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 heavy load Mg = 62.0 kN hangs at point E of the single cantilever truss shown in Fig. 12–81. Use a torque equation for the truss as a whole to determine the tension F_T in the support cable, and then determine the force $\overrightarrow{F_A}$ on the truss at pin A. Neglect the weight of the trusses, which is small compared to the load.

(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.]

The roof over a 9.0-m x 10.0-m room in a school has a total mass of 12,400 kg. The roof is to be supported by vertical wooden “2 x 4s” (2 x4 in inches, but actually about 4.0 x 9.0 cm) equally spaced along the 10.0-m sides. How many supports are required on each side, and how far apart must they be? Consider only compression, and assume a safety factor of 12.

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.

A board 8 m in length, 20 kg in mass, and of uniform mass distribution, is supported by two scales placed underneath it. The left scale is placed 2 m from the left end of the board, and the right scale is placed on the board's right end. A small object 10 kg in mass is placed on the left end of the board. Calculate the reading on the left scale. (Use g=10 m/s².)

BONUS:Calculate the reading on the right scale.

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 350-N, uniform, 1.50-m bar is suspended horizontally by two vertical cables at each end. Cable A can support a maximum tension of 500.0 N without breaking, and cable B can support up to 400.0 N. You want to place a small weight on this bar. (a) What is the heaviest weight you can put on without breaking either cable, and (b) where should you put this weight?

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?