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Chapter 12: Q19P (page 347)
Question: To crack a certain nut in a nutcracker, forces with magnitudes of at least 40 N must act on its shell from both sides. For the nutcracker of Figure, with distances L =12 cmand D = 2.6 cm , what are the force components F (perpendicular to the handles) corresponding to that 40 N?
Answer:
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Figure 12-49ashows a vertical uniform beam of length Lthat is hinged at its lower end. A horizontal force is applied tothe beam at distance yfrom the lower end. The beam remainsvertical because of a cable attached at the upper end, at anglewith the horizontal. Figure12-49agives the tension Tin the cableas a function of the position of the applied force given as a fraction y/Lof the beam length. The scale of the Taxis is set by.Figuregives the magnitude Fhof the horizontal force on thebeam from the hinge, also as a function of y/L. Evaluate (a) angleand (b) the magnitude of .
Question: In Fig.12-34, a uniform beam of weight 500 Nand length 3.00 m is suspended horizontally. On the left it is hinged to a wall; on the right it is supported by a cable bolted to the wall at distance Dabove the beam. The least tension that will snap the cable is 1200 N. (a) What value of D corresponds to that tension? (b) To prevent the cable from snapping, should Dbe increased or decreased from that value?
A gymnast with mass stands on the end of a uniform balance beam as shown in Fig. 12-80. The beam is 5.00 m long and has a mass of (excluding the mass of the two supports). Each support is from its end of the beam. In unit-vector notation, what are the forces on the beam due to (a) support 1 and (b) support 2?
The Figure represents an insect caught at the midpoint of a spider-web thread. The thread breaks under a stress of and a strain of . Initially, it was horizontal and had a length of and a cross-sectional area of . As the thread was stretched under the weight of the insect, its volume remained constant. If the weight of the insect puts the thread on the verge of breaking, what is the insect鈥檚 mass? (A spider鈥檚 web is built to break if a potentially harmful insect, such as a bumble bee, becomes snared in the web.)
Question: Figure 12-29 shows a diver of weight 580 N standing at the end of a diving board with a length of L =4.5 mand negligible v mass. The board is fixed to two pedestals (supports) that are separated by distance d = 1 .5 m. Of the forces acting on the board, what are the (a) magnitude and (b) direction (up or down) of the force from the left pedestal and the (c) magnitude and (d) direction (up or down) of the force from the right pedestal? (e) Which pedestal (left or right) is being stretched, and (f) which pedestal is being compressed?
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