3. The force applied to the bent pipe at B can be written in its Cartesian form

Question

3. The force applied to the bent pipe at B can be written in its Cartesian form as F= {80i-80j-40k} lb (a) Determine the moment of force Fabout point O. Report your answer in Cartesian vector form (b) The moment determined in part (a) can be partitioned into two components: one component about the axis of pipe segment OA and the other component about an axis perpendicular to pipe segment OA. Determine the magnitude of the component of the moment of force F about the axis of pipe segment OA F= 120lb 4 ft 2 ft (c) Report the component of the moment determined in part (b) in Cartesian vector form 4 ft (d) Determine the magnitude of the moment of force F about an axis perpendicular to pipe segment OA (a) Mo= (b) MoA = IO4 (d) M1OA=

Explanation / Answer

Given force F = {80i - 80j - 40k} lb

As the position vector of force is given by

R = {1i + 4j + 2k} ft

Hence momemt of force is given by cross product of R and F

Moment = R x F = {i(-160 + 160) -j(160 + 40) + k(320 + 80)} lb ft

Or

Moment = { 0i -200j + 400k} lb ft

(b)

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