cables_vector_soln%20rev%20class%2021[1]

# cables_vector_soln%20rev%20class%2021[1] - e e k A A A A T...

This preview shows pages 1–4. Sign up to view the full content.

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 TA 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. 0 0 A A B B C C T T T W = + + - = F e e e k

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
x y z A (4,-3,6) B(-4,-6,4) C (0,5,0) W = 3000 lb TA 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 B C A C A B = × = × = × r e e s e e t e e
If we dot this equilibrium equation with r similarly dotting the equilibrium equation with s and t gives This is done most effectively with vectors in MATLAB: since 0 A A B B C C T T T W + + - = e

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: e e k A A A A T W W T × = × × = × r e r k r k r e B B C C W T W T × = × × = × s k s e t k t e ( 29 ( 29 B B C B C B C C × = × × = × = × × = r e e e e r e e e e >> OA =[4 -3 6]; >> ea=OA/norm(OA); >> OB = [-4 -6 4]; >> eb =OB/norm(OB); >> OC = [ 0 5 0]; >> ec=OC/norm(OC); >> W = 3000*[ 0 0 1]; >> r =cross(eb, ec); >> s =cross(ea, ec); >> t =cross(ea, eb); >> TA = dot(W, r)/dot(r, ea) TA = 2.3431e+003 >> TB=dot(W, s)/dot(s, eb) TB = 2.4739e+003 EDU>> TC=dot(W, t)/dot(t, ec) TC = x y z A (4,-3,6) B(-4,-6,4) C (0,5,0) W = 3000 lb TA 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 A A W T × = × r k r e B B C C W T W T × = × × = × s k s e t k t e B C A C A B = × = × = × r e e s e e t e e...
View Full Document

## This note was uploaded on 10/17/2011 for the course EM 274 taught by Professor Boylan during the Fall '08 term at Iowa State.

### Page1 / 4

cables_vector_soln%20rev%20class%2021[1] - e e k A A A A T...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online