Given the following: F1 = 200 kN A = 45 deg F2 = 400 kN B = 30 deg F3 = 350 kN C

Question

Given the following:

F1 = 200 kN     A = 45 deg        

F2 = 400 kN     B = 30 deg     

F3 = 350 kN     C = 15 deg        

Using the Figure below, determine the magnitude, in kN, the direction, in degrees (as a positive number less than 90 degrees relative to the x-axis), and quadrant of the resultant for the coplanar concurrent force system shown below. Input your answers in the order shown by filling in the associated blanks with your answer. Express the value of the Quadrant as a whole number between 1 and 4. Express the resultant and angle to one decimal place. Example: 17.1 DO NOT INCLUDE UNITS WITH YOUR ANSWER  Note: When rounding your answers, round as the last step in the calculation process.

Resultant = ____ kN

Angle or direction = _____ degrees

Quadrant, ______

Explanation / Answer

Given the following:

f1 = 200 kN a = 45 deg        

f2 = 400 kN b = 30 deg     

f3 = 350 kN c = 15 deg

let their components along the X-axis be f1x, f2x, f3x

similarly f1y, f2y, f3y be their components along y axis

let resultant be f

fx=f1x - f2x - f3x

fx = 200cos45 - 400cos30 - 350cos15 = -543.06 KN

fy = f1y + f2y - f3y

fy = 200 sin(45) + 400 sin(30) - 350 sin(15) = 250.83 KN

f=(-543.06^2 + 250.83^2)^1/2 = 598.19 KN -------------- (Magnitude)

Angle or Direction = tan-1 (|fy|/|fx|) = 24.790

as fx is -ve and fy is +ve the resultant lies in Q2 or second Quadrant

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