Problems 43 PROBLEMS Introductory Problems 2/29 The 10-KN force is applied at point A. Determine the moment of F about point 0. Determine the points on the x- and y-axes about which the moment of F is Ans, Mg = 18 kN-m CW ) = (2.67, 0) m and (0, 2) m Problem 2/29 2/30 Determine the moment of the 800-N force about point A and about point 0. » if Problem 2/S0 2/31 Determine the moment of the 50-N foree (a) about, point O by Varignon’s theorem and (b) about point C by a vector approach. Ans. Mg = 519 N-mm CCW, Mp = 1616k N-mm mm $C(0,25) t B40, 10) I 20) | Problem 2/31 2/32 The force of magnitude F acts along the edge of the triangular plate. Determine the moment of F about point O. Problem 2/32 2/33 In steadily turning the water pump, a person exerts the 120-N force on the handle as shown. Determine the moment of this force about point 0. ‘Ans. Mo = 14.74 N-m CW Problem 2/3344 Chapter 2 Force Systems 2/34 The throttle-control sector pivots freely at O. If an internal torsional spring exerts a return moment M = 18 N-m on the sector when in the position shown, for design purposes determine the necessary throttle-cable tension so that the net moment about O is zero. Note that when T is zero, the sector rests against the idle-contro: adjustment screw at R. Problem 2/34 2/35 A force F of magnitude 60 N is applied to the gear. Determine the moment of F about point 0. Ans. Mo = 5.64.N-m CW Problem 2/35 2/36 Calculate the moment of the 250-N force on the han- dle of the monkey wrench about the center of the bolt. Problem 2/36 2/37 A mechanic pulls on the 13-mm combination wrench with the 140-N force shown, Determine the moment of this force about the bolt eenter O. ‘Ans. Mg = 13.10 N-m CCW F=140N Problem 2/37 2/38 As a trailer is towed in the forward direction, the force F = 500 N is applied as shown to the ball of the trailer hitch. Determine the moment of this force about point 0. + 215 mm ———. Problem 2/38Article 2/4 Problems 45 Representative Problems 2/39 A portion of a mechanical coin sorter works as fol- ows: Pennies and dimes roll down the 20° incline, the last triangular portion of which pivots freely about a horizontal axis through O. Dimes are light ‘enough (2.28 grams each) s0 that the triangular por- tion remains stationary, and the dimes roll into the right collection column. Pennies, on the other hand, are heavy enough (3.06 grams each) so that the tri- angular portion pivots clockwise, and the pennies roll into the left collection column, Determine the ‘moment about O of the weight of the penny in terms of the slant distance s in millimeters, ‘Ans. Mo = 0.1385 + 0.0282s N-mm (s in mm) pennies Problem 2/39 2/40 Blements of the lower arm are shown in the figure aay ‘The mass of the forearm is 2.3 kg with mass center at G, Determine the combined moment about the elbow pivot O of the weights of the forearm and the 3.6-kg homogeneous sphere. What must the biceps tension force be so that the overall moment about O 3.69.81) N - 325 mm ———+ Problem 2/40 A.150-N pull 7 is applied to a cord, which is wound securely around the inner hub of the drum. Deter- mine the moment of T about the drum center C. At ‘what angle 6 should 7'be applied so that the moment. about the contact point P is zero? Ans. Me = 18.75 N-m CW, 0 = 51.3" Problem 2/41er 2 Force Systems 2/42 A force of 200 N is applied to the end of the wrench 2/43 to tighten a flange bolt which holds the wheel to the axle. Determine the moment M produced by this force about the center O of the wheel for the position of the wrench shown. — 2/44 The uniform work platform, which has a mass per unit length of 28 kg/m, is simply supported by cross rods A and B. The 90-kg construction worker starts from point B and walks to the right. At what loca- tion s will the combined moment of the weights of the man and platform about point B be zero? Problem 2/42 In order to raise the flagpole OC, a light frame OAB is attached to the pole and a tension of 3.2 KN is de- veloped in the hoisting cable by the power winch D. Caleulate the moment Mo of this tension about the hinge point O. Ans. Mg = 6.17 kN-m CCW Problem 2/43 Problem 2/44 2/45 In raising the pole from the position shown, the ten- sion 7 in the cable mast supply a moment about O of 72KN-m. Determine T. Ans. T = 8.65 kN / om 7 / Problem 2/45Article 2/4 Problems 47 2/86 The foree exerted by the plunger of cylinder AB on _—2/48 Calculate the moment M, of the 200-N force about. the door is 40 N directed along the line AB, and this, point A by using three scalar methods and one vee- force tends to keep the door closed. Compute the mo- tor method. ment of this foree about the hinge O. What force F- ‘normal to the plane of the door must the door stop 200N at C exert on the door so that the combined moment about 0 of the two forces is zero? 280 A Problem 2/48 Dimensions in millimeters 2/49 An exerciser begins with his arm in the relaxed ver- tical position GA, at which the elastic band is un- stretched. He then rotates his arm to the horizontal position OB. The elastic modulus of the band is k = 60 Nim—that is, 60 N of force is required to stretch the band each additional meter of elongation. Deter- mine the moment about O of the force which the band exerts on the hand B. Ans, Mg = 26.8 N-m COW Problem 2/46 2/47 The 10-N force is applied to the handle of the hy- draulie control valve as shown. Calculate the mo- ment of this force about point 0. 81 Nvm CW Ans. Mo = Problem 2/47 Problem 2/4948 Chapter 2 Force Systems 2/30 (a) Caleulate the moment of the 90-N force about point O for the condition @ = 15°. Also, determine the value of # for which the moment about O is (6) zero and (c) a maximum, 600 mm —| Problem 2/50 2/31 The small crane is mounted along the side of a pickup bed and facilitates the handling of heavy loads. When the boom elevation angle is @ = 40°, the force in the hydraulic cylinder BC is 4.5 kN, and this force applied at point C is in the direction from B to C (the cylinder is in compression), Determine the ‘moment of this 4.5-kN force about the boom pivot point 0. Ans, Mo = 0.902 kN-m CW 2/52 Design criteria require that the robot exert the 90-N force on the part as shown while inserting a eylindri- cal part into the cireular hole. Determine the mo- ment about points A, B, and C of the force which the part exerts on the robot, 1p 150mm. 15" Problem 2/52 2/53 The masthead fitting supports the two forces shown. Determine the magnitude of T which will cause no bending of the mast (zero moment) at point O. ‘Ans, T = 4.04 kN Problem 2/532/54 The piston, connecting rod, and crankshaft of a diesel engine are shown in the figure. The crank throw OA is half the stroke of 200 mm, and the length AB of the rod is 350 mm. For the position in- dicated, the rod is under a compression along AB of 16 KN, Determine the moment M of this force about the crankshaft axis 0. Problem 2/54 2/55 The 120-N force is applied as shown to one end of the curved wrench. If a = 30°, calculate the moment of F about the center O of the bolt. Determine the value of « which would maximize the moment about: 0; state the value of this maximum moment. ‘Ans. Mo ~ 41.5 N-m CW = 88.2, (Mo)pax = 41.6 Nm CW Problem 2/55 Article 2/4 2/56 If the combined moment of the two forces about point is zero, determine (a) the magnitude of the force P (®) the magnitude R of the resultant of the two forces (c) the coordinates x and y of the point A on the rim of the wheel about which the combined moment of the two forces is a maximum (d) the combined moment M, of the two forces about A. ‘Ans. (a) P= 61.6N () R=1413N (©) x= 49.0 mm, y = 63.2mm (@) My = 15.7 N-m CW Problem 2/56