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Unformatted text preview: sec. 12Ā»? Elasticity ā43 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
10āā Nimz. Neglecting the mdās mass find {a} the shear stress
or: the red and {h} the vertical deflection ofāthe end ()f the rod. 35M [LW ā44 Figure 1254 Sh()WS the
stress~strain curve fer a mater ,
ā 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
Youngās modulus and (b) the Ā«A 0}
approximate yield strength for 0
this material? 0.002
Strain 9945 In Fig. 12ā55, a 103 kg
uttitāorm 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,;
ShGiātCIā 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] ā56 Figure 12ā56 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% HTā; in? Haw
meet; WQEK Liees the farce from
the machine {it} {at} the wire te
gredttce a strain at" U30 >< 1ā3ā? 0 1.0
Strain {ta3} Fiļ¬. @3533 Problem 46. ā47 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
Eāeengās meduli 0f the cylinders
3373 related by EA 3: 25a The {SK}. @267 Pmblem 47. 0004 L 9K3. 1254 Problem 44. iWire 15 FtG. 1255 Problem 45. W a.ā b . t .
:gitgttgfhhaaitieiiticai iengthās hefore the brick was; elaeed ea
.7 ā . at traetien of the briekāa mass is sap arted i' h C: finder A and {b} 13ā; Cyhader 8ā? The hQIāiZOlāltaipĆ©Ć©S: Eight Y
tweet: the center at mass of the brick aad the eehteļ¬iiili :2 the eviiittāieļ¬ ate {5 f " ā
, V,ā . at a Gnyitļ¬ļ¬sļ¬fļ¬ at ā Iā ' ā ā
What is the ratie gig/ā83? mi (18 f0? Ciliļ¬def 8ā KC} wee Figure l258 shows an
approximate plot of stress verā
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 ewļ¬itā} Figure 3250 repteĀ» itlāiz 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 inĀ» gnidpoirtt of a spiderāweb seetās 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 tiltā; 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} ā0553533 50ā
mass 0.388 g and speed 0.428 min? Wouid to) the fruit fly and tmgth of? 2,06 em and a cross (ā3) the humbie i366 bfļ¬ļ¬k ā¬116 thread? 3% sectional area of 8.00 is 10āD 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 . _ . . Ā» . . , . .
āg? A tunnel Of length L 150 m. height H 7āā 131ā ant; Breaking. what is the insects massā.> (A spider 3 web is hush [m width 5,8 m (with a ļ¬at roof) is to be constructed at distance
55 x 60m beneath the grouhd. (See Fig. 12ā59.) The tunnet
roof is to he supported entirely by square steel columns. each
with a crossāsectional 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 eeeļ¬ā} Figure 124% is an overhead View of a rigid T05 . COEUmļ¬ at (meāhalting 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 Ā«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 ā:35? iārehiem at? ļ¬at? After a felt. a: 93 he, rock ehmher ļ¬nds hintaettā dartgtieg egg. 325% 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 Youngās modtiins. Ć©? in Fig. 12276, 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 Ā£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 miniā
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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 Spring '11
 KostadinkaBizheva
 mechanics

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