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9 February, 22:41

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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  1. 9 February, 22:55
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    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
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