Equilibrium Of A Rigid Body

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:

A_x = 343 kip, A_y = -172.5 kip, FCD = 447 kip

B:

A_x = 205 kip, A_y = -57.5 kip, FCD = 268 kip

C:

A_x = 241 kip, A_y = -172.5 kip, FCD = 375 kip

D:

A_x = 220 kip, A_y = -70.1 kip, FCD = 288 kip

Answer: A

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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:

B_x = 0 N, B_y = 141.4 N

B:

B_x = -15.89 N, B_y = 120.7 N

C:

B_x = 20.7 N, B_y = 157.3 N

D:

B_x = 0, B_y = 100.0 N

Answer: B

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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: A

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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:

A_x = 0, A_y = 0, A_z = 267 N, B_z = 150 N, F_DC = 283 N

B:

A_x = 0, A_y = 0, A_z = 450 N, B_z = 800 N, F_DC = 550 N

C:

A_x = 0, A_y = 0, A_z = 200 N, B_z = 200 N, F_DC = 300 N

D:

A_x = 0, A_y = 0, A_z = 467 N, B_z = 350 N, F_DC = 117.1 N

Answer: C

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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: A

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