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习题练习:Physics Unit10: Fluids Related Topics

 作者: admin   总分: 80分  得分: _____________

答题人: 游客未登录  开始时间: 22年07月29日 13:02  切换到: 整卷模式

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1#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The three common phases of mvm6bstpzj. x 73 7;yfuatter are

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2#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Density is

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3#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Substance A has a defof tsb6dgy2 2mo1o:, nsity of $3.0 \; g/cm^{3}$ and substance B has a density of $4.0 \; g/cm^{3}$. In order to obtain equal masses of these two substances, the ratio of the volume of A to the volume of B will be equal to

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4#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Pressure is

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5#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Which of the following is nw:dn.db hp+q7lv;m64e dqq p*kn/ .kcot a unit of pressure?

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6#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Consider three drinking glasses. All three have the same area ba-oqykjxfu /6k .a(ba9i;cd 9 kse, and all three are filled to the same depth with water. Glass A is cylindrical. Glass B is wider at the top than at the bottom, and so holds more water than A. Glass C is narrower at the top than at the bottom, and so holds less water than A. Which glass has the greatest liquid pressure at t. 9q/kcyu(;bf6a j k9kix od-ahe bottom?

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7#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the difference between the pressure.3 chu kw3sn+dfhcl-,s inside and outside a tire called?

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8#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  When atmospheric pressure changes, wha:a odc+4 n+ugqt happens to the absolute pressure at the bottom ofa c4o+qu+ d:gn a pool?

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9#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  You are originally 1.0 m beneath the surface od8kjcs+l u- 4gf a pool. If you dive to 2.0 m beneath the surface, what happens to the absolute pressudjul+4gc 8sk -re on you?

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10#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
State Pascal's princi,5h;im8 lvcb66gwql1r*a/4 cp ps zpk ple.
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11#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
State Archimedes' prino6 v k5ck.pu+y2ylc j-ciple.
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12#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  $50 \; cm^{3}$ of wood is floating on water, and $50 \; cm^{3}$ of iron is totally submerged. Which has the greater buoyant force on it?

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13#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  As a rock sinks deeper and deeper into wateb934 zwru ee2 b3ky)afr of constant density, what happens to the buoyant force ofa4bz)92b w uyrk33een it?

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14#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Salt water has greater densit.w p 21 crj g+arawg)-1vkzvr-6p -oboy than fresh water. A boat floats in both fresh water and in salt water. Where is the buoyant force grzp bv r-+a- r2o )ck.6 rg-owwpg1ajv1eater on the boat?

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15#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Salt water is more dense than fresw77eml9 yd qu)h water. A ship floats in both fresh water and salt water. Compared to the fuyq ld97 mwe)7resh water, the volume of water displaced in the salt water is

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16#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A steel ball sinks in water but fco4pn/l fly1e6 5/aictd /0ykloats in a pool of mercury. Where is the buoyant force on the ball grl6p/1olcy0i ced/n kt a /4yf5eater?

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17#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 10-kg piece of aluminum s23tiwnc0w/w n its at the bottom of a lake, right next to a 10-kg piece of lead. Whii0wt3c/w2 nn wch has the greater buoyant force on it?

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18#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A piece of iron rests on top ofwh 50iw ejn67 s1rqf3q a piece of wood floating in a bathtub. If the iron is removed from the wood, 5qh r wf6s 17eqw0j3inwhat happens to the water level in the tub?

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19#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A piece of wood is floating in a bathtub. z y4 ur05lq3gr )vjil, A second piece of wood sits on top of the first piece, and does not30 l45vlrig yqr)u j,z touch the water. If the top piece is taken off and placed in the water, what happens to the water level in the tub?

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20#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Water flows through eiycifr4rx( )2 fg68ht:s n/ba pipe. The diameter of the pipe at point B is larger than at point A. Where is the speed of the 648ybi )ftrhis grxen/c(:2f water greater?

