14. Three coplanar forces act at a point, as shown. Calculate the magnitude of the force F so that their resultant is minimum. y 70 N 45° 30 50 N 2 of 2
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- The forces are in static equilibrium. The 140 lb force is directed along the x-axis and the 300 lb force is directed along the negative z- axis. Determine the magnitude of the unknown force, R. Z X R Ox лог 140lb A (-50, 80, 160) lb By 300 lb у4. The 500-kg uniform beam is subjected to the three external loads shown. Compute the reactions at the support point O. The x-y plane is vertical. 15 kN-m 130% × 8 kN A B Lief 1.4 kN 1.8 m 1.8 m 1.2 m +A 422 N was applied to a 273 kg block, find the normal force if the angle 0 = 66.1 degrees. F Select one: Oa 2849.0997 N Ob. 2507.1603 N Oc. 2292.3148 N Od 2678.1300 N
- SAQ 1 1.2 m D C 80 kN m An 80-kn.m couple shown in the plate is caused by a pair of parallel forces of magnitude F (not shown). 1.6 m Determine: a) the smallest possible value of F, and b) the value of F if the forces act at points A and C and are parallel to the dashed line shown at A. A В 60°Determine the equivalent force-couple system at the center O for each of the three cases of forces (F = 340 N) being applied along the edges of a square plate of side d = 230 mm. The couple is positive if counterclockwise, negative if clockwise. y y F d F -d- F Answers: (a) R=( i i+ i j) N, Mo = i N-m (b) R= ( i i+ j) N, Мо- N-m (c) R= ( i i+ j) N, Mo = N-m63. To find the resultant of a concurrent force system, express each force as a Cartesian vector and add the i, j. k components of all the forces in the system. True False 64. A position vector ir ates one point in space relative to another point. True False 65. The tensile force developed in a continuous cable that passed over a frictionless pulley must have a constant magnitude throughout the cable to keep it in equilibrium. O True False 66. A cable can support only a compressive or "pulling" force. True False 67. In equilibrium, IF includes all the known and unknown forces which act on the particle. True O False
- There are four forces acting on a pole, A = 10i N, B = 20j N, C = -30j N, D = -40i N. What should be the magnitude of force E that must be exerted on the pole to maintain static equilibrium? Note: i and j are unit vectors a. 24.65 N b. 31.62 N c. 46.20 N d. 52.78 N e. No AnswerDetermine the equivalent force-couple system at the center O for each of the three cases of forces (F = 370 N) being applied along the edges of a square plate of side d = 480 mm. The couple is positive if counterclockwise, negative if clockwise. y F y y F d - x F Answers: (a) R = j) N, Mo = N-m (b) R = j) N, Mo = N-m (c) R = j ) N, Mo = N-m +Figure shows the two cables AO and BO tied together at O and the loadings are also shown. A В 30° 30° (a) Derive the expressions relating the tension in each cable as a function of a. 150N 200N (b) Write a MATLAB program to plot the tension in each cable for 0° < a < 90°. (c) Determine the value of a for which both cables OA and OB are in tension.
- 3. 4.00 m F13 7 F23 37.0° Compute for the total force exered on 92 to but 93 イ 3.00m to 5-00m 9, メ 9, = Ic q2 = -20 - 3C 93=30 olyhThe following forces are acting on a particle: 500 N due east; 300 N 30o E of S; Z Newton 60o West and X Newton 40o S of W. If the particle is in equilibrium, solve for Z and X.The two planks are connected together by cable BC and a smooth spacer DE. Determine the reactions at the smooth supports A and F.and also find the force developed in the cable and spacer. Match the answers. 100 lb 200 lb -2 ft--2 ft- ft2 ft- 182 160 180 1. reaction at A= 168 2. reaction at F = 176 3. Foc- 128 4. FDE 5. 150 120 140