For Q2, you are asked to represent the two forces F_A and F_B by a single result

Question

For Q2, you are asked to represent the two forces F_A and F_B by a single resultant force F_R and a resultant moment M_R at O. (i) Determine the vector force F_R and vector moment M_R (ii) Determine the unit vector u_F in the direction of F_R. (iii) Determine the component of M_R parallel to the direction of F_R. (iv) Determine the component of M_R perpendicular to F_R. (v) Convert the normal moment in (iv) and F_R to an equivalent single force F_R passing through another location X_c and Y_c on x-y plane (Z_c = 0). Determine X_c and Y_c. (vi) Replace the given forces F_A and F_B by a wrench force system and determine the location of its intersection with x-y plane (z=0).

Explanation / Answer

Q3. i)
Assume a force Fr and Moment Mr at O
From force Balance
Fr = Fa + Fb
Froom moment balance
Mr = (0.36i - 0.08k) x Fb + (0.16i + 0.08k)xFa
ii) unit direction vector in direction of Fr, uf = (Fa + Fb)/|Fa + Fb|
iii) Component of Mr parallel to Fr = Mr.uf
iv) Component of Mr perpendicular to Fr = Mr x uf

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