Physics: Principle and Applications, 7e (Giancoli) Chapter 9 Static Equilibrium; Elasticity and Fracture
9.1 Conceptual Questions 1) If the sum of the external forces on an object is zero, then the sum of the external torques on it must also be zero. A) True ) !alse Ans"er# $ar# 1 %) If the sum of the external torques on o n an object is zero, then the sum of the external forces on it must also be zero. A) True ) !alse Ans"er# $ar# 1 &) If the sum of both the external torques an' the external forces on an object is zero, then the object must be at rest. A) True ) !alse Ans"er# $ar# 1 () If an object remains at rest, then the sum of both the external torques an' the external forces on the object must be zero. A) True ) !alse Ans"er# A $ar# 1 ) *hen a car is "ei+he', it is 'rien slo"l- on a horizontal floor oer a scale that recor's a rea'in+ as the front "heels +o oer the scale, an' then recor's a secon' rea'in+ as the rear "heels +o oer the scale. The "ei+ht of the car is equal to A) the "ei+ht un'er the front "heels. ) the "ei+ht un'er the rear "heels. C) the aera+e of the t"o "ei+hts. ) the sum of the t"o "ei+hts. /) the 'ifference of the t"o "ei+hts. Ans"er# $ar# 1
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3) A croquet mallet balances "hen suspen'e' from its center of mass, as sho"n in the left part of the fi+ure. If -ou cut the mallet into t"o pieces at its center of mass, as sho"n in the ri+ht part of the fi+ure, ho" 'o the masses of the t"o pieces compare4 5There coul' be more than one correct choice.)
A) The masses are equal. ) The piece "ith the hea' of the mallet has the +reater mass. C) The piece "ith the hea' of the mallet has the smaller mass. ) It is impossible to tell. Ans"er# , $ar# 1 6) Tensile stress is A) the strain per unit len+th. ) the same as force. C) the ratio of the chan+e in len+th. ) applie' force per cross7sectional area. Ans"er# $ar# 1 8) Tensile strain is A) the ratio of the chan+e in len+th to the ori+inal len+th. ) the stress per unit area. C) the applie' force per unit area. ) the ratio of stress to elastic mo'ulus. Ans"er# A $ar# 1 9) *hich one of the follo"in+ is an accurate accu rate statement4 A) The ratio of tensile stress to tensile strain is calle' oun+:s oun+:s mo'ulus. ) ;
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1) The +raph in the fi+ure sho"s the tensile stress as a function of the tensile strain in a certain "ire. *hat 'oes the slope of this +raph +ie us for this "ire4
A) the pressure in the "ire ) oun+:s mo'ulus for the material of the "ire C) the tensile stress in the "ire ) the tension in the "ire /) the percent chan+e in the len+th of the "ire Ans"er# $ar# 1 11) A lar+e 67=+ li+htin+ fixture can be hun+ from "ires of i'entical size an' shape ma'e of aluminum, brass, or copper. The alues of oun+:s mo'ulus for these metals are .6 > 111 2a 5aluminum), .91 > 111 5brass), an' 1.1 > 111 5copper). *hich "ire "oul' stretch the least 'istance4 A) aluminum ) brass C) copper ) The- "ill all stretch the same 'istance. Ans"er# C $ar# 1 1%) A %7=+ piece of equipment can be hun+ b- steel "ires of len+th 1. m, %. m, or &. m. If all the "ires hae the same 'iameter, "hich one "ill stretch the +reatest 'istance4 A) the 1.7m "ire ) the %.7m "ire C) the &.7m "ire ) The- "ill all stretch b- the same 'istance. Ans"er# C $ar# 1 1&) A %7=+ piece of equipment can be hun+ b- steel "ires of len+th 1. m, %. m, or &. m. If all the "ires hae the same 'iameter, "hich one "ill stretch the +reatest percent4 A) the 1.7m "ire ) the %.7m "ire C) the &.7m "ire ) The- "ill all stretch b- the same percent. Ans"er# $ar# 1
