthe center of the rope
∑Fy = 0
2T₁y - W = 0
2 ( T*sin( 11.38°) - 3470 N = 0
2T*sin( 11.38°) = 3470 N
0.3946 * T = 3470 N
[tex]T= \frac{3470 N}{0.3946}[/tex]
T= 8793 .04 N