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21#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An ideal fluid flows at 12c47h16 zxe 2 ylad7uft m/s in a horizontal pipe. If the pipe widens to twice its original radius, what is the flow 2ca7dz6u17 txey lf 4hspeed in the wider section?

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22#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An ideal fluid flows at 12 m/s in a horizontal pipe. If 4d/cr +jur q.bthe pipe narrows to half its+ d4 jrqc.ur/b original radius, what is the flow speed in the narrower section?

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23#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
State Bernoulli's principl g ae ;6 q /lglo.amkr6xds*/zu;o3t*pe.
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24#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Which one of the following is associated with the law l*ne lr /0w.n(phipe0of conservation of energy i(0i0lp*n.repwlh /e n n fluids?

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25#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  As the speed of a moving fluid increases, the prv wf ((7v( u+zsmlkl2qessure in the fluid

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26#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Water flows through a-l8urkfszq3 t g*; 3sp pipe. The diameter of the pipe at point B is larger than at point A. Where is the wategtq p38f*3k;sus -zrlr pressure greatest?

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27#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  When you blow some air above a paper strip, c39t9lb *.)qhw1 inzaq8vctjthe paper rises. This is because

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28#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A sky diver falls through tz dli avx*6nvza6x):-he air at terminal velocity. The force of air resistance-ali*6n ) 6zvvz:adxx on him is

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29#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Two Styrofoam balls, ohtde:dw do-8 x hu4w/8f radii R and 2R, are released simultaneously from a tall towerd/x8 -u8whd ewt:4odh. Which will reach the ground first?

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30#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  When a small spherical roca:ic hl, gw/:5j o9mlck of radius r falls through water, it experiences a drag fo,ih mc: lwl/5a:gc j9orce $F=arv$, where $v$ is its velocity and $a$ is a constant proportional to the viscosity of water. From this, one can deduce that if a rock of diameter 2.0 mm falls with terminal velocity, $v$, then a rock of diameter 4.0 mm will fall with terminal velocity .

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31#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Which has the greatest effect on qexj a 0*bwbi()d(qp6the flow of fluid through a narrow pipe? That is, if you made a 10% change in each j*deq) q(bb0w(6xp ia of the quantities below, which would cause the greatest change in the flow rate?

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32#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Two horizontal pipes are the same length, but pipe B has twice the diameter of ptjqlv +yj*,+r*n;a dzipe A. Water undergoes viscous flow in both pipes, subject to the same pressure difference across the lengths of the pipes. If the flow rate in pipe A is Q, what is the flow rate in pin a;,dl*jyqz +*v+t jrpe B?

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33#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Two horizontal pipes have the same diameter, but pipe B is twic8j6nau+ 3 ypnxe as long as pipe A. Water undergoes viscous flow in both pipes, subject to the same pressure difference across the lengths of the pipes. If th+6a38nuy npxj e flow rate in pipe B is Q, what is the flow rate in pipe A?

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34#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  When soup gets cold, it often tastes greasy. This "greasy" taste seems to be am wegz p/n66)pssociated with oil spreading out all over th)6pzep/wnm g 6e surface of the soup, instead of staying in little globules. To us "physikers", this is readily explained in terms of

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35#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  When a tube of diameter d is placed in water, the waterbdk*7,(ydlm/n1o96 kz rryhx rises to a height h. If the diamet k*don (dryrhm/,9blky17x6z er were half as great, how high would the water rise?

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36#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Certain insects, such as the water bug, are sufficiently lightweink)prk)*)c* ;wfo ls eght that they can run on top of water without breaking the surface tension. Water bug A has weight W. Water bug B is twice as big as bug A, in all dimes)ncp;*) *oelf rkw )knsions. That is, bug B is twice as long, twice as wide, etc. What is the weight of bug B?

