Problem Set 2Problem 2.1 Extremizing a Moment Due to a ForceDetermine the direction θ of the force F = 40 lb. so that it producesa) the maximum moment about point A, andb) the minimum moment about point A.Figure P2.1: Problem 2.1Problem 2.2 Moment of a Force-Vector FormulationDetermine the magnitude of the force F that should be applied at theend of the lever such that this force creates a clockwise moment about pointO of 15 N m when θ = 30◦.Figure P2.2: Problem 2.2Problem 2.3Figure P2.3: Problem 2.3Problem 2.4Figure P2.4: Problem 2.4Problem 2.5Figure P2.5: Problem 2.5Problem 2.6a) Determine the resultant of the forces F1= F1xı + F1y + F1zk, F2=F2xı + F2y + F2zk, and F3= F3xı + F3y + F3zk, which are concurrent atthe point P (xP, yP, zP), where F1x= 2, F1y= 3.5, F1z= −3, F2x= −1.5,F2y= 4.5, F2z= −3, F3x= 7, F3y= −6, F3z= 5, xP= 1, yP= 2,and zP= 3. b) Find the total moment of the given forces about the originO(0, 0, 0). The units for the forces are in Newtons and for the co ordinatesare given in meters.Problem 2.7a) Determine the resultant of the three forces shown in Fig. P2.7. Theforce F1acts along the x-axis, the force F2acts along the z-axis, and the di-rection of the force F3is given by the line O3P3, where O3= O(xO3, yO3, zO3)and P3= P (xP3, yP3, zP3). The application point of the forces F1and F2isthe origin O(0, 0, 0) of the reference frame as shown in Fig. P2.7. b) Find thetotal moment of the given forces about the point P3. Numerical application:|F1| = F1= 250 N, |F2| = F2= 300 N, |F3| = F3= 300 N, O3= O3(1, 2, 3)and P3= P3(5, 7, 9). The coordinates are given in meters.3F2OzyxF1F3PO3Figure P2.7: Problem 2.7Problem 2.8Replace the three forces F1, F2, and F3, shown in Fig. P2.8, by a resultantforce, R, through O and a couple. The force F2acts along the x-axis, theforce F1is parallel to the y-axis, and the force F3is parallel to the z-axis.The application point of the forces F2is O, the application point of theforces F1is B, and the application points of the force F3is A. The distancebetween O and A is d1and the distance between A and B is d2as shown inFig. P2.8. Numerical application: |F1| = F1= 250 N, |F2| = F2= 300 N,|F3| = F3= 400 N, d1= 1.5 m and d2= 2 m.F2dzyxF1F3O1ABd2Figure P2.8: Problem P2.8Problem 2.9Determine the magnitude of the moments of the force F about the x, y,and z axes. Solve the problem a) using a Cartesian vector approach and b)using a scalar approach.Figure P2.9: Problem 2.9% input dataFx = 4; % lbFy = 12; % lbFz = -3; % lba = 4; % ftb = 3; % ftc = 2; % ftProblem 2.10Determine the moment of the force F about an axis extending betweenA and C. Express the result as a Cartesian vector.Figure P2.10: Problem 2.10% input dataFx = 4; % lbFy = 12; % lbFz = -3; % lba = 4; % ftb = 3; % ftc = 2; %