The door shown is supported by cable CE and hinges at A and

The door shown is supported by cable CE and hinges at A and B. 1 he tension in cable CE is 373N. Determine a) the Moment with respect to A. M_A; and b) the moment with respect to line AB, M_AB.

Solution

C = (480 ,-200 , 400)

A=(0,0,0)

E =(240 , 400,0)

B=(480 -200 , 0)

CA = (-480 ,200,-400)

CA UNIT VECTOR = ( -12/SQRT(269) , 5/sqrt(269) , -8/sqrt(269) )

CE =( -240 ,600,-400)

CE unit vector =(-0.315 , 0.789 , -0.526)

AB =(480 , -200 ,0)

So Tension = 373 * ( -0.315 i + 0.789 j -0.526k) = -117.539 i + 293.655 j -195.899k

Now Ma = Rca x T

= (-480 i +200j -400k ) x ( -117.539 i + 293.655 j -195.899k) N- mm

= 78.28 i -47.015 j -117.446 k N-m

Similarly

Mab = Rab x T

= (-480 i +200j ) x ( -117.539 i + 293.655 j -195.899k) N-mm

= -39.179 i -94.031 j -117.446 k N-m