In order to design the foundation for the utility pole shown to the right, replace the system of three applied forces with an equivalent force- couple system applied at point A.

Identify the conditions under which a given system of forces can be reduced to a single force (Check all that apply) O One can replace the force -couple system at O by a single force R acting along a new line of action if R and M, are mutually tangential. One can replace the force -couple system at O by a single force R acting along a new line of action if R and M, are mutually perpendicular. O One can replace the force -couple system at O by a single force R acting along a new →R line of action if R and M, are mutually parallel.

Replace the forces and couple system acting on the T member with an equivalent force couple at A. Express your answers as Cartesian vectors. 1 m 120 N 50 N 120 N 1 m 60° 60° 45° 1m 1m | 2 m 40 N 35 N

Express and identify the resultant of the two forces and one couple shown acting on the shaft angled in the x-z plane. Assume F = 350 lb, M = 310 lb-ft, a = 8 in., b = 22 in., 0 = 17% 10 F. a -M k) lb-in. i Answer: M = (i b F Ө i+ i j+

If P= 20 lb in the figure, replace the three couples with a single equivalent couple, specifying its magnitude and the direction of its axis.

Calculate the moment Mg of the 895-N force about the bolt at B. Simplify your work by first replacing the force by its equivalent force- couple system at A. The moment is positive if counterclockwise, negative if clockwise. Assume F = 895 N, r= 155 mm, h = 490 mm, 0 = 30% = 38° OC Answer: Mg = i 0 h N-m

Replace the force and couple moment system acting on the system by a single resultant force and specify its location along the horizontal beam measured from point O. Be specific as to where the resultant force is pointing (i.e. provide an angle and quadrant).

The figure below shows three forces of 20 lb each applied to a rectangular block1. Reduce the three forces to a single force and a single couple at the origin O2. Can the system be reduced to a single force? Please explain your answer3. Can the system be reduced to a single couple? Please explain your answer