The block is subjected to a couple moment and force as shown

The block is subjected to a couple moment and force as shown. Determine the equivalent resultant couple moment acting at the origin, point O.

Solution

couple moment of the original, M1 = 300 lb.ft (i) <------ i = unit vector along +x axis

Now, moment of the force,

M2 = r * F

= (4j + 3i) * (600 k)

= 2400 i - 1800 j

So, net couple moment,

Mnet = M1 + M2 = (300 + 2400) i - 1800 j

So, Mnet = 2700 i -1800 j (lb-ft) <---------answer