Statics and Strength of Materials HW1 part 1 1) A vector V has a magnitude of 20 units and lies in the x-y plane. If its direction cosine with respect to the y-axis is -0.6 and if its xcomponent is positive, write the vector expression for V using unit vectors i and j. Write the unit vector n in the direction of V. 2) Calculate the following operations by graphically and analytically. a) 2V1+V2 b) V2-2V1 Fig 2 3) a) If the two equal tensions T in the pulley cable together produce a force of 5 kN on the pulley bearing, calculate T. b) If the equal tensions T in the pulley cable are 400 N, express in vector notation the force R exerted on the pulley by the two tensions. Determine the magnitude of R. Fig 3 4) The 600-N force applied to the bracket at A is to be replaced by two forces, Fa in the a-a direction and Fb in the b-b direction, which together produce the same effect on the bracket as that of the 600-N force. Determine Fa and Fb. Fig 4 5) Combine the two forces shown acting on the A-frame into a single force R. Express R in vector notation using unit vectors i and j, and determine its magnitude R and the angle q it makes with the x-axis. If R were to be applied at a point D on member AB, find the distance s from A to D. Fig 5 6) Two cylindrical body positioned in the container having rectangular prism. Calculate all reaction forces acting on each body. Fig 6 7)Aforce system is shown in figure. a) Find the resultant R. b) Find the line of the resultant. c) Translate R to the point O. d) Find the components of the R along the m-m direction and the direction passing through the pointsA(-2,1) and (1,6). Fig 7 8) Find the components of the 10-kN force P in the I, II and III directions. Fig 8 9) The 50-kg homogeneous smooth sphere rests on the 30-deg incline A and bears against the smooth vertical wall B. Calculate the contact forces at A and B. Fig 9 10) The uniform bar AB has a mass of 50-kg and supports the 200-kg load at A. Calculate the tension in the supporting cable and the magnitude FB of the force supported by the pin at B. Fig 10 11) Determine the force P required to begin rolling the uniform cylinder of mass m over the obstruction of height h. Fig 11 12)Soil pressure acting on the concrete retaining wall is presented as a loading per foot length of wall. If concrete has a specific weight of 25 kN/m3, determine the magnitudes of the soil distribution, w1 and w2 and the frictional force F for equilibrium. Fig 12 Fig 13 13) If neither the pin at A nor the roller at B can support a load no greater than 6 kN, determine the maximum intensity of the distributed load w, measured in kN/m, so that failure of a support does not occur. 14 and 15) Determine the coordinates of the centroid xc and yc of the shaded area. y h 4 cm 10 cm Fig 14 10 cm 10 cm x Fig 15 Due date : 19 March 2015 ! This is the first part of the first homework. It must be done fully and written properly with a cover page.