MCQOPTIONS
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MCQOPTIONS
This section includes 16 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. |
A boy twirls a 15-lb bucket of water in a vertical circle. If the radius of curvature of the path is 4 ft, determine the minimum speed the bucket must have when it is overhead at A so no water spills out. |
| A. | v = 11.35 ft/s |
| B. | v = 0 |
| C. | v = 6.26 ft/s |
| D. | v = 2.83 ft/s |
| Answer» B. v = 0 | |
| 2. |
The spool, which has a weight of 2lb, slides along the smooth horizontal spiral rod, r = (2) ft, where is in radians. If its angular rate of rotation is constant and equals = 4 rad/s, determine the tangential force P needed to cause the motion and the normal force that the spool exerts on the rod at the instant = 90°. |
| A. | P = 0.499 lb, N = 5.03 lb |
| B. | P = 5.50 lb, N = 15.65 lb |
| C. | P = 3.35 lb, N = 2.43 lb |
| D. | P = 1.677 lb, N = 4.77 lb |
| Answer» E. | |
| 3. |
Each of the three barges has a mass of 30 Mg, whereas the tugboat has a mass of 12 Mg. As the barges are being pulled forward with a constant velocity of 4 m/s, the tugboat must overcome the frictional resistance of the water, which is 2 kN for each barge and 1.5 kN for the tugboat. If the cable between A and B breaks, determine the acceleration of the tugboat. |
| A. | a = 0.1667 m/s2 |
| B. | a = 0.1042 m/s2 |
| C. | a = 0.0278 m/s2 |
| D. | a = 0.01961 m/s2 |
| Answer» D. a = 0.01961 m/s2 | |
| 4. |
Determine the acceleration of block A when the system is released. The coefficient of friction and the weight of each block are indicated in the figure. Neglect the mass of the pulleys and cords. |
| A. | aA = 7.50 ft/s2 Up the slope |
| B. | aA = 7.50 ft/s2 Down the slope |
| C. | aA = 4.28 ft/s2 Up the slope |
| D. | aA = 4.28 ft/s2 Down the slope |
| Answer» E. | |
| 5. |
A truck T has a weight of 8,000 lb and is traveling along a portion of a road defined by the lemniscate r2 = 0.2(106) cos 2 , where r is measured in feet and is in radians. If the truck maintains a constant speed of vr = 4 ft/s, determine the magnitude of the resultant frictional force which must be exerted by all the wheels to maintain the motion when = 0. |
| A. | F = 29.2 lb |
| B. | F = 859 lb |
| C. | F = 87.5 lb |
| D. | F = 26.7 lb |
| Answer» E. | |
| 6. |
A tobbogan and rider have a total mass of 100 kg and travel down along the (smooth) slope defined by the equation y = 0.2x2. At the instant x = 8 m, the toboggan's speed is 4 m/s. At this point, determine the rate of increase in speed and the normal force which the toboggan exerts on the slope. Neglect the size of the toboggan and rider for the calculation. |
| A. | at = 8.32 m/s2, N = 520 N |
| B. | at = 8.32 m/s2, N = 537 N |
| C. | at = 9.36 m/s2, N = 310 N |
| D. | at = 9.36 m/s2, N = 293 N |
| Answer» D. at = 9.36 m/s2, N = 293 N | |
| 7. |
A smooth can C, having a mass of 2 kg, is lifted from a feed at A to a ramp at B by a forked rotating rod. If the rod maintains a constant angular motion of = 0.5 rad/s, determine the force which the rod exerts on the can at the instant = 30°. Neglect the effects of friction in the calculation. The ramp from A to B is circular, having a radius of 700 min. |
| A. | F = 19.62 N |
| B. | F = 11.33 N |
| C. | F = 10.63 N |
| D. | F = 12.03 N |
| Answer» C. F = 10.63 N | |
| 8. |
A block having a mass of 2 kg is placed on a a spring scale located in an elevator that is moving downward. If the scale reading, which measures the force in the spring, is 20 N, determine the acceleration of the elevator. Neglect the mass of the scale. |
| A. | a = 10.00 m/s2 |
| B. | a = 0.1900 m/s2 |
| C. | a = 0.1900 m/s2 |
| D. | a = 10.00 m/s2 |
| Answer» C. a = 0.1900 m/s2 | |
| 9. |
A 1.5-lb brick is released from rest A and slides down the inclined roof. If the coefficient of friction between the roof and the brick is = 0.3, determine the speed at which the brick strikes the gutter G. |