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1() T"o "ires are ma'e out of the same metal, but one "ire is t"ice as lon+ as the other "ire. *hich "ire "ill hae the +reatest elastic mo'ulus4 A) the shorter "ire ) the lon+er "ire C) It "ill be the same for both "ires. Ans"er# C $ar# 1 1) *hich of the follo"in+ are
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19) A piece of iron sin=s to the bottom of a la=e "here the pressure is %1 times "hat it is at the surface. *hich statement best 'escribes "hat happens to the density of that piece of iron4 A) There has been no chan+e in the 'ensit- of the iron. ) Its 'ensit- 'ecreases sli+htl-. C) Its 'ensit- increases sli+htl-. ) Its 'ensit- becomes %1 times +reater than "hat it "as at the surface. /) Its 'ensit- becomes 1@%1 "hat it "as at the surface. Ans"er# C $ar# 1 %) T"o bloc=s are ma'e of the same material, but one has t"ice the olume of the other bloc=. *hich bloc= "ill hae the +reater shear mo'ulus4 A) It "ill be the same for both of them. ) the lar+er one C) the smaller one Ans"er# A $ar# 1 %1) As one stretches a metal "ire, "hich con'ition is reache' first4 A) the elastic limit ) the brea=in+ point C) the proportional limit Ans"er# C $ar# 1
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9.% 2roblems 1) A 17=+ chil' is sittin+ on a pla-+roun' teeter7totter, 1. m from the piot. *hat is the ma+nitu'e of the minimum force, applie' .& m on the other si'e of the piot, that is nee'e' to ma=e the chil' lift off the +roun'4 A) 6 ? ) 6( ? C) %& ? ) (( ? /) 33 ? Ans"er# $ar# 1 %) A 17=+ chil' is sittin+ on a pla-+roun' teeter7totter, 1. m from the piot. *hat is the minimum 'istance, on the other si'e of the piot, such that a %%7? force "ill ma=e the chil' lift off the +roun'4 A) 1. m ) 1. m C) .1 m ) 9.8 m /) %.( m Ans"er# A $ar# 1 &) An 8%7=+ painter stan's on a lon+ horizontal boar' 1 . m from one en'. This %67=+ boar' is uniform, . m lon+, an' supporte' at each en' b- ertical posts. 5a) *hat is the ma+nitu'e of the total force proi'e' b- both posts4 5b) *ith "hat force 'oes the post that is closest to the painter push up"ar' on the boar'4 Ans"er# 5a) 11 ? 5b) 61 ? $ar# 1 () An 8%7=+ 'ier stan's at the e'+e of a li+ht .7m 'iin+ boar', "hich is supporte' b- t"o ertical pillars that are 1.3 m apart, as sho"n in the fi+ure. !in' the ma+nitu'e an' 'irection of the force exerte' b- each pillar.
Ans"er# A# 1.6 =? 'o"n"ar', # %. =? up"ar' $ar# 1
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) An irre+ularl- shape' object that is 1 m lon+ is place' "ith each en' on a scale. If the scale on the ri+ht rea's "hile the scale on the left rea's ho" far from the left en' is the center of +rait- of this object4 A) .6 m ) 6.( m C) (.& m ) 1( m Ans"er# A $ar# B 3) A uniform 1%7? piece of me'ical apparatus that is &. m lon+ is suspen'e' horizontall- bt"o ertical "ires at its en's. A small but 'ense 7? "ei+ht is place' on the apparatus %. m from one en', as sho"n in the fi+ure. *hat are the tensions, A an' B, in the t"o "ires4
A) A 88 ?, B 88 ? ) A 8( ?, B 91 ? C) A 9 ?, B 8% ? ) A 91 ?, B 8( ? /) A 8% ?, B 9 ? Ans"er# $ar# 1 6) A meter stic= balances at the .7cm mar=. If a mass of . + is place' at the 9.7cm mar=, the stic= balances at the 31.&7cm mar=. *hat is the mass of the meter stic=4 A) 1%6 + ) 168 + C) 89.6 + ) &%.3 + /) 6&.( + Ans"er# A $ar# 1
