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Chapter 9: Q9-16Q (page 230)
The ball at points A, B, and C is in unstable equilibrium, stable equilibrium, and neutral equilibrium, respectively.
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(III) Four bricks are to be stacked at the edge of a table, each brick overhanging the one below it, so that the top brick extends as far as possible beyond the edge of the table. (a) To achieve this, show that successive bricks must extend no more than (starting at the top) \(\frac{{\bf{1}}}{{\bf{2}}}{\bf{,}}\frac{{\bf{1}}}{{\bf{4}}}{\bf{,}}\frac{{\bf{1}}}{{\bf{6}}}\) and \(\frac{{\bf{1}}}{{\bf{8}}}\)of their length beyond the one below (Fig. 9鈥�75a). (b) Is the top brick completely beyond the base? (c) Determine a general formula for the maximum total distance spanned by n bricks if they are to remain stable. (d) A builder wants to construct a corbeled arch (Fig. 9鈥�75b) based on the principle of stability discussed in (a) and (c) above. What minimum number of bricks, each 0.30 m long and uniform, is needed if the arch is to span 1.0 m?
A 2.0-m-high box with a 1.0-m-square base is moved across a rough floor as in Fig. 9鈥�89. The uniform box weighs 250 N and has a coefficient of static friction with the floor of 0.60. What minimum force must be exerted on the box to make it slide? What is the maximum height h above the floor that this force can be applied without tipping the box over? Note that as the box tips, the normal force and the friction force will act at the lowest corner.
(I) Calculate the mass m needed in order to suspend the leg shown in Fig. 9鈥�47. Assume the leg (with cast) has a mass of 15.0 kg, and its CG is 35.0 cm from the hip joint; the cord holding the sling is 78.0 cm from the hip joint.
A 15.0-kg ball is supported from the ceiling by rope A. Rope B pulls downward and to the side on the ball. If the angle of A to the vertical is 22掳 and if B makes an angle of 53掳 to the vertical (Fig. 9鈥�85), find the tensions in ropes A and B.
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