Question

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

Answer 1

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