Questions for system of forces in vector mechanics PDF

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Questions for practice for exam as well as challenging exercises . it is useful for Bachelor level of engineering( civil and mechanical) ...

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TUTORIAL 1 / APPLIED MECHANICS I

By Er. Prem N. Adhikari

1. Determine the x and y components of each of the forces shown.

2. Tension in cable BC is 725-N, determine the resultant of the three forces exerted at point B of beam AB.

3. Knowing that the tension in rope AC is 365 N, determine the resultant of the three forces exerted at point C of post BC.

TUTORIAL 1 / APPLIED MECHANICS I

By Er. Prem N. Adhikari

4. Two cables are tied together at C and are loaded as shown. Determine the tension (a) in cable AC, (b) in cable BC.

5. Two cables are tied together at C and are loaded as shown. Determine the tension (a) in cable AC, (b) in cable BC.

6. Two cables are tied together at C and loaded as shown. Determine the tension (a) in cable AC, (b) in cable BC.

TUTORIAL 1 / APPLIED MECHANICS I

By Er. Prem N. Adhikari

 Two cables tied together at C are loaded as shown. Knowing that the maximum allowable

tension in each cable is 800 N, determine (a) the magnitude of the largest force P that can be applied at C, (b) the corresponding value of 

8. Determine (a) the x, y, and z components of the 900-N force, (b) the angles that the force forms with the coordinate axes.

9. Knowing that the tension in cable AB is 1425 N, determine the components of the force exerted on the plate at B.

TUTORIAL 1 / APPLIED MECHANICS I

By Er. Prem N. Adhikari

10. Knowing that the tension in cable AC is 2130 N, determine the components of the force exerted on the plate at C.

11. Find the magnitude and direction of the resultant of the two forces shown knowing that force P = 600 N and Q = 450 N.

12. Three cables are used to tether a balloon as shown. Knowing that the balloon exerts an 800-N vertical force at A, determine the tension in each cable.

TUTORIAL 1 / APPLIED MECHANICS I

By Er. Prem N. Adhikari

13. Three cables are connected at A, where the forces P and Q are applied as shown. Knowing that Q = 0, find the value of P for which the tension in cable AD is 305 N.

14. Three cables are connected at A, where the forces P and Q are applied as shown. Knowing that P =1200 N, determine the values of Q for which cable AD is taut.

15. A container of weight W is suspended from ring A. Cable BAC passes through the ring and is attached to fixed supports at B and C. Two forces P = Pi and Q = Qk are applied to the ring to maintain the container in the position shown. Knowing that W = 376 N, determine P and Q. (Hint: The tension is the same in both portions of cable BAC.)

TUTORIAL 1 / APPLIED MECHANICS I

By Er. Prem N. Adhikari

16. A horizontal circular plate weighing 60 lb is suspended as shown from three wires that are attached to a support at D and form 30 angles with the vertical. Determine the tension in each wire.

17. A rectangular plate is supported by three cables as shown. Knowing that the tension in cable AD is 520 N, determine the weight of the plate.

TUTORIAL 1 / APPLIED MECHANICS I

By Er. Prem N. Adhikari

18. A horizontal circular plate is suspended as shown from three wires that are attached to a support at D and form 30 angles with the vertical. Knowing that the x component of the force exerted by wire AD on the plate is 110.3 N, determine (a) the tension in wire AD, (b) the angles  x, y, and  z that the force exerted at A forms with the coordinate axes.

19. A 100-kg container is suspended from ring A, to which cables AC and AE are attached. A force P is applied to end F of a third cable that passes over a pulley at B and through ring A and then is attached to a support at D. Draw the free-body diagram needed to determine the magnitude of P. (Hint: The tension is the same in all portions of cable FBAD.)

TUTORIAL 1 / APPLIED MECHANICS I

By Er. Prem N. Adhikari

20. Knowing that the tension in cable AC is 1065 N, determine the moment about each of the coordinate axes of the force exerted on the plate at C.

21. Knowing that the tension in cable AB is 570 N, determine the moment about each of the coordinate axes of the force exerted on the plate at B.

22. Four forces act on a 700*375-mm plate as shown. (a) Find the resultant of these forces. (b) Locate the two points where the line of action of the resultant intersects the edge of the plate.

TUTORIAL 1 / APPLIED MECHANICS I

By Er. Prem N. Adhikari

23. Four forces are applied to the machine component ABDE as shown. Replace these forces with an equivalent force-couple system at A.

24. The ramp ABCD is supported by cables at corners C and D. The tension in each of the cables is 810 N. Determine the moment about A of the force exerted by (a) the cable at D, (b) the cable at C.

25. A 6-m telephone pole weighing 1600 N is used to support the ends of two wires. The wires form the angles shown with the horizontal axis and the tensions in the wires are, respectively, T1 = 600 N and T2 = 375 N. Determine the reaction at the fixed end A.

TUTORIAL 1 / APPLIED MECHANICS I

By Er. Prem N. Adhikari

26. A 2.4-m boom is held by a ball-and-socket joint at C and by two cables AD and AE. Determine the tension in each cable and the reaction at C.

