Reference no: EM13966451
To find the resultant of multiple forces using Cartesian components and to determine the direction of this resultant from its components. As shown, three forces act on the tip of a pole. F1=-60 i +150 j +45 k lb. F2=120 lband forms the following angles with the x, y, and zaxes, respectively: a=52.7°, ß=68.1°, and Φ=134.6°. F3=90 lb, forms the angle θ=30° with the z axis, and forms the angle θ=27° between the x axis and the projection of F3 in the xy plane.
Part A - Resultant of adding F1 and F3 Find the resultant of adding F1 and F3. Express your answer in component form. R13=?
Part B - Resultant of adding F1 and F2 and F3 Find the resultant of adding F1, F2, and F3. Express your answer in component form. R123=?
Part C - Direction of a resultant For the given forces, F1, F2, and F3, find the three direction angles aR, ßR, and ?R between the resultant force R123 found in Part B and the x, y, and z axes, respectively. aR, ßR, ?R=?
Part D - Find the direction angle a when given direction angles ß and ? As shown, a force of 280 lb acts at the tip of a tower. Two of the force's direction angles are known, ßR1=39° and ?R1=63°, that define the angles between the force and the y and z axes, respectively. Find aR1, the angle between the x axis and the force.
Given
Fl = -60i + 150j + 45k
F2 = 120(cos(α)i + cos(β).i + cos(γ)k)
F2 = 72.72i + 44.76j - 83.36k
F3 = F3[(COS(Φ)k sin(Φ)cos(θ)i - sin(Φ)sin(θ)j]
The projection of F3 on the z-axis is F3 cos(phi) and on the xy plane is F3 sin(phi) Now resolve the F3 sin(phi) into two components on the x and y axis respectively
F3 = 40.1i - 20.43j + 77.94k
A) Resultant of 1 and 3 are
R13 = F1 + F3 = -601+150 j + 45 k + 40.11-20.43 j + 77.94 k
R13 = -19.91+ 129.57 j + 122.94 k
B) The resultant is
R=F1+F2 +F3=R13 +F2= -19.91+ 129.57j+ 122.94 k+ 7272 i+ 4476j-8336 k R = 52.82 1+ 174.33 j + 39.58 k
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