Given the following: F1 = 200 lbs A = 40 deg F2 = 80 lbs B = 60 deg F3 = 120 lbs

Question

Given the following:

F1 = 200 lbs    A = 40 deg        

F2 =   80 lbs    B = 60 deg    

F3 = 120 lbs    C = 30 deg            

F4 =   50 lbs    D = 20 deg

Using the Figure below, determine the magnitude, in lbs, 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 = _______lbs

Angle or direction = ________ degrees

Quadrant, _____

Explanation / Answer

F1 = 200 lbs, A = 40 deg

F1 = 200*cos 40 deg i + 200*sin 40 deg j = 153.21 i + 128.56 j

F2 = 80 lbs, B = 60 deg

F2 = -80*cos 60 deg i + 80*sin 60 deg j = -40 i + 69.28 j

F3 = 120 lbs , C = 30 deg

F3 = -120*cos 30 deg i - 120*sin 30 deg j = -103.92 i - 60 j

F4 = 50 lbs , C = 20 deg

F3 = 50*cos 20 deg i - 50*sin 20 deg j = 46.98 i - 17.10 j

So Net force will be:

Fnet = F1 + F2 + F3 + F4

Fnet = (153.21 - 40 - 103.92 + 46.98) i + (128.56 + 69.28 - 60 - 17.10) j

Fnet = 56.27 i + 120.74 j

|Fnet| = sqrt (56.27^2 + 120.74^2)

|Fnet| = 133.21 N

Direction = arctan (120.74/56.27)

Angle of direction = 65.01 deg

Since both (Fnet)x and (Fnet)y are positive, which means net force is in first quadrant.

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