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37#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Certain insects, such as the water bug, are sufficvp3f1qb s+4.fl fr g)m/uzq*siently lightweight that they can run on top of water without breaking the surface tension. This is possible because the water, due to surface tension, exerts an upward force on the bottom of the bug's feet. Suppose that the maximum possible upward force on the feet of water bug A is F. Now suppose that water bug B is twice as big as bug A in every dimension. That is, bug B is twice as long, twice as wide, etc. What l34rg . 1ffzq+fq supm *v/)sbis the maximum upward force on the feet of bug B?

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38#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A plastic block of dimensions 2.00 cfo9,f je7 nd-la 36vmem x 3.00 cm x 4.00 cm has a mass of 30.0 g. What is its densite d- 7mo9lf 6,nvfj3aey?

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39#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A liquid has a specifo3.m) etk* ku*a * zvl1plktr:up)p;uic gravity of 0.357. What is its density?

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40#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A brick weighs 50.0 m y9e93qxv gy.g.h 4tiN, and measures 30.0 cm x 10.0 cm x 4.00 cm. What is the maximum pressure it can exert on a horizonta. eg.h4yygixmq9t v9 3l surface?

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41#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A person weighing 900 N is standing on snowshon ux2f6.lvd7 h 7ag8 n3 r+7lcyw 8ld+fo-dxtfes. Each snowshoe has area $2500 \; cm^{2}$. What is the pressure on the snow?

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42#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  How much pressure (absolute) must a submarine withstand at a depth of 120.0a vt28x-mt;q i1tx8gsw mi68u m in the oceaniq;gi68w - mtxt8 stu1m2av x8?

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43#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A circular window of 30 cmb57szv6r70uy i.mz qj diameter in a submarine can withstand a maximum forcezy m7jbq60iv u 5r.7sz of $5.20 \times 10^{5} \; N$. What is the maximum depth in a lake to which the submarine can go without damaging the window?

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44#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the gauge pressure if the absolute pressure is 300q6 k2eo;m 2 dv/7*hi3ui5a snxrrm3l d kPa?

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45#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the gauge pre*v+id(b7wv (myo0 nylssure at a location 15.0 m below the surface of sea? (The densit (+w*iond yyl07vb(vmy of seawater is $1.03 \times 10^3 \; kg/m^{3}$.)

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46#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the absolute p(/..fidolh)fh,afqdh ) pg n;ressure at a location 15.0 m below the surface of sea? (The density of seawater is )hni fpf.oqddh(,.f;h /ag)l $1.03 \times 10^3 \; kg/m^{3}$.)

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47#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 500-N weight sits on the small pisto j; v;-9armeijn of a hydraulic machine. The small piston hae;r9;-aiv mj js area $2.0 \; cm^{2}$. If the large piston has area $40 \; cm^{2}$, how much weight can the large piston support?

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48#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  In a hydraulic garage lift, the sm +lldz4qa v +m*(cp;:sfa)ewv all piston has a radius of 5.0 cm and the large piston has a radius of 15 cm. What force must be applied on the small piston in order to lift a car weighing 20,000 N ov* ac:ld 4es+ z;flp +(wmv)qan the large piston?

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49#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 13,000 N vehicle is to be lo4r2yi mo;pcvx e1a fad,hh1/db5 ,.f ifted by a 25 cm diameter hydraulic piston. What force needs to be applied to a .v1e142h pdhaod, mbyf5xc,r/a oif ;5.0 cm diameter piston to accomplish this?

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50#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The small piston of a hydraulic lift has a diameter of 8.0 cm4 +bs/w vcnu8o, and its large pist bu8c+/oswnv4 on has a diameter of 40 cm. The lift raises a load of 15,000 N.
(a) Determine the force that must be applied to the small piston    $N$ (fill in numerical value only)
(b) Determine the pressure applied to the fluid in the lift    $\times 10^5 \; Pa$ (fill in numerical value only)

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51#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A block of metal weighs 40 N in air and 30 N in water. j xt j;xxt713h What is the buoyant force of the;7jxtx1 h3txj water?

