(3) For the three forces applied on the box, determine the resultant moment vector at point B using the geometric method. Ans: M=-1.21 +2.4j N-m B 50 mm 110 mm 120 N 80 mm x 40 mm- 120 N B 40 mm 60 N
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- (5) The turnbuckle is tightened to produce a 1.2 kN tension force in cable AB acting at point A of the arm. Use vector cross product to determine the moment vector of the tension about point O and then calculate its magnitude. Ans: Mo=-1.371 +2.19j+1.097 kN·m, Mo 2.81 kN·m 1.6 m 2 m 1.5 m 0.8 m BQ2: A boat is moved uniformly along a canal by two horses pulling with force P-890 N and Q=1068 N acting under an angle a=60 . Determine the magnitude of the resultant pull on the boat and the angles B and y as shown in the figure.A basket of flowers of mass 3 kg is placed on a flat grassy slope that makes an angle θ with the horizontal. The coefficient of static friction between the basket and the slope is 0.45 and the basket is on the point of slipping down the slope. Model the basket of flowers as a particle and the grassy slope as a plane. Take the magnitude of the acceleration due to gravity, g, to be 9.8 m s−2 Express the forces in component form, in terms of θ and unknown magnitudes where appropriate. Write down the equilibrium condition for the basket and hence show that tan θ = 0.45. Determine the angle, in degrees, that the slope makes with the horizontal.
- (7) The effect of a slam dunk can be simulated by a force F = 47 lb acting at the front edge of the rim at point A shown. Use the scalar components approach to determine the moments of the force F about point O Mo and point B MB. Ans: Mo=81.5 lb-ft CCW, MB = 115.9 lb-ft CW -36"- B 12" 28" 10' FFind u · (v ✕ w).The force P = 15 lb is applied to the cable and the cords slip on the smooth surfaces of the non- rotating pulleys. Determine the magnitude and direction of the acceleration of the 36-lb cylinder if (a) the pulleys are massless, (b) the pulleys are 4 lb each. (a = 21.5 ft/sec², a = = 6.9 ft/sec²) P W
- (5) The 16 N force is applied to the foot valve AC at point A as shown with a = 28°. Determine (a) the force component perpendicular to line BA and (b) then calculate the moment produced by the force about point B. Ans: (a) 7.51 N (b) MB = 1.277 N·m CCW 20° 16 N 170 mm 80 mm(6) The tension force in cable AB is T = 40 kN acting on the crane as shown. Use vector cross product to compute the moment vector of the tension about point C. Note that point B is located at the center of the container top, and the distance between O and C is OC=45 m. Ans: M = 745 +548ĵ+718k kN·m 20 m 3 m 45 m B 13 m 5 m 9 m 8 m 12 m 16 mFind the acceleration vector r(t)=(6cost)i+(9sint)j
- Just explain thxConsider an object moving according to the functionfrom position r(t) = acoswt i + asenwt j. To determine: a) tangent and normal vectors (T and N), represent the same;b) tangential and normal components at and an(5) Cable AB exerts a 10 kN tension force on boom BC at point B. Express the tension force as vector and determine the angles which the tension force forms with +x-, +y-, and +z-axes. Ans: T = 4.061-7.61ĵ+5.07Â kN, = 0x 66.1°, 0, 139.5°, 0₂ = 59.5° = t 4 m T = 10 kN B 5 m 5 m 2.5 m