Engineering Mechanics (Statics) 491 Time clement: 3.0 hours & 30 minutes aaa eee Problem 801: Three forces, 20 N, 30 N and 40 N are in equilibrium. Find the largest angle they make with each other. = A. 104.48° B. 105.58" Cc, 106.69" D. 107.96° Problem602z: ME Board October 1996 Two forces of 20 units and 30 units act at right angle. What is the magnitude of. the resultant force? A. 36 B. 42 Cc, 40 D. 44 Problemso3: What is the magnitude of the resultant force of the two forces 200 N at 20° and 400 N at 144°? 332.5 N 323.5 N 313.5 N 233.5 N com> Problemso4: ECE Board November 1998 A load of 100 Ib is hung from the middle of a rope, which is stretched between two rigid walls 30 ft. apart. Due to the load, the rope sags 4 feet in the middle. Determine the tension in the rope. A. 165 lbs B. 173 lbs CG. 194 Ibs D. 149 Ibs492 1001 Solved Problems in Engineering Mathematics by Tiong & Rojas Problems05: A boat moving at 12 kph is crossing a river 500 m wide in which a current is flowing at 4 kph. In what direction should the boat head if itis to reach a point on the other side of the river directly opposite its starting point? 19.47° downstream 19.47° upstream 18.43" downstream 18.43° upstream pom> Problem8oé: EE Board October 1997 A 100 kg weight rest on a 30° incline plane. Neglecting friction, how much pull must one exert to bring the weight up the plane? A 88.67 kg B, 100 kg C. 70.71 kg D. 50kg Problem 807: ECE Board November 1998 A block weighing 500 kN rest on a ramp inclined at 25° with the horizontal. The force tending to move the block down the ramp is : A. 121kN B. 265kN C. 211kN D. 450 kN Problem 908: CE Board November 1994 A 200 kg crate impends to slide down a ramp inclined at an angle of 19.29° with the horizontal. What is the frictional resistance? A. 612.38.N B. 628.38 N C. 648.16 N D. 654.12 N Problem $09: EE Board October 1993, Aman can exert a maximum pull of 1000 N but wishes to lift a new stone door for his cave weighing 20,000 N. If he uses a lever, how much closer must the fulcrum be to the stone than to his hand? 10 times nearer 20 times farther 10 times farther 20 times nearer compEngineering Mechanics (Statics) 493 Problem 810: A beam rests on a fulcrum, 1.2 m from one end. A weight of 350 kg is suspended from this end causing the beam to balance. If the weight of 350 kg is suspended on the opposite end of the beam, it is necessary to suspend a 1000 kg weight on the first end in order to effect an even balance. Find the length of the beam. A. 248m B, 324m c. 343m D. 421m Problem 811; EE Board October 1991 A simply supported beam is 5 meters in length. it carries a uniformly distributed load including its own weight of 300 N/m and a concentrated load of 100 N, 2 meters from the left end. Find the reactions if reaction A is at the left end and reaction B at the right end. A. Ra=810N&Rp=700N B. Cc. D. Ra= 700N & Re =810N Problem 812: A beam of span “x" meters with uniform loading of ‘w" kilograms per meter is supported at one end (A) and a distance of 2 m from the other end (B). Find the reaction at support A. wet A 3K) e 2 s D. aa kg. 5 Problem 813: ‘When one boy is sitting 1.2 m from the center of a see-saw, another boy must to sit on the other side 1.5 m from the center to maintain an even balance. However, when the first boy carries an additional weight of 14 kg and sit 1.8 m from the center, the second boy must move to 3m from the center to balance. Neglecting the weight of the see-saw, find the weight of the heavier boy. 30 kg 42 kg 34 kg 45 kg on,494 1001 Solved Problems in Engineering Mathematics by Tiong & Rojas Problem 814: CE Board November 1996 40 kg block is resting on an inclined plane making an angle of 20° from the horizontal. If the coefficient of friction is 0.60, determine the force parallel to the incline that must be applied to cause impending motion down the plane. A. 82 Bt: Cc. 87 D.. 72 Problem 81§: EE Board October 1997 A 250 Ib block is initially at rest on a flat surface that is inclined at 30°, If the coefficient of kinetic friction 0.30 and the coefficient of static friction is 0.40, find the force required to start the black moving up the plane. A. 190\b B. 212 tb C. 125 |b D. 751b Problem 816: A600 N block rests in a surface inclined at 30°, Determine the horizontal force P required to prevent the block from sliding down. Angle of friction between the block and the inclined plane is 15°. A, 160.75 N B. 198.55 N C. 164.60 N D. 180.45 N Problem 817: ME Board March 1998 Assume the three force vectors intersect at a single point. F, =4i+ 2)+ 5k Fe = -21+7)-3k F; =2i-)+6k What is the magnitude of the resultant force vector, R7 14 12 13 15 son> Problem 818: EE Board March 1998 Given the 3-dimensional vectors: A= (xy) + | (2yz) + k (zx) B =i (yz) + j (22x) + k (Sxy) Determine the magnitude of the vector sum |A+B| al coordinates (3,2, 1). A. 32.92Engineering Méchanies (Statics) 495 8. 