To determine the resultant force and angle, we can use vector addition. Given the magnitudes and angles of the forces:
S = 3.8 kip
T = 4.1 kip
U = 5.0 kip
θ₁ = 300°
θ₂ = 40°
First, let's resolve the forces into their x and y components:
Sx = S * cos(θ₁)
Sy = S * sin(θ₁)
Tx = T * cos(θ₂)
Ty = T * sin(θ₂)
Ux = -U (since U acts in the opposite direction of the x-axis)
Uy = 0 (since U acts along the x-axis)
Next, let's add the x and y components of the forces:
Rx = Sx + Tx + Ux
Ry = Sy + Ty + Uy
Finally, we can calculate the resultant force (R) and the angle (θ) it makes with the y-axis:
R = √(Rx² + Ry²)
θ = atan(Rx / Ry)
Substituting the values and calculating:
Rx = (3.8 kip * cos(300°)) + (4.1 kip * cos(40°)) - 5.0 kip
Ry = (3.8 kip * sin(300°)) + (4.1 kip * sin(40°)) + 0
R = √((Rx)² + (Ry)²)
θ = atan(Rx / Ry)
After evaluating these equations, you will obtain the magnitude and angle of the resultant force.