Question

For the figure, what is the moment caused by the two forces F, and FAB about a line starting at point P and extending to point Q? Use a Cartesian vector approach to solve this problem Hint: it would be easier to find the resultant vector first, but it is not necessary Given: - F = (334i + 540; -838 k) lb • FAB = 3.1 kip - Point Q has coordinates of (-0.167,3.500,0.417) ft Note In the US Customary (also known as English) system of units, we often write lengths as shown below. Note that 4.2" is said as "4 feet 2 inches and is equal to 4 12 + 2 = 50". It is not 4 feet minus 2 inches Find: A The moment caused by the two forces about the point Q. B. The scalar moment caused by the two forces about the line starting at point P and extending to point Q.

Answer 1

h Coordinates $ AC-2-3, 6-7", 1) - AC-225, 6.589,30 - B(0,0,1) fb ,Q(-0.167, 3.5, 0.417) A = 60 -(-251) i +[0-6-58)j + (1 - 1] K AD = (2-251 -6.5€3j+ ok) ft FAB = FAB AB = 3.1 (2-251–6.500 17-25766:58)) = (1.00251-2.933;) Kaips TQA = -2.083° +3.083) + 0.583k Ma = NQAX (F+ FAB) = (.0631+ 3.087) + 0.583k) * (0.3341 +0.5&j -0-838k +1.0025 - 2.4335) = 62.0831'+ 3.0839+0-503k) *(1-33651 – 2-393) -08381) mQ = 1 Ï j k -2.083 3.083 0.513 11.335 -2-393 -0.678 = [(-1.1884) -360.9663) + (0.8641) - tl.1884 -0.9663) +0.8641k) kip-ft- mg = [1188.41-966-3) +864.1k) lb-ft PO = od - op OP = 4.16671 +3.3333 Pa = 60.1671 +3.5j +0.4476) – (4.16670'+3.372) = -4.33371 + 0.167+0.417%.

Scalar moment, Mpa = pol. me -643371 +0.1673 +0.417K) • (-1188.41–966.3j+864.1k) Mpa. = - 4.3376–188.4) + 0.167(-966-3) + 0.417(564.1) 1MPa = 5353.048 lb-ft /