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52#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An object has a volume onc3ybd40uua2p :(xl 5v6hzcu(,ux buf $4.0 \; m^{3}$ and weighs 40,000 N. What will its weight be in water?

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53#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 4.00-kg cylinder of solid iron is supported b b*qsexw lyw6 v p6++.z;0mhimy a string while submerged in water. What is the tension in the string? b* m6l++. vih;psw em0yxw6qz (The specific gravity of iron is 7.86.)

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54#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  If the density of gold v/au k7cb mlv)8 n,8xs,ht-0q f2rbzris $19.3 \times 10^3 kg/m^{3}$, what buoyant force does a 0.60-kg gold crown experience when it is immersed in water?

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55#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A crane lifts a steel submarine (density = ji1b*42 vsqka $7.8 \times 10^3 \; kg/m^{3}$) of mass 20,000 kg. What is the tension in the lifting cable (1) when the submarine is submerged, and (2) when it is entirely out of the water?

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56#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An object weighs 7.84 b4l5ob2map(ol6 viv7+f jjo8N when it is in air and 6.86 N when it is immersed in water. What is the specific gravity of th47(fov8+blli o6 jompa5b vj 2e object?

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57#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A container of water is placed zgc5c3w46y:ctx/t/ ;l pa ;qqxg.jiw on a scale, and the scale reads 120 g. Now a 20-g piece of copper (specific gravity = 8.9) is suspended from a thread and lowg/gwci4 /zq5a cc; .3xqwxt tjl y;p:6ered into the water, not touching
the bottom of the container. What will the scale now read?

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58#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A piece of aluminum withz(0 o7qd ys(m0i6bss7o vl; ce a mass of 1.0 kg and density of $2700 \; kg/m^{3}$ is suspended from a string and then completely immersed in a container of water. The density of water is $1000 \; kg/m^{3}$.
(a) Determine the volume of the piece of aluminum    $\times 10^{-4} \; m^3$ (fill in numerical value only)
(b) Determine the tension in the string after the metal is immersed in the container of water $N$ (fill in numerical value only)

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59#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A cylindrical rod of length 12 cm and diameter 2.0 cm will just barely float i4ul +i4x4( uvs0w /epair x-g8u +dkqxn water. What is ++40qkl4 p-xgwux /8i suxr 4iaeudv(its mass?

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60#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A rectangular box of negligibqrcdxi(+f :r3le mass measures 5.0 m long, 1.0 m wide, and 0.50 m high. How many kilograms of mass can be loaded onto the box beffi3q r d(:xr+core it sinks in a lake?

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61#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A $1.0 m^{3}$ object floats in water with 20% of it above the waterline. What does the object weigh out of the water?

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62#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An object floats wit1 hue3t;nrvc bdd6-b5h half its volume beneath the surface of the water. The weight of th3 - ur;6nd hv1ed5bbtce displaced water is 2000 N. What is the weight of the object?

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63#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A solid object floats in water n2 8/-wgwmop7h+a3: if gecxh with three-fourths of its volume beneath the surface. What8cg7ww f:o-xhen/2mi ap+ 3gh is the object's density?

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64#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 200-N object floats w+6rymo+q rk,y;mft. wcxlq) .ith three-fourths of its volume beneath the surface of the wat)6xqy +fmrr;wqc+.olmy., kt er. What is the buoyant force on the object?

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65#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A polar bear of mass 200 kg stands on d5xofe mll)ee9vx 3) :an ice floe 100 cm thick. What is the minimum area of the floe that will just support the bear in saltwater of specific gravity 1.03? T: vxe5ll9)emd3x) eof he specific gravity of ice is 0.98.

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66#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Liquid flows through a pkigo+mo1 t,:s x x74qmipe of diameter 3.0 cm at 2.0 m/s. Find the flow rate.

