The cantilevered beam shown below is composed of three lengths (L1, L2, and L3). Design a multi-variable function that calculates the moment about point A as a function of
the force magnitudes and lengths.

Calculate the moment about point A for the following cases (express your answer in lbf-ft):

A.) F1 = 50 lbf, L1 = 15 in , F2 = 50 lbf , L2 = 6 ft , F3 = -75 lbf , and L3 = 1.4 ft

B.) F1 = 250 lbf, L1 = 2 ft , F2 = 800 lbf , L2 = 6 in , F3 = -125 lbf , and L3 = 5 ft

C.) Assign F1 = 600 lbf , L1 = 1ft, F2 = 240 lbf, L2 = 4ft, and L3 = 2.5 ft. Plot your defined function used in the previous portion in the range of F3 = -250 lbf to F3 = 250 lbf.

With these circumstances (C), at which value of F3 is the beam balanced that causes no reaction moment about point A? Verify your solution by comparing the algebra to the plotted function
of (C)

Notes:
(1) You do not need to draw a FBD of the system.
(2) Force F1 is acting at the centerline of the beam.


r 

A L1 F1 30 L2 F2 0.75* L3 F3 50 lbm