Statics - Problem 2.24

 Statics, Chapter 2 - Force Vectors

In (Figure 1), the resultant F_R of the two forces acting on the jet aircraft should be directed along the positive x axis and have a magnitude of 11 kN,

▼ PART A

Determine the angle θ of the cable attached to the truck at B so that F_B is a minimum. Express your answer in degrees to three significant figures.

▼ PART B

What is the magnitude of force in cable  B when this occurs? Express your answer to three significant figures and include the appropriate units.

▼ PART C

What is the magnitude of force in cable  C when this occurs? Express your answer to three significant figures and include the appropriate units.

F_R = resultant, which is directed along the x-axis and = 11 kN.

θ = ? to have to be minimum...

since F_y = 0, F_c sin(20) = F_b sin(θ)

F_x = F_R = F_c cos(20) + F_b cos(θ) = 11 kN

Let's solve for F_c using the equation for Fy

Now simply the 1/sin(20) and plug F_c  in the equation for F_R

Now, take the derivative of 2.92sin(θ) + cos(θ) in order to get the maximum value that compliments the equation

Set the right hand side = 0, and solve the equation.

Divide every term by cos(θ).

Using trigonometric identities, evaluate -sin(θ)/cos(θ) = -tan(θ)

Take the inverse tan of both sides; arctan(2.92) = 71.1

Part A answ = 71.1°

Now plug in 71.1° in this equation from above...

... to get our value for F_b or F_b(min)

when doing so, our Part B answer is, F_b = 11/3.09 or 3.56 kN

Now for Part C, we can plug in what we now know to find F_c re-using the equation below...

F_c = 9.84 kN