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67#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Liquid flows through a 4.0 cm diameter pipe at 1.55 gum8h ) p 61xxzbls2h4wyhu0 m/s. There is a 2.0 cm diameter restr2y4hbx sulzwu518m 6gh5pxh)iction in the line. What is the velocity in this restriction?

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68#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Water flows at 12 m/s in a horizonteltbu7 t38s9i al pipe with a pressure of $3.0 \times 10^4 \; N/m^2$. If the pipe widens to twice its original radius, what is the pressure in the wider section?

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69#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  How much pressure does it take for a pump to supply a drinking fountain with 38 48:yy2v;dwedoe s xd00 kPa, if the fountain isoe v;s8 de8xd2:4 ydwy 30.0 m above the pump?

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70#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A hole of radius 1.0 mm occurs in tvs*0e1 j2eg1 6 opepjvhe bottom of a water storage tank that holds water at a depvp*1vo60 2eesjg pje1th of 15 m. At what rate will water flow out of the hole?

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71#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Water flows through a horizontal pipe of cross-sectionac t8uth7t*. u.2 zvs cknb48ial area $10.0 \; cm^{2}$ at a pressure of 0.250 atm. The flow rate is $1.00 \times 10^{-3} \; m^{3}/s$. At a valve, the effective cross-sectional area of the pipe is reduced to $5.00 \; cm^{2}$. What is the pressure at the valve?

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72#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  SAE No. 10 oil has a viscosity of 0.20 Pa-s. How long would it take to pousm t50; p4.pkkcghw g2,fmxnga9 h6l.r 4.0 L of oil through a funnel wit9pm, mnkl6g .p.th5x4 0hacws;2gfkg h a neck 15 cm long and 2.0 cm in diameter? Assume the surface of the oil is kept 6 cm above the top of the neck, and neglect any drag effects due to the upper part of the funnel.

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73#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Suppose that the build-up of fatty tissue on the wall of an artery decr7een ylz8(k 1ttu*e0ieased the radius by 10%. By how much would the pressure provided by the heart have to be inke (ile8yt*zt0 7uen1creased to maintain a constant blood flow?

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74#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Two narrow tubes are placed *x+ . z3xq2vxzfqal,s in a pan of water. Tube A has twice the diameter of tube B. If water rises 24 2vfx ,s q ql+z.xz3a*xcm in tube A, how high will it rise in tube B?

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75#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The surface tension of watq.1j;w; tm(dlx/rl ca er is 0.073 N/m. How high will water rise in a capillary tube of di/ j(m ;wdt.r1l calx;qameter 1.2 mm?

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76#
 
  232

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77#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  To what height would water at 0 degree Celsius risen e 22hro2dvr6qw;v b .d*f3bs in a glass capillary tube with a diameter o 2qfdsb ed6 3o2bvn;r.2v rw*hf
0.50 mm?

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78#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A narrow tube is placed vertically in a pan of water, and the water rises in thmpjlrfj;nl+-p 2 3shgw71; nvn5c ha(e tube to 4.0 cm above the level of the pan. The surface tension in the liquid is lowered to one-half its origina3j7w ( cfvprnh1sn-; l l;nh+5 2gmpjal value by the addition of some soap. What happens to the height of the liquid column in the tube?

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79#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Consider a rectangular frame of length 0.120 m and width4:78sk0e+hejkx1 a /pjxnb cw+piz y 4 0.600 m with a soap film formed within its confined area. If the surface tensikcxkxy+4aze: ji48nse/ h 1 b0pwp+ j7on of soapy water is 0.0260 N/m, how much force does the soap film exert on the 0.600 m side?

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80#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An adjustable rectangular frame has length 12 cm and width 5 cme78:)wo1p mpfd3r fbv, and is built in such a way that one of the longer sides can be moved wit 3 fr :vmfew718opdpb)hout bursting the soap film contained in the frame. Soapy water has surface tension 0.026 N/m. How much work is required to move the adjustable long side so that the frame is 12 cm square?

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