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8) As sho"n in the fi+ure, a uniform rectan+ular crate .( m "i'e an' 1. m tall sits on a horizontal surface. The crate "ei+hs (3 ?, an' its center of +rait- is at its +eometric center. A horizontal force of ma+nitu'e F is applie' at a 'istance h aboe the floor. !riction at the floor is +reat enou+h to preent the crate from sli'in+. If "hat minimum alue of F is require' to ma=e the crate start to tip oer4
Ans"er# 1&& ? $ar# B 9) As sho"n in the fi+ure, a 1. m lon+ bar is attache' b- a frictionless hin+e to a "all an' hel' horizontal b- a li+ht rope that ma=es an an+le θ (9D "ith the bar. The bar is uniform an' "ei+hs *hat 'istance x from the hin+e shoul' a 1. =+ mass be suspen'e' for the tension in the rope to be 166 ?4
Ans"er# 1 m $ar# B 1) A uniform la''er 1% meters lon+ rests a+ainst a ertical frictionless "all, as sho"n in the fi+ure. The la''er "ei+hs ( ? an' ma=es an an+le θ 1D "ith the floor. A man "ei+hin+ 86( ? climbs slo"l- up the la''er. *hen he is 68 m from the bottom of the la''er, it just starts to slip. *hat is the coefficient of static friction bet"een the floor an' the la''er4
Ans"er# .(9 $ar# B
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11) A chil' is tr-in+ to stac= t"o uniform bric=s, each %( cm lon+, so the- "ill protru'e as far as possible oer the e'+e of a table "ithout tippin+ oer, as sho"n in the fi+ure. *hat is the maximum possible oerhan+ 'istance d 4
A) 1 cm ) 1% cm C) 1( cm ) 13 cm /) 18 cm Ans"er# / $ar# 1 1%) A uniform (7? boar' supports t"o chil'ren "ei+hin+ ? an' & ?. If the support is at the center of the boar' an' the 7? chil' is 1. m from its center, ho" far is the &7? chil' from the center4 A) 1.1 m ) 1. m C) %.1 m ) %.6 m Ans"er# C $ar# 1 1&) To 'etermine the location of the center of mass 5or center of +rait-) of a car, the car is 'rien oer a scale on a horizontal floor. *hen the front "heels are oer the scale, the "ei+ht recor'e' b- the scale is 8 ?, an' "hen the rear "heels are oer the scale, the scale rea's 3 ?. The 'istance bet"een the front an' rear "heels is measure' to be &.% m. Eo" far behin' the front "heels is the center of mass locate'4 A) .8( m ) 1. m C) 1.9 m ) 1.39 m /) 1.6% m Ans"er# $ar# 1
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1() A 1%7=+ refri+erator that is %. m tall an' 8 cm "i'e has its center of mass at its +eometrical center. ou are attemptin+ to sli'e it alon+ the floor b- pushin+ horizontall- on the si'e of the refri+erator. The coefficient of static friction bet"een the floor an' the refri+erator is .&. epen'in+ on "here -ou push, the refri+erator ma- start to tip o er before it starts to sli'e alon+ the floor. *hat is the hi+hest 'istance aboe the floor that -ou can push the refri+erator so that it "ill not tip before it be+ins to sli'e4 A) .61 m ) 1. m C) 1.% m ) 1.( m /) 1.3 m Ans"er# $ar# 1 1) A uniform ro' "ei+hs ( ? an' is 1. m lon+. It is hin+e' to a "all at the left en', an' hel' in a horizontal position at the ri+ht en' b- a ertical strin+ of ne+li+ible "ei+ht, as sho"n in the fi+ure. *hat is the ma+nitu'e of the torque 'ue to the strin+ about a horizontal axis that passes throu+h the hin+e an' is perpen'icular to the ro'4 The hin+e is er- small "ith ne+li+ible friction.
