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If S= 3.8 kip, T- 4.1 kip, U = 5.0 kip, 0₁-300, and 02- 40°, determine the resultant force and angle it makes with the y axis.

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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.

User Rgksugan
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