15. Rotational Equilibrium

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.

(II) 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.

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(III) 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?

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(II) A heavy load M g = 62.0 kN hangs at point E of the single cantilever truss shown in Fig. 12–81.

(a) 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 F→_A on the truss at pin A. Neglect the weight of the trusses, which is small compared to the load.

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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.

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.]

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