A) ( ? m ) 1 ? m C) . ? m ) % ? m /) & ? m Ans"er# $ar# 1 13) A 17m uniform beam "ei+hin+ 1 ? is supporte' b- t"o ertical ropes at its en's. If a (7? person sits at a point %. m from the left en' of the beam, "hat is the tension in each rope4 Ans"er# &6 ? 5left rope), 1& ? 5ri+ht rope) $ar# 1 16) A li+ht boar' that is 1 m lon+ is supporte' b- t"o sa"horses, one at one en' of the boar' an' a secon' at the mi'point. A (7? "ei+ht is place' bet"een the t"o sa"horses, &. m from the en' an' %. m from the center. *hat ma+nitu'e forces 'o the sa"horses exert on the boar'4 Ans"er# 13 ? at the en', %( ? at the mi'point $ar# 1
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18) A li+ht boar' that is 1 m lon+ is supporte' b- t"o sa"horses, one at one en' of the boar' an' a secon' at the mi'point. A (7? object is place' bet"een the t"o sa"horses, &. m from the en' an' %. m from the center. A secon' object, "ith a "ei+ht of 1 ?, is place' on the supporte' en'. *hat ma+nitu'e forces 'o the sa"horses exert on the boar'4 Ans"er# 1. ? at the en', ( ? at the mi'point $ar# 1 19) The mobile sho"n in the fi+ure is perfectl- balance', an' the horizontal supports hae insi+nificant masses. *hat must be the masses of the suspen'e' objects m1, m%, an' m& to maintain balance4
Ans"er# m1 1 +, m% % +, an' m& ( + $ar# 1 %) A mobile is sho"n in the fi+ure. The horizontal supports hae ne+li+ible mass. Assume that all the numbers +ien in the fi+ure are accurate to t"o si+nificant fi+ures. *hat mass M is require' to balance the mobile4
A) 18 + ) & + C) &3 + ) 3 + /) 9 + Ans"er# C $ar# 1
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%1) An athlete hol's a 6.7=+ shot put in his han' "ith his lo"er arm horizontal, as sho"n in the fi+ure. Eis lo"er arm has a mass of %.8 =+ an' its center of +rait- 5or center of mass) is 1% cm from the elbo"7joint piot. Eo" much force must the extensor muscle 5"hich is F in the fi+ure) in the upper arm exert on the lo"er arm4
A) 1 ? ) ? C) 1 ? ) 1 ? Ans"er# C $ar# 1 %%) A store:s si+n has a mass of % =+ an' is &. m lon+. It is uniform, so its center of +rait- is at the center of the si+n. It is supporte' horizontall- b- a small loose bolt attache' to the "all at one en' an' b- a "ire at the other en', as sho"n in the fi+ure. *hat is the tension in the "ire4
A) (3 ? ) %& ? C) 1% ? ) % ? /) & ? Ans"er# $ar# 1
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%&) A store:s si+n has a mass of % =+ an' is &. m lon+. It is uniform, so its center of +rait- is at the center of the si+n. It is supporte' horizontall- b- a small loose bolt attache' to the "all at one en' an' b- a "ire at the other en', as sho"n in the fi+ure. *hat is the ma+nitu'e of the net force that the bolt exerts on the si+n4
A) (3 ? ) %& ? C) % ? ) 1% ? /) & ? Ans"er# $ar# 1 %() A (7=+ uniform la''er that is . m lon+ is place' a+ainst a smooth "all at a hei+ht of h (. m, as sho"n in the fi+ure. The base of the la''er rests on a rou+h horizontal surface "hose coefficient of static friction "ith the la''er is .(. An 87=+ buc=et is suspen'e' from the top run+ of the la''er, just at the "all. *hat is the ma+nitu'e of the force that the la''er exerts on the "all4
