Question

4 ft 3 ft 2 ft

Determine the magnitude of the moments of the force F about the x, y, and z axes.

a. Solve the problem using a Cartesian vector approach. Express your answer in terms of the unit vectors i, j, and k.

b. Solve the problem using a scalar approach. Express your answers using three significant figures separated by commas.

Answer 1

Coordinate of point at which force F^rightarrow acts (4, 3, - 2) ft So r^rightarrow = (4 i^cap + 3 j^cap - 2k^cap)ft F^rightarrow = (4 i^cap + 12 j^cap - 3k^cap) lb so tau^rightarrow = r^rightarrow times F^rightarrow = (4i^cap + 3j^cap - 2k^cap) times (4 i^cap + 12 j^cap - 3k^cap) = Vertical-bar i^cap 4 4 j^cap 3 12 k^cap -2 -3 Vertical-bar lb ft = (15 i^cap - 4j^cap + 36 k^cap)lb ft tau^rightarrow = 15 i^cap - 4 j^cap + 36 k^cap lb ft and tau_x = 15 lb ft tau_y = -4 lb ft tau_z = 36 lb ft Vertical-bar r^rightarrow Vertical-bar = squareroot = 13 ft r^rightarrow middot F^rightarrow = 16 + 36 + 6 = 58 cos theta = r^rightarrow middot F^rightarrow/ Vertical-bar r^rightarrow Vertical-bar