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-mThere 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 Answer
- 63. 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 FalseFigure 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.Determine 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 +
- 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 guy wires AB and AC are attached to the top of the transmission tower. The tension in cable AB is 8.2 kN. Determine the required tension Tin cable AC such that the net effect of the two cables is a downward force at point A. Determine the magnitude R of this downward force. Assume a -41 m, b - 52 m, c-22 m, and d - 29 m. L B Answers: T- i KN R- i KN XXXI