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MEE 1168 ENGINEERING MECHANICS TUTORIAL N0 1 Force Systems 1. Determine the x and y components of the forces shown below in Figure 1(using scalars and Vectors) 2. Compute the x and y components of each of the four forces shown in Figure 2(using scalars and Vectors) Jean de la Croix-UR-CST-MEE Page 1 3. Determine the magnitude of the resultant, its pointing and its direction cosines for the following system of non-coplanar, concurrent forces. 300 lb (+3, -4, +6); 400 lb (-2, +4, -5); 200 lb (-4, +5, -3). Using Scalars and Vectors 4. Determine the magnitude of the resultant, its pointing, and its direction cosines for the following system of non-coplanar concurrent forces. 200 lb (4, 5, –3); 400 lb (–6, 4, –5); 300 lb(4, –2, –3). 5. Determine the components of the 160-N force perpendicular and parallel to the axis of the nail. 6. The connecting rod AB exerts a 2-kN force on the crankshaft at B. Resolve this force into components acting perpendicular to BC and along BC. 7. The weight W is supported by the boom AB and cable AC. Knowing that the horizontal and vertical components of the cable force at A are 5 kN and 3 kN as shown in Figure 5, determine the distance d. Jean de la Croix-UR-CST-MEE Page 2 8. Determine the magnitude and direction of the resultant force acting on the beam as shown in Figure 6. 9. Express F shown in Figure 7 in terms of x, y, and z components. 10. Determine the x, y, and z components of the 26-N force shown in Figure 8. Also determine the coordinate direction angles of the force. Jean de la Croix-UR-CST-MEE Page 3 11. Determine the magnitude and coordinate direction angles of the resultant of the three forces acting on the mast shown in Figure 9. 12. Two forces, F1 and F2 act on the bracket as shown in Figure 10. If the resultant of F1 and F2 lies in the xy plane, determine the magnitude of F2. Also determine the magnitude of the resultant. Jean de la Croix-UR-CST-MEE Page 4 Remark: For the calculation of the moments in the following exercises assume that the clockwise moment is negative and the counterclockwise moment is positive 13. In the Figure 11 assuming clockwise moment as positive, compute the moment of force F =4.5 kN and of force P = 3.61 kN about points A, B, C and D. Each block is of 1m2. 14. A horizontal line PQRS is 12 m long, where PQ = QR = RS = 4m. Forces of 1000, 1500, 1000and 500 N act at P, Q, R and S respectively with downward direction. The lines of action ofthese make angle of 90º, 60º, 45º and 30º respectively with PS as shown in Figure 12. Find the magnitude, directionand position of the resultant force. Jean de la Croix-UR-CST-MEE Page 5 15. Replace the two parallel forces of Figure 13 acting on the control lever by a single equivalent force R. 16. A square block of each side 1.5 m is acted upon by a system of forces along its sides as shown in Figure 14. If the system reduces to a couple, determine the magnitude of theforces P and Q, and the couple. Jean de la Croix-UR-CST-MEE Page 6 17. Two parallel forces are acting at point A and B respectively are equivalent to a force of 100 N acting downwards at C and couple of 200Nm. Find the magnitude and sense of forceF1 and F2 shown in Figure 15. 18. A system of parallel forces is acting on a rigid bar as shown in Figure 16. Reduce this system to (i) a single force (ii) A single force and a couple at A (iii) A single force and a couple at B. Jean de la Croix-UR-CST-MEE Page 7

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