High School

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Use this free body diagram to help you find the magnitude of the force needed to keep this block in static equilibrium.

А.15.3 newtons

В.36.3 newtons

C. .63.5 newtons

D. 95.5 newtons

Use this free body diagram to help you find the magnitude of the force needed to keep this block in static equilibrium А 15 3

Answer :

Answer:

the Answer is D 95.5

Explanation:

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Rewritten by : Barada

Split F₁ into its horizontal and vertical components:

F₁ = F₁ cos(θ) i + F₁ sin(θ) j

(boldface = vector; regular font = magnitude)

By Newton's second law, if the object is in equilibrium, then

• the net horizontal force on the block is

∑ F = F₁ cos(θ) - F₃ = 0 → F₁ cos(θ) = 70 N

• the net vertical force is

∑ F = F₁ sin(θ) + F₂ - W = 0 → F₁ sin(θ) = 65 N

Recall that cos²(θ) + sin²(θ) = 1 for any θ, so we have

(F₁ cos(θ))² + (F₁ sin(θ))² = (70 N)² + (65 N)²

F₁² = 9125 N²

F₁ = √(9125 N²) ≈ 95.5 N