27. A man raises a 10 kg joist, of length 4 m, by pulling on a rope. Find the tension in the rope and the reaction at A.

28. Knowing that  = 35°, determine the resultant of the three forces shown.

TUTORIAL 1 / APPLIED MECHANICS I

By Er. Prem N. Adhikari

29. A load Q is applied to the pulley C, which can roll on the cable ACB. The pulley is held in the position shown by a second cable CAD, which passes over the pulley A and supports a load P. Knowing that P = 750 N, determine (a) the tension in cable ACB, (b) the magnitude of load Q.

30. Cable AB is 65 ft long, and the tension in that cable is 3900 lb. Determine (a) the x, y, and z components of the force exerted by the cable on the anchor B, (b) the angles, x, y and  defining the direction of that force.

31. The end of the coaxial cable AE is attached to the pole AB, which is strengthened by the guy wires AC and AD. Knowing that the tension in wire AC is 120 lb, determine (a) the components of the force exerted by this wire on the pole, (b) the angles x, y, and  z that the force forms with the coordinate axes.

TUTORIAL 1 / APPLIED MECHANICS I

By Er. Prem N. Adhikari

32. Knowing that the tension is 510 lb in cable AB and 425 lb in cable AC, determine the magnitude and direction of the resultant of the forces exerted at A by the two cables.

33. A transmission tower is held by three guy wires attached to a pin at A and anchored by bolts at B, C, and D. If the tension in wire AB is 630 lb, determine the vertical force P exerted by the tower on the pin at A.

34. A container of weight W is suspended from ring A. Cable BAC passes through the ring and is attached to fixed supports at B and C. Two forces P = Pi and Q = Qk are applied to the ring to maintain the container in the position shown. Knowing that W = 376 N, determine P and Q. (Hint: The tension is the same in both portions of cable BAC.)

TUTORIAL 1 / APPLIED MECHANICS I

By Er. Prem N. Adhikari

35. A plane contains the vectors A and B. Determine the unit vector normal to the plane when A and B are equal to, respectively, (a) i + 2j − 5k and 4i − 7j − 5k, (b) 3i − 3j + 2k and −2i + 6j − 4k. 36. The vectors P and Q are two adjacent sides of a parallelogram. Determine the area of the parallelogram when (a) P = −7i + 3j −3k and Q = 2i + 2j + 5k, (b) P = 6i − 5j − 2k and Q = −2i + 5j − k.

37. A line passes through the Points (20 m, 16 m) and (−1 m, −4 m). Determine the perpendicular distance d from the line to the origin O of the system of coordinates. 38. Determine the moment about the origin O of the force F = 4i − 3j + 5k that acts at a Point A. Assume that the position vector of A is (a) r = 2i + 3j − 4k, (b) r = −8i + 6j − 10k, (c) r = 8i − 6j + 5k. 39. The wire AE is stretched between the corners A and E of a bent plate. Knowing that the tension in the wire is 435 N, determine the moment about O of the force exerted by the wire (a) on corner A, (b) on corner E.

40. A precast concrete wall section is temporarily held by two cables as shown. Knowing that the tension in cable BD is 900 N, determine the moment about Point O of the force exerted by the cable at B.

TUTORIAL 1 / APPLIED MECHANICS I

By Er. Prem N. Adhikari

41. A couple of magnitude M = 54 lb  in. and the three forces shown are applied to an angle bracket. (a) Find the resultant of this system of forces. (b) Locate the points where the line of action of the resultant intersects line AB and line BC.

42. A couple M and the three forces shown are applied to an angle bracket. Find the moment of the couple if the line of action of the resultant of the force system is to pass through (a) Point A, (b) Point B, (c) Point C.

43. The maximum allowable value of each of the reactions is 180 N. Neglecting the weight of the beam, determine the range of the distance d for which the beam is safe.

44. A tower guy wire is anchored by means of a bolt at A. The tension in the wire is 2500 N. Determine (a) the components F x , F y , F z of the force acting on the bolt, ( b ) the angles x, y, and  z defining the direction of the force.

TUTORIAL 1 / APPLIED MECHANICS I

By Er. Prem N. Adhikari

45. A 200-kg cylinder is hung by means of two cables AB and AC, which are attached to the top of a vertical wall. A horizontal force P perpendicular to the wall holds the cylinder in the position shown. Determine the magnitude of P and the tension in each cable.

46. A 5 * 8-ft sign of uniform density weighs 270 lbs. and is supported by a ball-and-socket joint at A and by two cables. Determine the tension in each cable and the reaction at A.

47. A 4.80-m-long beam is subjected to the forces shown. Reduce the given system of forces to ( a ) an equivalent force-couple system at A, (b) an equivalent force-couple system at B, (c) a single force or resultant. Note . Since the reactions at the supports are not included in the given system of forces, the given system will not maintain the beam in equilibrium.

48. A force of 800 N acts on a bracket as shown. Determine the moment of the force about B.

TUTORIAL 1 / APPLIED MECHANICS I

By Er. Prem N. Adhikari

49. A rectangular plate is supported by brackets at A and B and by a wire CD . Knowing that the tension in the wire is 200 N, determine the moment about A of the force exerted by the wire on point C.

50. A cube of side a is acted upon by a force P as shown. Determine the moment of P (a) about A , ( b ) about the edge AB , ( c ) about the diagonal AG of the cube, ( d ). Using the result of part c, determine the perpendicular distance between AG and FC....