| A. | v = 3.00 ft/s |
| B. | v = 2.68 ft/s |
| C. | v = 5.61 ft/s |
| D. | v = 15.23 ft/s |
| Answer» E. | |
| 10. |
The 30-lb crate is being hoisted upward with a constant acceleration of 6 ft/s2. If the uniform beam AB has a weight of 200 lb, determine the components of reaction at A. Neglect the size and mass of the pulley at B. |
| A. | Ax = -48.3 lb, Ay = 248.3 lb, MA = 258 lb-ft CCW |
| B. | Ax = -48.3 lb, Ay = 248.3 lb, MA = 741 lb-ft CCW |
| C. | Ax = -35.6 lb, Ay = 236 lb, MA = 678 lb-ft CCW |
| D. | Ax = -30.0 lb, Ay = 230 lb, MA = 650 lb-ft CCW |
| Answer» D. Ax = -30.0 lb, Ay = 230 lb, MA = 650 lb-ft CCW | |
| 11. |
A ball having a mass of 2 kg slides without friction within a vertical circular slot. If it is released from rest when = 10°, determine the force it exerts on the slot when it arrives at points A and B. |
| A. | NA = 38.6 N, NB = 96.6 N |
| B. | NA = 30.9 N, NB = 61.8 N |
| C. | NA = 30.9 N, NB = 81.2 N |
| D. | NA = 38.6 N, NB = 77.3 N |
| Answer» B. NA = 30.9 N, NB = 61.8 N | |
| 12. |
A particle having a mass of 1.5 kg, moves along a three-dimensional path defined by the equations r = 94 + 3t) m, = (t2 + 2) rad, and z = (6 - t3) m, where t is in seconds, and the z-axis is vertical. Determine the r, , and z components of force which the path exerts on the particle when t = 2 s. |
| A. | Fr = 0, F2 = 30 N, Fz = -18.00 N |
| B. | Fr = -240 N, F2 = 66.0 N, Fz = -3.29 N |
| C. | Fr = 0, F2 = 3 N, Fz = -18.00 N |
| D. | Fr = -160.0 N, F2 = 44.0 N, Fz = -12.00 N |
| Answer» C. Fr = 0, F2 = 3 N, Fz = -18.00 N | |
| 13. |
The pendulum bob B has a weight of 5 lb and is released from rest in the position shown, =0°. Determine the tension in string BC just after the bob is released, = 0°, and also at the instant the bob reaches point D, = 45°. |
| A. | T0 = 0, T45 = 10.61 lb |
| B. | T0 = 0.1551 lb, T45 = 10.61 lb |
| C. | T0 = 0, T45 = 7.07 lb |
| D. | T0 = 0.1551 lb, T45 = 7.07 lb |
| Answer» B. T0 = 0.1551 lb, T45 = 10.61 lb | |
| 14. |
The 300-kg bar B, originally at rest, is being towed over a series of small rollers. Computer the force in the cable when t = 5s, if the motor M is drawing in the cable for a short time at a rate of v = (0.4t2) m/s, where t is in seconds (0 t 6 s). How far does the bar move in 5 s? Neglect the mass of the cable, pulley P, and the rollers. |
| A. | T = 5.00 kN, s = 0.300 m |
| B. | T = 1.200 kN, s = 1.25 m |
| C. | T = 5.00 kN, s = 4.00 m |
| D. | T = 1.200 kN, s = 16.67 m |
| Answer» E. | |
| 15. |
The 2-kg shaft CA passes through a smooth journal bearing at B. Initially, the springs, which are coiled loosely around the shaft, are unstretched when no force is applied to the shaft. In this position s = sª = 250 and the shaft is originally at rest. If a horizontal force of F = 5 kN is applied, determine the speed of the shaft at the instant s = 50 mm, sª = 450 mm. The ends of the springs are attached to the bearing at B and the caps at C and A. |
| A. | v = 31.6 m/s |
| B. | v = 14.14 m/s |
| C. | v = 44.7 m/s |
| D. | v = 30.0 m/s |
| Answer» E. | |
| 16. |
Rod OA rotates counterclockwise with a constant angular rate of = 5 rad/s. The double collar B is pin-connected together such that one collar slides over the rotating rod and the other slides over the horizontal curved rod, of which the shape is a limacon described by the equation r - 1.5(2 - cos ) ft. If both collars weigh 0.75 lb, determine the normal force which the curved path exerts on one of the collars, and the force that OA exerts on the other collar at the instant = 90°. |
| A. | FOA = 0.873 lb, Fcurve = 1.953 lb |
| B. | FOA = 0, Fcurve = 1.953 lb |
| C. | FOA = 1.747 lb, Fcurve = 0 |
| D. | FOA = 2.87 lb, Fcurve = 6.41 lb |
| Answer» B. FOA = 0, Fcurve = 1.953 lb | |