DO NOT CONVERT UNITS As shown, a uniform beam that has a mass 40.0 k g is attach

Question

DO NOT CONVERT UNITS
As shown, a uniform beam that has a mass 40.0kg  is attached to a wall at point A.  The beam is subjected to three forces, F1 = 18.0N , F2 = 6.50N , and F3 = 16.0N . (Figure 1) The line of action of F2 passes through point A. If the wall can sustain a maximum moment of 675N?m  about point A, what is the largest value for d, the beam's length, that preserves static equilibrium? The beam's width is negligible. Express your answer numerically in meters to three significant figures As shown, a uniform beam that has a mass 40.0kg is attached to a wall at point A. The beam is subjected to three forces, F1 = 18.0N , F2 = 6.50N , and F3 = 16.0N . (Figure 1) The line of action of F2 passes through point A. If the wall can sustain a maximum moment of 675N?m about point A, what is the largest value for d, the beam's length, that preserves static equilibrium? The beam's width is negligible. Express your answer numerically in meters to three significant figures

Explanation / Answer

For the condition of static equilibrium, moment about A is zero, ?M=0
==>F2 passes through point A, so it has no contribution in moment about A.
==>F1 has two components. 18(3/5)N also passes through point A, so it also has no contribution in moment about A. but 18(4/5)N has some moment about A.
==>F3 also has some value of moment about A.
==>weight of beam 40(9.8)N also has a moment about A
==>when max moment is to be obtained, then d will be largest.
Now applying ?M= 675 N.m (about A, take clockwise as positive)
40(9.8)(d/2) + 18(4/5)d/2 + 16(d) = 675 N.m
by solving, d = 3.079 m

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