A) 6( ? ) 1& ? C) 98 ? ) 9 ? /) 11 ? Ans"er# A $ar# B
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%) A 17=+ nonuniform boom that is 3. m lon+ is loosel- pinne' at the piot at 2. A 37=+ concrete bloc= is suspen'e' from the en' of the boom at A, as sho"n in the fi+ure. The boom forms a &D an+le aboe the horizontal, an' is supporte' b- a (.7m cable bet"een points an' . 2oint is (. m from 2, an' point is (. m aboe 2. The center of mass of the boom is at point C, "hich is %. m from 2. Assume that all the quantities sho"n in the fi+ure are accurate to t"o si+nificant fi+ures. *hat is the tension in the cable connecte' bet"een points an' 4
A) 9& ? ) 8( ? C) 81 ? ) 6 ? /) 39 ? Ans"er# A $ar# 6 %3) In the fi+ure, a uniform la''er of "ei+ht % ? an' len+th 1 m leans a+ainst a perfectlsmooth "all. A firefi+hter of "ei+ht 3 ? climbs a 'istance x up the la''er. The coefficient of static friction bet"een the la''er an' the floor is .. *hat is the maximum alue of x for "hich the la''er "ill not slip4
A) &.9 m ) . m C) 3. m ) 3.& m /) 8.( m Ans"er# $ar# 1
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%6) A &.7m7lon+ la''er, "ei+hin+ % ?, leans a+ainst a smooth ertical "all "ith its base on a horizontal rou+h floor, a 'istance of 1. m a"a- from the "all. The la''er is not completeluniform, so its center of +rait- is 1.% m from its base. *hat force of friction must the floor exert on the base of the la''er to preent the la''er from sli'in+ 'o"n4 A) 9&.& ? ) 1& ? C) %8.& ? ) 1% ? /) 1 ? Ans"er# C $ar# %8) A .7m7lon+ uniform la''er, "ei+hin+ % ?, rests a+ainst a smooth ertical "all "ith its base on a horizontal rou+h floor, a 'istance of 1.% m a"a- from the "all. The coefficient of static friction bet"een the la''er an' the floor is .%. Eo" far up the la''er, measure' alon+ the la''er, can a 37? person climb before the la''er be+ins to slip4 A) 1. m ) 1.%3 m C) 1. m ) &.9 m /) (.3 m Ans"er# / $ar#
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%9) A stepla''er consists of t"o hales that are hin+e' at the top an' connecte' b- a tie ro' "hich =eeps the t"o hales from sprea'in+ apart. In this particular instance, the t"o hales are %. m lon+, the tie ro' is connecte' to the center of each half an' is 6 cm lon+. An 87? person stan's &@ of the "a- up the stepla''er, as sho"n in the fi+ure. The la''er is li+ht enou+h that "e can ne+lect its "ei+ht, an' it rests on an extremel- smooth floor. *hat is the tension in the tie ro'4 5 Note: To sole this problem, it is helpful to ima+ine cuttin+ the la''er in half erticall- an' consi'er the forces an' torques actin+ on each half of the la''er.)
A) 1( ? ) %( ? C) %8 ? ) &3 ? /) 3 ? Ans"er# A $ar# 1 &) A &%7+ ball an' a (7+ ball are attache' to the t"o en's of a strin+ that +oes oer a pulle"ith a ra'ius of 8.6 cm. ecause of friction in its axle, the pulle- 'oes not be+in to rotate. *hat is the ma+nitu'e of the frictional torque at the axle of the pulle- if the s-stem remains at rest "hen the balls are release'4 A) .38 ? m ) .31 ? m C) .69 ? m ) .3& ? m /) .6 ? m Ans"er# A $ar# 1 &1) A 7=+ buc=et of concrete is suspen'e' from a steel "ire that is 1. mm in 'iameter 1. mm an' 11.% m lon+. *hat 'istance "ill the "ire stretch4 oun+:s mo'ulus for steel is %. x 111 2a. Ans"er# & mm $ar# 1
