Exercise: Equilibrium Of A Rigid Body

Questions for: Equilibrium Of A Rigid Body

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: C
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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: D
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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: D
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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: B
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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: D
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