20.92 c. 27.20 D. 24.73 Problem 619: At what angle does the force F = 6.23i—2.38) + 4.92 k N makes with the x-axis? 39.2" 40.2" 41.3" 42.2" popPr Problem $20: ME Board October 1996 Assume the three force vectors intergect at a single point. F, =1+3j+ 4k Fg =2i+7j-k Fs =-i+4)+2k What is the magnitude of the resultant force vector, R? A 15 B. 13.23 Cc. 14.73 D. 16.16 Problem 821: EE Board October 1991 A certain cable is suspended between two supports at the same elevation and 500 ft apart, the load is 500 Ibs per horizontal foot including the weight of the cable. ‘The sag of the cable is 30 ft. Calculate the total length of the cable. 503.76 ft. 502.76 ft 504.76 ft 501.76 ft pop> Problem $22: EE Board April 1994 A cable supported at two points of same level has a unit weight , o of 0.02 kg per meter of horizontal distance. The allowed sag is 0.02 m and a maximum tension at the lowest paint of 1200 kg and a factor of safety of 2. Calculate the allowable spacing of the poles assuming a parabolic cable. A. 6402m B. 668.37m Cc, 87.76m D, 69.28m Problem 823: A cable carries a horizontal load of 20 kg/m, Neglecting its own weight, find the maximum tension on the cable if the distance between the supports is 100 m and the sag is 5m. A. 5099kg496 100! Solved Problems in Engineering Mathematics by Tiong & Rojas B. 5059 kg C. 5199 kg D. 5215kg Problem 824: CE Board May 1993 Determine the sag of a flexible wire cable weighing 60 N/m over two frictionless pulleys 100 m apart and carrying one 10 kN weight at each end. Assume the weight of the cable to be uniformly distributed horizontally, The cable extends 5 m beyond each pulley to the point they are attached to the weights. A. 72m B. 74m c. 76m D. 7.8m Problem 825: EE Board October 1993 A copper cable is suspended between two supports on the sameé level, Spaced 600 m apart. The cable hangs under the influence of its own weight only, Under these conditions, it is desired to calculate the maximum sag (at the center of the span) when the maximum stress in the material is 1000 kg/cm’, The cross-section of the cable is 1.77 sq. cm. Weight of cable = 1.6 kg/m. Use parabolic equation. 42.26m 43.26 m 44.268m 45.26m oom, Problem 8z6: A cable weighing 0.4 kg/m and 800 m long is to be suspended with a sag of 80 m. Determine the maximum tension, A. 414kg B. 420kg C. 418kg D. 400 kg Problem 827: A cable weighing 60 N/m is suspended between two supports on the same level at 300 m apart. The sag is 60 m. Compute the distance of the lowest point of the cable from the ground level. 205.5m 196.8 m 200.5 m 188.2 m omyEngineering Mechanics (Statics) 497 Problem 828: Find the location of the centroid of the composite area consisting of a 10-inch ‘square surmounted by a semi-circle. The centroid of a semicircle is located 4r/3x above the base (diameter) of the semi-circle of radius r. A. 6.0 inches from the bottom B. 6.2 inches from the bottom C. 6.4 inches from the bottom D. 7.0 inches from the bottom Problem 829: EE Board March 1998 Electrical loads are arranged on horizontal x, y axes as follows: Load x-coordinate_|_y-coordinate | Kilowatt load oO 2 100 4 1 180 1 3 200 2 o 4120 2 4 150 3 1 200 3 3 180 4 2 100 A. B. Cc. DB. Problem 830: A rectangle has a base of 3.cm and a height of 6 cm. What is its second moment of area (in cm‘) about an axis through the center of gravity and parallel to the base? 64 34 44 54 oom Problem 831: EE Board March 1998 A cifcle has a diameter of 20 cm. Determine the moment of inertia of the circular area relative to the axis perpendicular to the area through the center of the circle in om’. A 14,280 B. 15,708 CG. 17,279 D. 19,007498 1001 Solved Problems in Engineering Mathematics by Tiong & Rojas Problem 832: ME Board October 1993 The moment of inertia of a section 2" wide x 2’ 0" high about an axis 1'0" above the bottom edge of the section is: A. 1834 in* B, 384in" C. 9214 int D. 2304 in* Problem 633: An isosceles triangle has a 10 cm base and a 10 cm altitude. Determine the moment of inertia of the tiangular area relative to a line parallel to the base and through the upper vertex in cm*. A. 2750 B. 3025 Cc. 2500 D. 2273 Problem 834: ECE Board April 1999 What is the moment of inertia of a cylinder of radius 5 m and mass of 5kg? A, 120 kg-m? B. 80 kg-m C. 62.5kg-m* D. 72.5 kg-m? Problem 835: ECE Board April 1993 What Is the inertia of a bowling ball (mass = 0.5 kg) of radius 15 cm rotating at an angular speed of 10 rpm for 6 seconds? A. 0.001 kg-m? 8. 0,002 kg-m? C. 0.005 kg-m* D. 0.0045 kg-m* RATING | 30-35 Topnotcher iy el-24 Passer [_] 17-20 conditional Q O-1b Failed If FAILED, repeat the test