Determine the magnitude of the moment of the force F 50i 3

Determine the magnitude of the moment of the force F = {50i - 30 j - 80k} N about the base line C A of the tripod. Express your answer to three significant figures and include the appropriate units. M_CA =

Solution

>> Force, F = 50 i - 30 j - 80 k , and it is acting at point D

Writing Coordinates:

A = (0,2,0)

B = (3.5,2.5,0)

C = (2,0,0)

D = (2.5,2,4)

>> So, r = Position Vector dfrom O to D = 2.5 i + 2 j + 4 k

and, CA = 2 i - 2 j

Unit Vector along CA = (2 i - 2 j)/[2² + (-2)²]^1/2 = 0.707 i - 0.707 j

>> As, Moment of Force about Origin = r X F = (2.5 i + 2 j + 4 k) X (50 i - 30 j - 80 k)

=> Mo = - 40 i + 400 j - 175 k

So, Moment about axis CA = Dot Product of unit vector along CA & Mo = (0.707 i - 0.707 j) . ( - 40 i + 400 j - 175 k)

= 311.08 N-m ........ANSWER.......