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&%) A 6.7=+ pipe is hun+ from a steel "ire that is %. m lon+ an' has a 'iameter of .6 mm. oun+:s mo'ulus for steel is %. > 111 ?@m%. 5a) - "hat 'istance 'oes the "ire stretch4 5b) If the "ire 'iameter "ere 'ouble', "hat "oul' be the stretch4 Ans"er# 5a) 1.9 mm 5b) .(9 mm $ar# 1 &&) A steel "ire, &.% m lon+, has a 'iameter of 1.% mm. The "ire stretches 1.3 mm "hen it bears a loa'. oun+:s mo'ulus for steel is %. × 111 2a. The mass of the loa' is closest to A) 1% =+. ) 13 =+. C) % =+. ) %( =+. /) %8 =+. Ans"er# A $ar# 1 &() An aluminum "ire an' a steel "ire, each of len+th %. m, are hun+ from the ceilin+. A .7=+ mass is suspen'e' from the lo"er en' of each "ire. The aluminum "ire has a 'iameter of %.% mm. *hat must be the 'iameter of the steel "ire if it is to stretch the same 'istance as the aluminum "ire, so that the t"o "ires maintain equal len+ths after the masses are attache'4 oun+:s mo'ulus for aluminum is .6 × 111 2a an' for steel it is %. × 111 2a. Ans"er# 1.& mm $ar# 1 &) *hen a 1%7=+ piece of equipment is hun+ from a steel "ire of 'iameter 3. mm, it stretches the "ire b- (. mm. If instea' the "ire ha' a 'iameter of &. mm, but all else "ere the same, b- "hat 'istance "oul' the same equipment stretch the "ire4 A) 13. mm ) 8. mm C) (. mm ) %. mm /) 1. mm Ans"er# A $ar# 1 &3) *hen a 1%7=+ piece of equipment is hun+ from a steel "ire of len+th 6 cm, it stretches the "ire b- (. mm. If instea' the "ire ha' a len+th of 1 cm, but all else "ere the same, b- "hat 'istance "oul' the same equipment stretch the "ire4 A) 13. mm ) 8. mm C) (. mm ) %. mm /) 1. mm Ans"er# $ar# 1 17
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&6) A cable is 17m lon+ an' has a cross7sectional area of 1. mm%. A 17? force is applie' to stretch the cable. oun+:s mo'ulus for the cable is 1. > 111 ?@m%. Eo" far 'oes the cable stretch4 A) .1 m ) .1 m C) 1. m ) 1 m Ans"er# C $ar# 1 &8) A soli' steel column is (. m lon+ an' .% m in 'iameter. oun+:s mo'ulus for this steel is %. > 111 ?@m%. - "hat 'istance 'oes the column shrin= "hen a 7=+ truc= is supporte' b- it4 A) 8. > 176 m ) &.% > 173 m C) 6.8 > 173 m ) &.1 > 17 m Ans"er# $ar# 1 &9) A "ire of 'iameter .% mm stretches b- .%G "hen a 3.%87? force is applie' to it. *hat is oun+:s mo'ulus for this "ire4 A) %. > 11 2a ) 1. > 111 2a C) %. > 11% 2a ) 1. >11% 2a Ans"er# $ar# 1 () A 7=+ loa' is suspen'e' from a steel "ire of 'iameter 1. mm an' len+th 11.% m. - "hat 'istance "ill the "ire stretch4 oun+:s mo'ulus for steel is %. > 111 2a. A) 1. cm ) %. cm C) &. cm ) (. cm Ans"er# C $ar# 1
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(1) A bri'+e pilin+ has a cross7sectional area of 1.% m% an' supports a loa' of 186 ?. *hat is the stress on the column4 A) 186 ? ) 186 ?@m% C) 1 ?@m% ) %&(( ?@m% Ans"er# C $ar# 1 (%) An aluminum "ire %. m lon+ an' %. mm in 'iameter supports a 1.7=+ fixture. *hat is the stress in the "ire4 oun+:s mo'ulus for aluminum is 6. > 11 ?@m%. A) &.1 > 16 ?@m% ) 3.% > 16 ?@m% C) 9.& > 16 ?@m% ) 1.% > 18 ?@m% Ans"er# A $ar# & (&) A brass "ire %. m lon+ an' %. mm in 'iameter supports a 1.7=+ fixture. - "hat 'istance 'i' this fixture stretch the "ire4 oun+:s mo'ulus for brass is 1 > 11 ?@m%. A) .11 mm ) .%% mm C) .&& mm ) .3% mm Ans"er# $ar# 3 (() A ertical &7cm steel ro', 1. cm in 'iameter, supports a &7=+ mass. *hat is the chan+e in len+th of the ro' cause' b- this mass4 oun+:s mo'ulus for steel is %. > 111 ?@m%. A) .3 > 17 m ) 3. > 17 m C) .3 > 173 m ) 3. > 173 m /) 3. > 17( m Ans"er# A $ar# 1
