MCQOPTIONS
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MCQOPTIONS
This section includes 17 Mcqs, each offering curated multiple-choice questions to sharpen your Engineering Mechanics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The crane provides a long-reach capacity by using the telescopic boom segment DE. The entire boom is supported by a pin at A and by the telescopic hydraulic cylinder BC, which can be considered as a two-force member. The rated load capacity of the crane is measured by a maximum force developed in the hydraulic cylinder. If this maximum force is developed when the boom supports a mass m = 6 Mg and its length is l = 40 and = 60°, determine the greatest mass that can be supported when the boom length is extended to l = 50 m and = 45°. Neglect the weight of the boom and the size of the pulley at E. Assume the crane does not overturn. Note: when = 60° BC is vertical; however, when = 45° this is not the case. |
| A. | m = 7.50 Mg |
| B. | m = 4.80 Mg |
| C. | m = 3.26 Mg |
| D. | m = 4.61 Mg |
| Answer» D. m = 4.61 Mg | |
| 2. |
Determine the tension in the supporting cables BC and BD and the components of reaction at the ball-and-socket joint A of the boom. The boom supports a drum having a weight of 200 lb. at F. Points C and D lie in the xy plane. |
| A. | Ax = 0, Ay = 150 lb, Az = 562 lb, TBC = 300 lb, TBD = 212 lb |
| B. | Ax = 0, Ay = 150 lb, Az = 456 lb, TBC = 150 lb, TBD = 212 lb |
| C. | Ax = 0, Ay = 267 lb, Az = 843 lb, TBC = 533 lb, TBD = lb |
| D. | Ax = 0, Ay = 150 lb, Az = 500 lb, TBC = 212 lb, TBD = 212 lb |
| Answer» B. Ax = 0, Ay = 150 lb, Az = 456 lb, TBC = 150 lb, TBD = 212 lb | |
| 3. |
There is a ball and socket connection at A. At B there is a roller that prevents motion in the z direction. Corner C is tied to D by a rope. The triangle is weightless. Determine the unknown force components acting at A, B, and C. Use a scalar analysis. |
| A. | Ax = 0, Ay = 0, Az = 267 N, Bz = 150 N, FDC = 283 N |
| B. | Ax = 0, Ay = 0, Az = 450 N, Bz = 800 N, FDC = 550 N |
| C. | Ax = 0, Ay = 0, Az = 200 N, Bz = 200 N, FDC = 300 N |
| D. | Ax = 0, Ay = 0, Az = 467 N, Bz = 350 N, FDC = 117.1 N |
| Answer» D. Ax = 0, Ay = 0, Az = 467 N, Bz = 350 N, FDC = 117.1 N | |
| 4. |
The sports car has a mass of 1.5 Mg and mass center at G. If the front two springs each have a stiffness of kA=58 kN/m and the rear two springs each have a stiffness of kB = 65 kN/m, determine their compression when the car is parked on the 30° incline. Also, what frictional force FB must be applied to each of the rear wheels to hold the car in equilibrium? |
| A. | xA = 16.1 mm, xB = 42.2 mm, FB = 6.37 kN |
| B. | xA = 65.9 mm, xB = 39.2 mm, FB = 6.37 kN |
| C. | xA = 53.2 mm, xB = 50.5 mm, FB = 3.68 kN |
| D. | xA = 76.1 mm, xB = 45.3 mm, FB = 3.68 kN |
| Answer» D. xA = 76.1 mm, xB = 45.3 mm, FB = 3.68 kN | |
| 5. |
Compute the horizontal and vertical components of force at pin B. The belt is subjected to a tension of T=100 N and passes over each of the three pulleys. |
| A. | Bx = 0 N, By = 141.4 N |
| B. | Bx = -15.89 N, By = 120.7 N |
| C. | Bx = 20.7 N, By = 157.3 N |
| D. | Bx = 0, By = 100.0 N |
| Answer» C. Bx = 20.7 N, By = 157.3 N | |
| 6. |
