15. Rotational Equilibrium

For a simply supported beam of length $L$ with a uniformly distributed load $w$ along its entire length, which of the following correctly describes the shape of the shear force and bending moment diagrams?

Two wires run from the top of a pole 2.6 m tall that supports a volleyball net. The two wires are anchored to the ground 2.0 m apart, and each is 2.0 m from the pole (Fig. 12–70). The tension in each wire is 125 N. What is the tension in the net, assumed horizontal and attached at the top of the pole?

A 40 kg, 5.0-m-long beam is supported by, but not attached to, the two posts in FIGURE P12.61. A 20 kg boy starts walking along the beam. How close can he get to the right end of the beam without it falling over?

For a cantilever beam of length $L$ fixed at the left end and subjected to a downward point load $P$ at the free right end, which of the following best describes the shapes of the shear force and bending moment diagrams along the beam?

A uniform beam of length $L$ and mass $m$ rests horizontally on two supports, one at each end. If a downward force $F$ is applied at a distance $a$ from the left end, which expression gives the reaction force at the left support?

In the context of equilibrium with multiple supports, what is the name of a horizontal structure that is supported at only one end?

A uniform beam of length $L$ and mass $m$ rests horizontally on two supports, one at each end. If a point load $P$ is applied at a distance $a$ from the left end, which of the following correctly gives the reaction force at the left support?

A uniform horizontal beam of length $L$ and mass $m$ rests on two supports, one at each end. If a downward force $F$ is applied at a distance $d$ from the left end, which equation correctly expresses the condition for rotational equilibrium about the left support (taking counterclockwise moments as positive)?

(III) The truss shown in Fig. 12–82 supports a railway bridge. Determine the compressive or tension force in each strut if a 53-ton (1 ton = 10³kg) train locomotive is stopped at the midpoint between the center and one end. Ignore the masses of the rails and truss, and use only 1/2 the mass of train because there are two trusses (one on each side of the train). Assume all triangles are equilateral. [Hint: See Fig. 12–31.]

A diving board 3.00 m long is supported at a point 1.00 m from the end, and a diver weighing 500 N stands at the free end (Fig. E11.11). The diving board is of uniform cross section and weighs 280 N. Find the force at the support point.

A uniform beam of length $L$ and mass $m$ rests horizontally and is supported at two points, A and B, which are located at the ends of the beam. If the beam is in static equilibrium and no other forces act on it except gravity, what is the reaction force at support A?

Two springs, both having stiffness constant 225 N/m, are attached to a table and to a 0.500-kg uniform thin wooden board (Fig. 12–98). The board is exactly horizontal. What are the natural lengths of each spring? [Hint: One of the springs is stretched, the other compressed, from their natural equilibrium lengths.]

A person's center of mass is easily found by having the person lie on a reaction board. A horizontal, 2.5-m-long, 6.1 kg reaction board is supported only at the ends, with one end resting on a scale and the other on a pivot. A 60 kg woman lies on the reaction board with her feet over the pivot. The scale reads 25 kg. What is the distance from the woman's feet to her center of mass?

A shop sign weighing 215 N hangs from the end of a uniform 135-N beam as shown in Fig. 12–59. Find the tension in the supporting wire (at 35.0°), and the horizontal and vertical forces exerted by the hinge on the beam at the wall.

A heavy load M g = 62.0 kN hangs at point E of the single cantilever truss shown in Fig. 12–81. Determine the force in each member of the truss. Neglect the weight of the trusses, which is small compared to the load.