Question

The forces F1 = -4i + 3j - 2kkN and F₂ = 4i - 3j - 2kkN act on the end of the beam. Replace these forces by an equivalent force and couple moment acting at point O.

Answer 1

To replace the forces F1 and F2 by an equivalent force and couple moment at point O, we add the given forces as vectors. The equivalent force is -4k kN, and there is no need for a couple moment since there's no resultant in the i or j directions.

Step-by-step explanation:

The question pertains to the concept of replacing multiple forces acting at a point with an equivalent force and couple moment in the field of engineering mechanics. To find the equivalent force, we perform vector addition of the given forces F1 and F2.

F1 = -4i + 3j - 2k kN
F2 = 4i - 3j - 2k kN

Adding F1 and F2:

Sum of F1 and F2 = (-4i + 4i) + (3j - 3j) + (-2k - 2k) = 0i + 0j - 4k kN

Therefore, the equivalent force acting at point O is -4k kN. Since there is no resultant force in the i or j directions, there's no need for a couple moment about point O to balance out any forces in these directions.