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A guy-wire supports a pole that is 95 ft high. One end of the wire is attached to the top of the pole and the other end is anchored to the ground 50 ft from the base of the pole. Determine the horizontal and vertical components (in lb) of the force of tension in the wire if its magnitude is 90 lb. (Round your answers to the nearest integer.)

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hamzaahmeds

Answer:

Tₓ = 42 N

Ty = 80 N

Explanation:

The pole, guy-wire and ground make a right-angled triangle, as shown in the attached diagram. It is clear from figure that:

tan θ = Perp/Base = 95 ft/50 ft

θ = tan⁻¹ (1.9)

θ = 62.24°

Now, for the horizontal component of tension:

Tₓ = T Cos θ

where,

T = Tension = 90 lb

Tₓ = Horizontal Component of Tension = ?

Therefore,

Tₓ = (90 lb)(Cos 62.24°)

Tₓ = 42 N

Now, for the vertical component of tension:

Ty = T Sin θ

where,

T = Tension = 90 lb

Ty = Vertical Component of Tension = ?

Therefore,

Ty = (90 lb)(Sin 62.24°)

Ty = 80 N

Ver imagen hamzaahmeds
Lanuel

The horizontal and vertical components (in lb) of the force of tension in the wire is 42 and 80 lb respectively.

Given the following data:

  • Height of pole = 95 ft.
  • Distance = 50 ft.
  • Force of tension = 90 lb.

To calculate the horizontal and vertical components (in lb) of the force of tension in the wire:

The horizontal and vertical components of force.

First of all, we would determine the angle of inclination between the pole and the guy-wire by using this formula:

[tex]Tan (\theta) = \frac{Opp}{Adj} \\\\\theta= tan^{-}(\frac{Opp}{Adj})\\\\\theta= tan^{-}(\frac{95}{50})\\\\\theta= tan^{-}(1.9)[/tex]

Angle = 62.24°

For the horizontal component of tensional force:

Mathematically, the horizontal component of tensional force is given by this formula:

[tex]T_x=Tcos\theta\\\\T_x = 90cos(62.24)\\\\T_x = 90 \times 0.4658[/tex]

Tx = 41.92 ≈ 42 lb.

For the vertical component of tensional force:

Mathematically, the vertical component of tensional force is given by this formula:

[tex]T_y=Tsin\theta\\\\T_y = 90sin(62.24)\\\\T_x = 90 \times 0.8849[/tex]

Tx = 79.64 ≈ 80 lb.

Read more on horizontal component here: https://brainly.com/question/4080400