Eng Sample Test 4

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Mervin Stewart Thompson
6 years ago
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The triangular linkage ABC pivots on the trailer body at A.

1 1. An adjustable tow bar connecting the tractor unit H with the landing gear J of a large aircraft is shown in the figure. Adjusting the height of the hook F at the end of the tow bar is accomplished by the hydraulic cylinder CD activated by a small hand pump (not shown). The triangular linkage ABC pivots on the trailer body at A. For the position of the triangular linkage ABC shown (AC is vertical), calculate the force required in the hydraulic cylinder CD to maintain the rig in this position. The tow bar assembly has a total mass of 50 kg with center of mass at G. Neglect the mass of the hydraulic cylinder, linkage ABC and wheels at B. Note: the lengths of AB and AC are 500 mm, and ABC = ACB = 30. F CD 298 N 2. The excavator scoop shown below supports a vertical load of F = 1800 N located at G. Neglecting the mass of all other elements, determine the axial force (F DH ) in the hydraulic cylinder required to hold the scoop in static equilibrium. Assume: 1) link HL is rigidly attached to the excavator; and 2) points C, D and K lie in a vertical line. F DH 1701 N (T )

3. In the position shown, the excavator applies a 20 kn force on the ground (i.e. horizontal and to the right). Note: the force shown in the figure is that of the ground on the excavator.

2 3. In the position shown, the excavator applies a 20 kn force on the ground (i.e. horizontal and to the right). Note: the force shown in the figure is that of the ground on the excavator. There are two hydraulic cylinders AC to control arm OAB, and a single cylinder DE to control arm EBIF. Determine the forces in hydraulic cylinders AC and DE. Neglect the mass of all elements of the excavator arm. Indicate whether the cylinders are in tension (T ) or compression (C) when recording the forces in the table below. F AC (kn) F DE (kn) 4. In the frame shown below a cable is attached to element AC at B. The cable wraps around the pulley which is attached to element CE at D. The cable is then pulled vertically down by a force of 170 N. Determine the magnitude of the reactions at pin connections A, C and E in the frame. Assume the pulley has radius 60 mm and neglect the mass of all elements in the frame.

3 5. The right angle pipe OAB is rigidly attached to a wall at O. The tension in cable BC is 750 N. The force F applied at A has magnitude 500 N and is alligned with the y axis. Using Cartesian vector notation, determine the reactions at O required for static equilibrium. Note: section AB of the pipe is in a plane that is parallel to the y, z plane, and is rotated 30 down from the x, z plane. F R = î ĵ 50.25ˆk N M R = î ĵ 306.7ˆk N m 6. Determine the x, y, z components of the reactions exerted by the nut and bolt on the loaded bracket at O to maintain equilibrium. Write the reactions in Cartesian vector notation in the table below. F R = 1.028î 0.852ĵ + 1.2ˆk N M R = 0.117î ĵ ˆk N m

4 7. The bent rod lies in the horizontal x, y plane and is supported by a journal bearing at A, and cables BC and BD. Two forces F 1 and F 2 are applied to the rod. Determine the reactions F R and M R at A and the tensions T C and T D in cables BC and BD, respectively. Since this is a 3D problem you can use the given diagram as the FBD. Notes: (1) Points B, C and D all lie in a plane parallel to the y, z plane; and (2) a rod can rotate in and slide through a journal bearing. 8. The boom AB lies in the vertical y, z plane and is supported by a ball and socket joint at B and by two cables at A. Calculate the tension in each cable resulting from the 20 kn force acting in the horizontal x, y plane and applied at the midpoint of the beam M. Use Cartesian vector notation and neglect the mass of the boom. Since this is a 3D problem you can use the given diagram as the FBD. T 1 T 2 (kn) (kn)

5 9. Member AB is supported by a cable at B (BC ) and at A by a smooth fixed square rod which fits loosely through the square hole in the collar. If F = 50ĵ 80ˆk lb is applied at D, determine the tension, T, in cable BC, and the reactions at A, F R and M R. Use Cartesian vector notation and neglect the mass of AB and the cable. Since this is a 3D problem you can use the given diagram as the FBD. T (lb) FR (lb) MR (lb ft) 10. After a long trip a 100 kg crate, with center of mass at G, is resting on a slope of angle θ = 10. The coefficient of static friction between the slope and the crate is µ s = 0.6. A horizontal force P is applied to the crate as shown. Determine the minimum required magnitude of P to cause motion of the crate. Note: All dimensions are in meters.

6 11. Use the method of sections to determine the forces in members DE, DI and IJ in the truss shown below. Indicate whether the member is in tension (T ) or compression (C) when recording the forces in the table. You may use the given diagram as the FBD when determining the reactions at the supports only. 12. Use the method of sections to determine the forces in members DF, EF and EG in the truss shown below. Indicate whether the member is in tension (T ) or compression (C) when recording the forces in the table below. F DF = 28 kn (C) F EF = 5 kn (C) F EG = 32 kn (T )

7 13. Determine the forces in members AB, BC, BD, BE, CE and DE in the truss shown below. One force is applied at C and one force is applied at E. Indicate whether the member is in tension (T ) or compression (C) when recording the forces in the table below. F AB = 320 kn (T ) F BD = 240 kn (C) F CE = 100 kn (C) F BC = 0 F BE = 400 kn (T ) F DE = 215 kn (C) 14. Use the method of sections to determine the forces in members CD, DG and GF in the truss shown below. Indicate whether the member is in tension (T ) or compression (C) when recording the forces in the table. You may use the given diagram as the FBD when determining the reactions at the supports only. F CD (kn) F DG (kn) F GF (kn)

8 15. The truss shown below supports the 500 kg load at D and a 5 kn vertical force at E. Use the method of joints to determine the forces in members CD, CE, CB, DE and BG in the truss. Indicate whether the member is in tension (T ) or compression (C) when recording the forces in the table. You may use the given diagram as the FBD if you need to determine the reactions at the supports. Note: the length of CE is 2 m. F CD F CE F CB F DE F BG

Statics Chapter II Fall 2018 Exercises Corresponding to Sections 2.1, 2.2, and 2.3

Statics Chapter II Fall 2018 Exercises Corresponding to Sections 2.1, 2.2, and 2.3 2 3 Determine the magnitude of the resultant force FR = F1 + F2 and its direction, measured counterclockwise from the