There is a ball and socket connection at A. At B there is a roller that prevents motion in the —z direction. Corner C is tied to D by a rope. The triangle is weightless. Determine the unknown force components acting at A, B, and C. Use a scalar analysis. |
| A. | Ax = 0, Ay = 0, Az = 267 N, Bz = 150 N, FDC = 283 N |
| B. | Ax = 0, Ay = 0, Az = 450 N, Bz = 800 N, FDC = 550 N |
| C. | Ax = 0, Ay = 0, Az = 200 N, Bz = 200 N, FDC = 300 N |
| D. | Ax = 0, Ay = 0, Az = 467 N, Bz = 350 N, FDC = 117.1 N |
| Answer» D. Ax = 0, Ay = 0, Az = 467 N, Bz = 350 N, FDC = 117.1 N | |
| 7. |
The crane provides a long-reach capacity by using the telescopic boom segment DE. The entire boom is supported by a pin at A and by the telescopic hydraulic cylinder BC, which can be considered as a two-force member. The rated load capacity of the crane is measured by a maximum force developed in the hydraulic cylinder. If this maximum force is developed when the boom supports a mass m = 6 Mg and its length is l = 40 and = 60°, determine the greatest mass that can be supported when the boom length is extended to l = 50 m and = 45°. Neglect the weight of the boom and the size of the pulley at E. Assume the crane does not overturn. Note: when = 60° BC is vertical; however, when = 45° this is not the case. |
| A. | m = 7.50 Mg |
| B. | m = 4.80 Mg |
| C. | m = 3.26 Mg |
| D. | m = 4.61 Mg |
| Answer» D. m = 4.61 Mg | |
| 8. |
A Russell's traction is used for immobilizing femoral fractures C. If the lower leg has a weight of 8 lb, determine the weight W that must be suspended at D in order for the leg to be held in the position shown. Also, what is the tension force F in the femur and the distance which locates the center of gravity G of the lower leg? Neglect the size of the pulley at B. |
| A. | x = 1.44 ft, w = 10.8 lb, F = 12.61 lb |
| B. | x = 1.33 ft, w = 15.76 lb, F = 20.0 lb |
| C. | x = 1.56 ft, w = 9.75 lb, F = 12.69 lb |
| D. | x = 0.869 ft, w = 6.44 lb, F = 5.03 lb |
| Answer» B. x = 1.33 ft, w = 15.76 lb, F = 20.0 lb | |
| 9. |
The oil rig is supported on the trailer by the pin or axle at A and the frame at B. If the rig has a weight of 115,000 lb and the center of gravity at G, determine the force F that must de developed along the hydraulic cylinder CD in order to start lifting the rig (slowly) off B toward the vertical. Also compute the horizontal and vertical components of reaction at the pin A. |
| A. | Ax = 343 kip, Ay = -172.5 kip, FCD = 447 kip |
| B. | Ax = 205 kip, Ay = -57.5 kip, FCD = 268 kip |
| C. | Ax = 241 kip, Ay = -172.5 kip, FCD = 375 kip |
| D. | Ax = 220 kip, Ay = -70.1 kip, FCD = 288 kip |
| Answer» B. Ax = 205 kip, Ay = -57.5 kip, FCD = 268 kip | |
| 10. |
Determine the horizontal and vertical components of reaction at the pin A and the reaction at the roller support B required for equilibrium of the truss. |
| A. | Ax = 0, Ay = 333 lb, NB = 267 lb |
| B. | Ax = 462 lb, Ay = 66.7 lb, NB = 533 lb |
| C. | Ax = 267 lb, Ay = 223 lb, NB = 377 lb |
| D. | Ax = 154.0 lb, Ay = 333 lb, NB = 308 lb |
| Answer» E. | |
| 11. |
The flying boom B is used with a crane to position construction materials in coves and underhangs. The horizontal "balance" of the boom is controlled by a 250-kg block D, which has a center of gravity at G and moves by internal sensing devices along the bottom flange F of the beam. Determine the position x of the block when the boom is used to lift the stone S, which has a mass of 60 kg. The boom is uniform and has a mass of 80 kg. |
