Answer:
220.87 N.
Step-by-step explanation:
To determine the force F2 that is needed to balance the other forces and create a vertical resultant force with a magnitude of 373.15 N, we can use the principle of vector addition.
We know that the force F1 = 249 N acts at an angle of θ1 = 90° (upwards) relative to the horizontal.
We also know that F2 and F3 act at angles of θ2 = 26° and θ3 = 28° (arccos(5/3)) respectively, relative to the horizontal.
We can represent the forces F1, F2 and F3 using their horizontal and vertical components, using the following relationships:
F1x = F1 * cos(90) = 0 N
F1y = F1 * sin(90) = 249 N
F2x = F2 * cos(θ2)
F2y = F2 * sin(θ2)
F3x = F3 * cos(θ3)
F3y = F3 * sin(θ3)
the horizontal and vertical components of the resultant force, R, are the sum of the horizontal and vertical components of the individual forces.
Rx = F1x + F2x + F3x = F2 * cos(θ2) + F3 * cos(θ3)
Ry = F1y + F2y + F3y = F2 * sin(θ2) + F3 * sin(θ3) + 249 N
We know that the magnitude of the resultant force, R, is equal to 373.15 N and it is pointing upward (Ry direction)
R = sqrt(Rx^2 + Ry^2) = 373.15 N
Rx = 0 N (horizontal component is 0)
Ry = 373.15 N
From this equation and the fact that we know the value of F1y, we can find the value of F2y
F2y = Ry - F1y = 373.15 N - 249 N = 124.15 N
Using the equation of F2y = F2 * sin(θ2) we can find the value of F2
F2 = F2y / sin(θ2) = 124.15 N / sin(26) ≈ 220.87 N
So the force F2 that such that the resultant force is vertical with a magnitude of 373.15 N is 220.87 N.
It's worth to note that since the horizontal component of the resultant force (Rx) is 0, we don't know the value of F3 and it's not possible to find it.