Question

Draw a free-body diagram for the ear of a person properly wearing a mask. You may wish to refer to the figure

Answer 1

Answer:

  Rₓ - F cos θ = 0 ,     R_y - Fsin θ - W = 0

Explanation:

For this exercise we have a static equilibrium problem,

       ∑ F =0

In the attachment we have the forces involved, the weight (W) with vertical direction, the force towards the mask (F) and the reaction force of the ear that we will approximate by its vertical and horizontal components (Rₓ and R_y)

Let's use trigonometry to decompose the force F

       sin θ = Fₓ / F

        cos θ = F_y / F

       Fₓ = F sin θ

       F_y = F cos θ

we write the equations of equilibrium

X axis

           Rₓ - F cos θ = 0

Y axis

           R_y - Fsin θ - W = 0