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() A 7=+ air con'itioner is place' on top of a concrete pa' that is % cm thic= an' has a cross7 sectional area of &. m%. *hat is the chan+e in thic=ness of the pa' cause' b- the air con'itioner4 oun+:s mo'ulus for concrete is %.& > 11 ?@m%. A) 1.( > 179 m ) %.8 > 179 m C) 1.( > 178 m ) 1.( > 176 m /) %.8 > 178 m Ans"er# A $ar# 1 (3) A 1%7=+ car is bein+ raise' at a constant spee' if % cm@s b- a crane, usin+ a %7m lon+ steel cable that is 1. cm in 'iameter. oun+:s mo'ulus for steel is %. > 111 2a. *hat is the chan+e in len+th of the cable cause' b- the car4 A) 3.6 mm ) 3.6 cm C) &.& mm ) &.& cm /) &.& m Ans"er# A $ar# 1 (6) A 1%7=+ car is bein+ raise' "ith a constant acceleration of %.& m@s% b- a crane, usin+ a %7m lon+ steel cable that is 1. cm in 'iameter. oun+:s mo'ulus for steel is %. > 111 ?@m%. *hat is the chan+e in len+th of the cable cause' b- liftin+ the car4 A) 8.( mm ) 8.( cm C) (.9 mm ) (.9 cm /) (.9 m Ans"er# A $ar# 1 (8) A piano "ire has a ra'ius of . mm. Hne en' is fixe' an' the other is "rappe' aroun' a tunin+ pe+, "hich has a 'iameter of &. mm an' is 8 cm a"a-. After the "ire just becomes taut, the pe+ is +ien three full turns. *hat is the tension in the "ire4 oun+:s mo'ulus for steel is %. > 111 ?@m%. A) &.8 =? ) (.& =? C) 3. =? ) 8.6 =? /) 9.8 =? Ans"er# C $ar# 1
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Cop-ri+ht 0 %1( 2earson /'ucation, Inc.
(9) A "ire that is 1. mm in 'iameter an' &. m lon+ stretches &. mm "hen an 8.7=+ tool is hun+ from it. 5a) *hat is oun+:s mo'ulus for the material from this "ire is ma'e4 5b) *hat is the effectie sprin+ constant for the stretchin+ "ire4 Ans"er# 5a) 1. > 111 2a 5b) %.% > 1( ?@m $ar# 1 ) *hen the pressure applie' to an un=no"n liqui' is increase' from 1. × 16 2a to . × 16 2a, the olume of the liqui' 'ecreases b- .6G. Calculate the bul= mo'ulus of the liqui'. Ans"er# 3.( × 19 2a $ar# 1 1) A 1%7 olume of oil is subjecte' to pressure "hich pro'uces a olume strain of 7&. × 17(. The bul= mo'ulus of the oil is 3. × 19 2a an' is in'epen'ent of the pressure. The re'uction in the olume of the oil in milliliters is closest to A) %. m. ) %.( m. C) %.8 m. ) &.% m. /) &.3 m. Ans"er# / $ar# 1 %) A 1%7 olume of oil is subjecte' to pressure "hich pro'uces a olume strain of 7&. × 17(. The bul= mo'ulus of the oil is 3. × 19 2a an' is in'epen'ent of the pressure. The chan+e in the pressure of the oil in me+apascals is closest to A) 1.% F2a. ) 1.( F2a. C) 1.3 F2a. ) 1.8 F2a. /) %. F2a. Ans"er# $ar# 1 &) A 7? force compresses a steel bloc= b- .% cm. Eo" much force, applie' oer the same area, "oul' be nee'e' to compress the bloc= b- .1% cm4 A) 1, ? ) %, ? C) , ? ) %, ? Ans"er# $ar# 1
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Cop-ri+ht 0 %1( 2earson /'ucation, Inc.
