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PHY_122_Assignment_1

PHY_122_Assignment_1 - sec 12 Elasticity ‘43 A...

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Unformatted text preview: sec. 12»? Elasticity ‘43 A horizontal aluminum rod 4.3 cm in (liameter projects 5.3 em from a wall. A 1200 kg object is Suspended from the anti of the rod. The shear madulus of aluminum is 3.0 X 10“” Nimz. Neglecting the md’s mass find {a} the shear stress or: the red and {h} the vertical deflection of‘the end ()f the rod. 35M [LW ‘44 Figure 1254 Sh()WS the stress~strain curve fer a mater , ’ ial. {he scale of the strese axis is i set by S x 300, in units of l 1&6 Wm? What are (a) the i Young’s modulus and (b) the «A 0} approximate yield strength for 0 this material? 0.002 Strain 9945 In Fig. 12—55, a 103 kg uttit‘orm log hangs by two steel wires, A and B, both of radius , i 129 mm. Initially, wire A was t 2.59 m long and 2.00 min WW A g... JAM; (1,3,; ShGi’tCI‘ than wire B. The leg IS 3 : g haw horizontal. What are the magnitudes of the forces on it from (a) wire A and (b) wire B? {e} What is the ratio dA/[email protected] “56 Figure 12—56 shows the stress versus strain plot for an aluminum wire that is stretched by a machine pulling in apposite directions at the two emis of the wire The scale of the stress axis is set by s :C 7.0, it} units of 107 Nimzflhe wire has an initial length (if 0.800 m and an initial cresaseetionai area 0f 2.001% HT“; in? Haw meet; WQEK Liees the farce from the machine {it} {at} the wire te gredttce a strain at" U30 >< 1‘3“? 0 1.0 Strain {ta-3} Fifi. @3533 Problem 46. “47 In Fig. 1257, a lead brick rests horizontally en cylinders A and B. The areas of the top faces at" the cylinders 31%? {dated by AA 3 2A 1;; the E’eeng’s meduli 0f the cylinders 3373 related by EA 3: 25a The {SK}. @267 Pmblem 47. 0004 L 9K3. 12-54 Problem 44. iWire 15 FtG. 12-55 Problem 45. W a.“ b . t . :gitgttgfhhaaitieiiticai iength’s hefore the brick was; elaeed ea .7 ‘ . at traetien of the briek’a mass is sap arted i' h C: finder A and {b} 13‘; Cyhader 8‘? The hQI‘iZOl’ltaipééS: Eight Y tweet: the center at mass of the brick aad the eehtefiiiili :2 the eviiitt‘iefl ate {5 f " ‘ , V,‘ . at a Gnyitflfisfiffl at ’ I‘ ' ” ‘ What is the ratie gig/‘83? mi (18 f0? Cilifldef 8‘ KC} wee Figure l2-58 shows an approximate plot of stress ver— sus strain for a Spiderweb thread. out to the point of breaking at: a strain of 2.00. The vertical axis scale is set by (t z 0.12 (EN/m3. i; = 0.30 GN/mz. Stress (UN/m2) and E: z 0.80 (EN/in? Assume it it} M at} that the thread has an initial Strain length of 0.80 cmt an initial egg, 12.339 Problem 48. cross ectional area of 8.0 X ewfiit’} Figure 3250 repte» itl‘iz m3. and (during stretching) a constant volume. Assume gents an inseet caught at the also that when the singie thread snares a flying insect, the in» gnidpoirtt of a spider—web seet’s kinetic energy is transferred to the stretching of the thread. the. thread breaks utt- thread. (a) How much kinetic energy would put the thread on tier :3 stress of 820 X tilt“; Nlrn2 the verge of breaking? What is the kinetic energy of (b) a fruit and a strain of 2.00. initiaiiv, it fly of mass 6.00 mg and speed 1.70 mfs and (e) a bumble bee of was horizontal and had 8 WE 3243i} ”0553533 50’ mass 0.388 g and speed 0.428 min? Wouid to) the fruit fly and tmgth of? 2,06 em and a cross- (‘3) the humbie i366 bffiflk €116 thread? 3% sectional area of 8.00 is 10‘D n13.As the thread was stretehed under the weight of the insect. its volume remained eon... it the weight of the insect puts. the thread on the verge 3? m i r: F} ' E . _ . . » . . , . . “g? A tunnel Of length L 150 m. height H 7““ 131’ ant; Breaking. what is the insects mass‘.> (A spider 3 web is hush [m width 5,8 m (with a flat roof) is to be constructed at distance 55 x 60m beneath the grouhd. (See Fig. 12—59.) The tunnet roof is to he supported entirely by square steel columns. each with a cross—sectional area of 960 cm? The mass of l0 0an3 of the ground material is 2.8 g. (a) What is the total weight of the ground material the columns must support? (b) How many _ , . columns are needed to keep the compressive stress on each eeefi‘} Figure 124% is an overhead View of a rigid T05 . COEUmfl at (me—halting Ultimate Strength? turns about a vertical axle until the identicai rubber steal A and B are forced against rigid waits at distanees 21.; 2 '. _ and r3 «1 4.0 cm from the axle. Initially the stoppers touch walls without being compressed. Then force F oi magn 220 N is applied perpendicular to the rod at a distance! 5.0 cm from the axle. Find the magnitude of the force pressing (a) stopper A and (h) stopper B. Stopper A sea ”:35? i’rehiem at? fiat? After a felt. a: 93 he, rock ehmher finds hintaett” dartgtieg egg. 32-5% Prohiem 51. from the ego of a rope that had been :5 tr: ioeg anti 223.5 the: in diameter bet has stretched by 2.3 cm. Foe the rope, cateetete {a} the strain. {fo} the stress. and {e} the Young’s modtiins. é? in Fig. 12-276, a rectangttiar siah of state rests on a bedrock setfece inelined at angle :9 3 263. The stab has tength I. 2 43 in. thieitness T x 25 m. and width W 2 £2112. and Li) cm3 of it has a S3333 of 3.2 g. The coefficient of stetie friction between slab and bedrock is 0.39. (8) Calculate the component of the gravitational force on the stat: paraliei to the bedrock surface. {h} Calculate the magnitude of the static frietionat force on the slab. By comparing {a} and {b}. you can see that the slab is in danger of siiding.Thi. .3 presented only by chance protrusions of bedrock. {c} To stabiiize the stab. bolts are to be driven perpendieuiar to the bedrock surface {two hoits are shown}. if eeeh he}: has a erosseeetieoai area of {3,4 em: Strict Witt seep oeder a shearing stress of 3.5; X it? Nimz. whet is the mini“ atom heather of bolts needed? Assume that the bolts do not at- feet the normai force. 335% $83. 3236 Probiem er ...
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