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Chapter 12: Problem 71
If you pull the boom rope with constant speed, the angle the boom makes with the horizontal will a. increase at a constant rate. b. increase at an increasing rate. c. increase at a decreasing rate. d. decrease.
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A \(160-\mathrm{kg}\) highway sign of uniform density is \(2.3 \mathrm{~m}\) wide and \(1.4 \mathrm{~m}\) high. At one side it's secured to a pole with a single bolt, mounted a distance \(d\) from the top of the sign. The only other place where the sign contacts the pole is at its bottom corner. If the bolt can sustain a horizontal tension of \(2.1 \mathrm{kN}\), what's the maximum permissible value for the distance \(d\) ?
A construction worker leans a uniform board against a frictionless wall. Its bottom end rests on a concrete driveway where the coefficient of friction between board and driveway is \(0.483\). What's the minimum angle the board can make with the horizontal if it's not to slip?
Figure \(12.31\) shows a popular system for mounting bookshelves. An aluminum bracket is mounted on a vertical aluminum support by small tabs inserted into vertical slots. Contact between the bracket and support occurs only at the upper tab and at the bottom of the bracket, \(4.5 \mathrm{~cm}\) below the upper tab. If each bracket in the shelf system supports \(35 \mathrm{~kg}\) of books, with the center of gravity \(12 \mathrm{~cm}\) out from the vertical support, what is the horizontal component of the force exerted on the upper bracket tab?
The potential energy associated with a particle at position \(x\) is given by \(U=2 x^{3}-2 x^{2}-7 x+10\), with \(x\) in meters and \(U\) in joules. Find the positions of any stable and unstable equilibria.
What horizontal force applied at its highest point is necessary to keep a wheel of mass \(M\) from rolling down a slope inclined at angle \(\theta\) to the horizontal?
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