Question

determine the required values of the tension in ac and ad so that the resultant of the three forces applied at A is verticalFigure:A wire is coupled from three sides

Answer 1

Fac = 21 KN

Fad = 64.29 KN

Step-by-step explanation:

Step 1: Find the unit vectors in BA , CA, and DA directions

BA = -16 i + 48 j - 12 k

CA = -16 i + 48 j + 24 k

DA = 14 i + 48 j

The following magnitudes

mag (BA) = sqrt ( 16 ^2 + 48^2 + 12^2 ) = 52

mag (CA) = sqrt ( 16 ^2 + 48^2 + 24^2 ) = 56

mag (DA) = sqrt ( 14 ^2 + 48^2 ) = 50

Now compute unit vectors

unit (BA) = (-4 / 13) i + (12 / 13) j - (3 / 13) k

unit (CA) = (-2 / 7) i + (6 / 7) j - (3 / 7) k

unit (DA) = (7 / 25) i + (24 / 25) j

Step 2: Compute Force Vectors F(ml) dot unit( ML )

Fab = (-4*Fab / 13) i + (12*Fab / 13) j - (3*Fab / 13) k

Fac = (-2*Fac / 7) i + (6*Fac / 7) j - (3*Fac / 7) k

Fad = (7*Fad / 25) i + (24*Fad / 25) j

Step 3: Equilibrium force equations in x and z direction

Fr,x = 0 = 39*( -4 / 13 ) - Fac*( 2 / 7 ) + Fad*( 7 / 25 )

Fr,z = 0 = 39*( -3 / 13 ) + Fad*( 3 / 7 )

Step 4: Solve the above equations for Fca and Fda

Fca = 21 KN

Fda = 64.29 KN