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# Engineering Mechanics - Equilibrium of a Rigid Body

### Exercise

• General Questions
"Two things are infinite: the universe and human stupidity; and I'm not sure about the universe."
- Albert Einstein
1.

The girl has a mass of 17kg and mass center at Gg, and the tricycle has a mass of 10kg and mass center at Gt. Determine the normal reactions at each wheel for equilibrium.

 A. NA = 14.77 N, NB = NC = 6.12 N B. NA = 128.8 N, NB = NC = 68.0 N C. NA = 144.9 N, NB = NC = 60.0 N D. NA = 13.15 N, NB = NC = 6.93 N

2.

The sports car has a mass of 1.5 Mg and mass center at G. If the front two springs each have a stiffness of kA=58 kN/m and the rear two springs each have a stiffness of kB = 65 kN/m, determine their compression when the car is parked on the 30° incline. Also, what frictional force FB must be applied to each of the rear wheels to hold the car in equilibrium?

 A. xA = 16.1 mm, xB = 42.2 mm, FB = 6.37 kN B. xA = 65.9 mm, xB = 39.2 mm, FB = 6.37 kN C. xA = 53.2 mm, xB = 50.5 mm, FB = 3.68 kN D. xA = 76.1 mm, xB = 45.3 mm, FB = 3.68 kN

3.

Determine the tension in the supporting cables BC and BD and the components of reaction at the ball-and-socket joint A of the boom. The boom supports a drum having a weight of 200 lb. at F. Points C and D lie in the x—y plane.

 A. Ax = 0, Ay = 150 lb, Az = 562 lb, TBC = 300 lb, TBD = 212 lb B. Ax = 0, Ay = 150 lb, Az = 456 lb, TBC = 150 lb, TBD = 212 lb C. Ax = 0, Ay = 267 lb, Az = 843 lb, TBC = 533 lb, TBD = lb D. Ax = 0, Ay = 150 lb, Az = 500 lb, TBC = 212 lb, TBD = 212 lb

4.

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

5.

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