| A. | x = 2.500 m |
| B. | x = 0.340 m |
| C. | x = 1.180 m |
| D. | x = 0.600 m |
| Answer» C. x = 1.180 m | |
| 12. |
Determine the tension in the supporting cables BC and BD and the components of reaction at the ball-and-socket joint A of the boom. The boom supports a drum having a weight of 200 lb. at F. Points C and D lie in the x—y plane. |
| A. | Ax = 0, Ay = 150 lb, Az = 562 lb, TBC = 300 lb, TBD = 212 lb |
| B. | Ax = 0, Ay = 150 lb, Az = 456 lb, TBC = 150 lb, TBD = 212 lb |
| C. | Ax = 0, Ay = 267 lb, Az = 843 lb, TBC = 533 lb, TBD = lb |
| D. | Ax = 0, Ay = 150 lb, Az = 500 lb, TBC = 212 lb, TBD = 212 lb |
| Answer» B. Ax = 0, Ay = 150 lb, Az = 456 lb, TBC = 150 lb, TBD = 212 lb | |
| 13. |
The space truss is supported by a ball-and-socket joint at A and short links, two at C and one at D. Determine the x, y, z components of reaction at A and the force in each link. |
| A. | Ax = -1.050 kN, Ay = 1.050 kN, Az = 0.800 kN, Cy = -1.050 kN, Cz = 0.600 kN, Dx = 1.050 kN |
| B. | Ax = -1.400 kN, Ay = 1.400 kN, Az = 0.800 kN, Cy = -1.400 kN, Cz = 0.600 kN, Dx = 1.400 kN |
| C. | Ax = -2.49 kN, Ay = 1.867 kN, Az = 0.800 kN, Cy = -2.49 kN, Cz = 0.600 kN, Dx = 2.49 kN |
| D. | Ax = -1.867 kN, Ay = 1.867 kN, Az = 0.800 kN, Cy = -1.867 kN, Cz = 0.600 kN, Dx = 1.867 kN |
| Answer» E. | |
| 14. |
If the boom in the previous problem is to remain horizontal when the stone S is removed, what is x? |
| A. | x = 1.180 m |
| B. | x = 2.500 m |
| C. | x = 0.340 m |
| D. | x = 0.660 m |
| Answer» B. x = 2.500 m | |
| 15. |
The sports car has a mass of 1.5 Mg and mass center at G. If the front two springs each have a stiffness of kA=58 kN/m and the rear two springs each have a stiffness of kB = 65 kN/m, determine their compression when the car is parked on the 30° incline. Also, what frictional force FB must be applied to each of the rear wheels to hold the car in equilibrium? |
| A. | xA = 16.1 mm, xB = 42.2 mm, FB = 6.37 kN |
| B. | xA = 65.9 mm, xB = 39.2 mm, FB = 6.37 kN |
| C. | xA = 53.2 mm, xB = 50.5 mm, FB = 3.68 kN |
| D. | xA = 76.1 mm, xB = 45.3 mm, FB = 3.68 kN |
| Answer» D. xA = 76.1 mm, xB = 45.3 mm, FB = 3.68 kN | |
| 16. |
There is a ball and socket connection at A. At point B there is a connection that opposes motion in the x and z directions only. Determine the unknown force components at A and B. Use a scalar analysis. |
| A. | Ax = 5.5 kN, Ay = -1.0 kN, Az = 2.75 kN, Bx = 3.5 kN, Bz = 1.25 kN, FDC = 2.0 kN |
| B. | Ax = 1.5 kN, Ay = -1.0 kN, Az = 0.75 kN, Bx = -3.5 kN, Bz = 1.25 kN, FDC = 2.0 kN |
| C. | Ax = 5.5 kN, Ay = -1.0 kN, Az = 2.75 kN, Bx = 3.5 kN, Bz = -0.75 kN, FDC = 2.0 kN |
| D. | Ax = 1.5 kN, Ay = -1.0 kN, Az = 1.25 kN, Bx = -3.5 kN, Bz = 0.75 kN, FDC = 2.0 kN |
| Answer» E. | |
| 17. |
The girl has a mass of 17kg and mass center at Gg, and the tricycle has a mass of 10kg and mass center at Gt. Determine the normal reactions at each wheel for equilibrium. |
| A. | NA = 14.77 N, NB = NC = 6.12 N |
| B. | NA = 128.8 N, NB = NC = 68.0 N |
| C. | NA = 144.9 N, NB = NC = 60.0 N |
| D. | NA = 13.15 N, NB = NC = 6.93 N |
| Answer» C. NA = 144.9 N, NB = NC = 60.0 N | |