cables_vector_soln rev class 21

# cables_vector_soln rev class 21 - r similarly dotting the...

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x y z A (4,-3,6) B(-4,-6,4) C (0,5,0) W = 3000 lb Determine the tensions in the cables via a direct vector solution x y z A (4,-3,6) B(-4,-6,4) C (0,5,0) W = 3000 lb T A T B T C O O free body diagram This example problem can be solved by writing the equilibrium equations in terms of the x, y, z components and solving the three simultaneous equations for TA , TB , TC . But there is a more direct vector way to solve this problem.

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x y z A (4,-3,6) B(-4,-6,4) C (0,5,0) W = 3000 lb T A T B T C O free body diagram define the vector cross products these are three vectors (not unit vectors) that are orthogonal to the unit vectors in their definitions A B θ n A x B =ABsin θ n n is a unit vector perpendicular to A , B
If we dot this equilibrium equation with

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Unformatted text preview: r similarly dotting the equilibrium equation with s and t gives This is done most effectively with vectors in MATLAB: since &gt;&gt; OA =[4 -3 6]; &gt;&gt; ea=OA/norm(OA); &gt;&gt; OB = [-4 -6 4]; &gt;&gt; eb =OB/norm(OB); &gt;&gt; OC = [ 0 5 0]; &gt;&gt; ec=OC/norm(OC); &gt;&gt; W = 3000*[ 0 0 1]; &gt;&gt; r =cross(eb, ec); &gt;&gt; s =cross(ea, ec); &gt;&gt; t =cross(ea, eb); &gt;&gt; TA = dot(W, r)/dot(r, ea) TA = 2.3431e+003 &gt;&gt; TB=dot(W, s)/dot(s, eb) TB = 2.4739e+003 EDU&gt;&gt; TC=dot(W, t)/dot(t, ec) TC = 2700 x y z A (4,-3,6) B(-4,-6,4) C (0,5,0) W = 3000 lb T A T B T C O define W k define unit vectors define r,s,t solve for tensions TA = 2343 lb TC = 2700 lb TB = 2474 lb...
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## This note was uploaded on 09/07/2011 for the course EM 274 taught by Professor Boylan during the Fall '08 term at Iowa State.

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cables_vector_soln rev class 21 - r similarly dotting the...

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