The 7.2 N weight is in equilibrium under the influence of the three forces acting on it. The F force acts from above on the left at an angle of alpha with the horizontal. The 5.5 N force acts from above on the right at an angle of 48 degree with the horizontal. The force 7.2 N acts straight down. What is the magnitude of the force F? Answer in units of N. What is the angle alpha of the force F as shown in the figure above? Answer in units of degree.

Question

Physics

Boston Harrell

8 August, 14:02

The 7.2 N weight is in equilibrium under the influence of the three forces acting on it. The F force acts from above on the left at an angle of alpha with the horizontal. The 5.5 N force acts from above on the right at an angle of 48 degree with the horizontal. The force 7.2 N acts straight down. What is the magnitude of the force F? Answer in units of N. What is the angle alpha of the force F as shown in the figure above? Answer in units of degree.

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Answers (1)

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Cohen · Answer 1

F = 4.8 N

α = 40.2°

Explanation:

Equilibrium of forces

∑Fx=0

5.5 cos48° - Fcosα = 0

5.5 cos48° = Fcosα

Fcosα = 3.68 Equation (1)

∑Fy=0

5.5 sin48° + Fsinα - 7.2 = 0

Fsinα = 7.2 - 5.5 sin48°

Fsinα = 3.11 Equation (2)

Equation (2) : Equation (1)

Fsinα / Fcosα = 3.11 / 3.68

sinα / cosα = 3.11 / 3.68

tanα = 0.845

α = tan⁻¹ (0.845)

α = 40.2°

We replace α = 40.2° in the equation (1)

Fcosα = 3.68

Fcos (40.2) ° = 3.68

F = 3.68/cos (40.2) °

F = 4.8 N