Motion Problems (Mechanics)

1. Motion Problems (Mechanics)

2. Situation 1: Nov 2005A train traveling at aconstant speed of 75 kph and a cartravelling at aninitial speed of36 kph approachespoint O as shown inFigure ME-36.

3. 1. Which of the following most nearly gives the time for the train to reach the collision point, in seconds. A. 54 C. 32 B. 63 D. 48

4. 2. Which of the following most nearly gives the acceleration of the car if it reached the collision point 12 seconds ahead of the train, in m/s2. A. 0.86 C. 0.99 B. 0.75 D. 0.82

5. 3. Using the acceleration computed in part 2, which of the following most nearly gives the velocity of the car at the collision point, in kph. A. 164 C. 158 B. 153.5 D. 214.5

6. Situation 2:A car is traveling at the speed of vo on a straight, level road. After the brakes are applied at t = 0, the motion can be approximated by x = t3/100 – t2 + 17t , where x is the distance traveled in meters and t is the time in seconds.

7. 4. Which of the following most nearly gives the value of vo, in m/s. A. 12 B. 17 C. 19 D. 155. Which of the following most nearly gives the time required for the car to stop, in seconds. A. 18 B. 57 C. 10 D. 25

8. 6. Which of the following most nearly gives the maximum deceleration during braking, in m/s2. A. 2.5 C. 2 B. 1.4 D. 2.8

9. Situation 3:A particle moving in curvilinear motion is governed by the following conditions:vx = 40 – 15t y = 75 – 3t24where vx and vy are in m/s and t is time in seconds, and when t = 0, x = 0.

10. 7. Which of the following most nearly gives the time when x = 0 for the second time. A. 6.14 sec B. 3.58 sec C. 5.33 sec D. 4.52 sec

11. 8. Which of the following most nearly gives the velocity of the particle when x = 0 for the second time, in m/s. A. 36.87 C. 51.23 B. 45.21 D. 63.85

12. 9. Which of the following most nearly gives the acceleration of the particle when x = 0 for the second time, in m/s2. A. -16.16 C. -13.54 B. -15.85 D. -11.45

13. Beam Analysis (Strength)

14. Situation 4:The beam shown in Figure AN-57 carries a uniformly varying load and a concentrated load.

15. 10. Which of the following most nearly gives the reaction at B, in KiloNewtons. A. 45 C. 35 B. 52 D. 48

16. 11. Which of the following most nearly gives the location of the point of inflection from A, in meters. A. 1.87 C. 3.25 B. 2.14 D. 2.76

17. 12. Which of the following most nearly gives the maximum positive bending moment on the beam, in KiloNewton-Meter. A. 21.11 C. 8.79 B. 12.58 D. 15.63

18. Situation 5: For the beam shown in Figure 10B the force P will cause the tangent to the elastic curve over support B to be horizontal. EI = constant.

19. 14. Which of the following most nearly gives the value of P in kN. A. 56 C. 74 B. 65 D. 4815. Which of the following most nearly gives the deflection at D. A. 635/EI B. 874/EI C. 979/EI D. 1054/EI

20. 16. Which of the following most nearly gives the deflection at C. A. 387/EI B. 587/EI C. 456/EI D. 504/EI

21. Situation 6:The T-section has the dimensions givenin Figure ME-12. It isknown that the totaltensile stress at thebottom of the flangeis 10 MPa.

22. 17. Which of the following most nearly gives the location of the neutral axis measured from the bottom fiber, in mm. A. 80 C. 130 B. 90 D. 140

23. 18. Which of the following most nearly gives the total tensile force in the cross-section, in KiloNewton. A. 102 C. 98 B. 92 D. 96

24. 19. If this section is used as a beam that is simply supported over a length of 2.5 m, which of the following most nearly gives the uniform load on the beam, in KiloNewton per meter. A. 17.1 C. 12.5 B. 14.2 D. 8.7

25. Influence Diagram (Theory)

26. Situation 7:For the truss bridge shown in Figure AN-02.

28. 20. Which of the following represents the influence diagram for the reaction at A. A. Figure AN-02d B. Figure AN-02a C. Figure AN-02c D. Figure AN-02b

29. 21. Which of the following represents the influence diagram for the axial force on member DH. A. Figure AN-02f B. Figure AN-02h C. Figure AN-02g D. Figure AN-02e

30. 22. Which of the following most nearly gives the maximum compressive stress on member DH due to two moving loads of 60 kN and 80 kN 3 m apart, moving along the bottom chord, in KiloNewton. A. 78 C. 65 B. 87 D. 56

31. Reserved Problems

32. Situation 8:A beam is loaded as shown in Figure ME-856.

33. 23. Determine the reaction at B in kiloNewton. A. 57 B. 43 C. 68 D. 7824. Determine the location of maximum moment measured from A in meters. A. 6.38 C. 5.62B. 4.65 D. 7.89

34. 25. Determine the maximum moment on the beam in kNm. A. 234.8 C. 123.7B. 187.6 D. 153.4

35. -o0o-