() At a 'epth of 1& m in a=e ai=al 5a fresh "ater la=e in 19 2a. A) %.& > 17& m& ) &.& > 17& m& C) (.& > 17& m& ) .& > 17& m& Ans"er# C $ar# 1 ) A copper sphere that is 1 cm in 'iameter at an atmospheric pressure of 1.1 > 1 ?@m% is put into a chamber "here the pressure is 1. > 13 ?@m%. *hat is the chan+e in the 'iameter of the sphere cause' b- this chan+e in pressure4 The bul= mo'ulus for copper is 1.( > 111 2a. A) 7%.1 > 17( cm ) 7%.1 > 17 cm C) 76.1 > 17( cm ) 76.1 > 17 cm /) 76.1 > 173 cm Ans"er# $ar# 1 3) The base of a metal bloc=, "hich is fixe' in place, measures 9 cm b- 9 cm, an' the hei+ht of the bloc= is 3 cm. A force, applie' to the upper face an' parallel to it, pro'uces a shear strain of .3. The shear mo'ulus of this metal is & . × 11 2a. The 'isplacement of the upper face, in the 'irection of the applie' force is closest to A) &. mm. ) &.3 mm. C) (.% mm. ) (.8 mm. /) .( mm. Ans"er# $ar# 1 6) The base of a metal bloc=, "hich is fixe' in place, measures 9 cm b- 9 cm, an' the hei+ht of the bloc= is 3 cm. A force, applie' to the upper face an' parallel to it, pro'uces a shear strain of .3. The shear mo'ulus of this metal is & . × 11 2a. The shear stress on the bloc= in me+apascals is closest to A) 18 F2a. ) &3 F2a. C) 3 F2a. ) 6% F2a. /) 9 F2a. Ans"er# A $ar# 1 22
Cop-ri+ht 0 %1( 2earson /'ucation, Inc.
8) A shear force of ( ? is applie' to one face of an aluminum cube hain+ si'es of & cm each. *hat is the resultin+ 'isplacement of this face of the cube if the opposite face is hel' fixe'4 The shear mo'ulus for aluminum is %. > 11 ?@m%. A) 1.9 > 178 m ) (.( > 178 m C) .& > 178 m ) 8.% > 178 m Ans"er# C $ar# 1 9) Hpposin+ shearin+ forces of & ? are applie' to the &.7cm > (.7cm faces of a metal bloc= measurin+ &. cm > (. cm > . cm. - "hat 'istance 'oes the bloc= become slante'4 The shear mo'ulus for this metal is 8.1 > 11 ?@m%. A) 1.( > 173 m ) .3 > 176 m C) 9.88 > 176 m ) &.8 > 173 m /) 3.98 > 173 m Ans"er# A $ar# 1 3) Hpposin+ shearin+ forces of & ? are applie' to the (.7cm > .7cm faces of a metal bloc= measurin+ &. cm > (. cm > . cm. - "hat amount 'oes the bloc= become slante'4 The shear mo'ulus for this metal is 8.1 > 11 ?@m%. A) 1.( > 173 m ) .3 > 176 m C) 9.88 > 176 m ) &.8 > 173 m /) 3.98 > 173 m Ans"er# $ar# 1 31) A %7=+ teleision set rests on four rubber pa's, each one hain+ a hei+ht of 1. cm an' a ra'ius of .3 cm. A %7? horizontal force is applie' to the teleision set. Eo" far 'oes it moe si'e"a-s 'ue to the 'eformation of the rubber pa's if the pa's 'o not sli'e on the floor4 The shear mo'ulus of these rubber pa's is %.3 > 13 2a. A) 3.8 mm ) &.( mm C) 1.6 mm ) 1. mm /) 1.& mm Ans"er# C $ar# 1 23
Cop-ri+ht 0 %1( 2earson /'ucation, Inc.
3%) A %7=+ teleision set rests on four rubber pa's that are on the floor, each one hain+ a hei+ht of 1. cm an' a ra'ius of .3 cm. A horizontal force is applie' to the teleision set. *hen the pa's are just at the point of sli'in+ oer the floor, ho" far has the teleision set moe' si'e"a-s 'ue to the 'eformation of the pa's4 The coefficient of static friction bet"een the rubber an' the floor is 1. an' the shear mo'ulus of these rubber pa's is %.3 > 13 2a. A) 13 mm ) 8.( mm C) (.% mm ) %.1 mm /) 1.1 mm Ans"er# $ar# 1
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Cop-ri+ht 0 %1( 2earson /'ucation, Inc.
