Determine the magnitude of the moment of the F 320i 190j

Determine the magnitude of the moment of the F = {320i - 190j + 150k} N about the r axis. (Figure 1) Express your answer to three significant figures and include the appropriate units.

Solution

The Force vector is given by F = 320i^- 190j^+150k^ N

The position of force w.r.t the fulcrum is given by the displacement vector

r = 0.3i^+0.4j^-0.2k^

Moment vector M = r X F (cross-product of displacement vector and force vector)

= (0.3i^+0.4j^-0.2k^)x(320i^- 190j^+150k^)

= (22i^-109j^-185k^)

Hence magnitude of moment is 215.84 N-m