Problem 4 (10 Points) The pipe structure shown is comprised of 4 straight segmen

Question

Problem 4 (10 Points) The pipe structure shown is comprised of 4 straight segments. The structure is supported at A and subjected to a force F = {(-950.92) 1 + (-621.18)/ + (-787.29) k} N at the free end C. The lengths L1, L2, and, L3 are as follows: 10.47 m L2 = 0.91 m 10.64 m LI 2 3 0.3 m Complete the following: (A) Determine the position vector from point A to C(rAc). (B) Determine the moment of the force about point A (MA) due to the applied force F a. Provide the moment in Cartesian notation. (C) Determine the magnitude of the moment determined in part (B). (D) Determine the magnitude of the moment of the force about point B (MB) due to the applied force F

Explanation / Answer

A) coordinates of A=(0,0,0)

coordinates of C=(0.47,1.21,-0.64)

Coordinates of B = (0.47,0,0)

vector AC = (0.47i+1.21j-0.64k)

B)Moment about A=rACxF = (0.47i+1.21j-0.64k)x(-950.92i-621.18j-787.29k)

= -1350.1761i+978.6151j+858.6586k Nm

C)Magnitude of meoment = sqrt(1350.17612+978.61512+858.65862) = 1875.62 Nm

D)vector BC=rBC = 1.21j-0.64k

Moment about B = rBCxF = (1.21j-0.64k)x(-950.92i-621.18j-787.29k) =-1350.1761i+608.5888j+1150.6132k Nm

magnitude of moment = sqrt(1350.17612+608.58882+1150.61322)=1875.44 Nm

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