Question

Draw a free-body diagram for the ear of a person properly wearing a mask. You may wish to refer to the figure
below to aid you. Note that when properly worn, the mask will pull at an angle below the horizontal. Improper
usage, such as shown in the image on the right, may result in a completely horizontal pull (the arrows in the figure
are not force arrows), but we wish to avoid this. Choose your own labels for the forces but use the angle the
mask force makes with the horizontal.
Include your free-body diagram in your reply. Also, using the math editor, write the component equations of
equilibrium relative to vertical and horizontal axes. Use the labels for your forces, as well as the angle. You may
substitute for the force of gravity, using the mass of the ear.

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