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习题练习:Physics Unit10: Fluids Related Topics



 作者: physics   总分: 80分  得分: _____________

答题人: 匿名未登录  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 maq p g-dp5qp85otter 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 de xr6.nrcubkl+(3:l:bvv skd7nsity 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 not y.( zvl13s(lh cze9i ya 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 ep /08gp p0me *g3zvmqloj)tf74:kwg. All three have the same area base, 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 wa lo)3jpzm*ev0/:740t kmge 8g p qgpfwter than A. Which glass has the greatest liquid pressure at the 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 pressures inside and outsid ki2/muwtj5,z1pe ub- e 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, what happens to the absolutj i:0wiqn3s/ fe pressure at the bottom of a pool fj:i0w3q/ isn?

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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 benvk1pbm9dtx 2uvw07 1reath the surface of a pool. If you dive to 2.0 m beneath the surface, wt11x 0mpuwbrd v2v7 9khat happens to the absolute pressure 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 principle.faxk zo5 6b;isno08 f(
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11#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
State Archimedes' pr:dl u 3s;z*iupinciple.
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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 deepe /tlhhqrf0o*r. 5b rd5nb y-;mr into water of constant density, what happens to the buoyant force onr *.0nbhh lm fry-5od;q5trb/ 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 density than fresh waterjevz;lv1 *b .6 i3f+6eb mdkdm. A boat floats in both fresh water and in salt water. Wherejdvf+ezb; 1.d6 lm6emb3 *ikv is the buoyant force greater 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 fresh water. A ship floats in bo7wnc ( (lufqr+th fresh water and salt water. Compared to tn rf(qu(l +wc7he fresh 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 floats in a pool of mercury. Wher4*qhjbk+ gwr xn;vat k0; 69vte is the buoyant forcethjn 4v bvatx09wk;6g;kr+q * on the ball greater?

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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 sit dwbhye;6i);v4wk2 eks at the bottom of a lake, right next to a 10-kg piece of lead. Which has the k2e 4b we)wdyhv;k;i6greater 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 of a piece of wood floating in a batgd4y 2+s1 j7t0lj s1ort ,nmbki+xt-qhtub. If the iron is removed from the wood, what happens to the water levedt sj qy0n tj2+,4+gbs1tr-x7oi k1lml 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 cung hhvpb:6 5 krf0v1v 5rt30bathtub. A second piece of wood sits on top of the first pievncbv3:fpg th5k 61rur 0v05hce, and does not 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 a pipe. The diameter of the pipe at point B is lar3unm d8mm dlznlbwrbwkt 3k78/t* .8:ger than at point A. Where is the sdt bkznl /w8bk. :r8u m7*mdlmn38 3wtpeed of the 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 12 m/s in a horizontal pipe. If the pipe wlat k;mgp v).// (dne;gv ih;jidens to twice its original radius, what is the flow speedl p;j/nth)(iade;./gmvkg; v 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/tw,hcpu ;g t nh6s5aw-hgivo1 /3*g3w s in a horizontal pipe. If the pipe narrows to half its original radius, what is the flow spee gaih w;h6 w/wt*3, ovphgc u1sn-5g3td 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 princiau05d 6rey9hlxs +3nj ple.
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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 of conservation of energy r *ut7q +*yktein fluids+ekr*ytt *qu7?

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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 incre:6s p3aqghb7fir bf75xy t(n6 ases, the pressure 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 hhm; 20gxu6d c fq1a3iq6;b-ftxyk6x a pipe. The diameter of the pipe at point B is larger than at point A. W;6; x0ixfuqdmq- x hg 6ct 21f6ky3ahbhere is the water 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, the paper rises. This is be.gpq6fjg(8 khx gj 4l9;u1vos cause

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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 the air at terminal velocity. The force of air m/9h;i gvfa j68c;citresistance otfh8i69;av ic;jm/g cn 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, of radii R and 2R, are released simul6v*mg:tgjw s (taneously from a tall tower. Which will 6gv:(gs*wt mj 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 rock of radius r falls through water, it exr3ce *gxco3v9akp06o+d- x7.h ksx;w6 ypfboperiences a drag forcepe90od36cky6 3 vf7xs .o;rgp *-xcxhwba+k o $F=arv$, 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 the flow of fluid througho6po: zjn+3d k z57vav a narrow pipe? That is, if you made a 10% change in each of the quantities below, which would cause the greatest c+ o7a zpkj3ovdvz:n 65hange 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 dialzrrojupfx)x b :s4p 0,5ah;-meter of pipe 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 flo;40prxzs5r)la p u,: xj-ohbf w rate in pipe 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 t,.qnu sw4j1d8nf lib.t+92lgn gqw7pipe B is twice as long as pipe A. Water undergoes viscous flow in both pipes, subject to the ss q ,u.t n9n.7bitjg g dfw4qnwl182l+ame pressure difference across the lengths of the pipes. If the 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 toniaz.wle8i.2 2+ z gkw be associated with oil spreading out all over the surface of the soup, instead of staying in little globules. To us "p2w2ki. g zilzwane.8+ hysikers", 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 plac8wwa3glgzr +.z6 d q8rz+vny7ed in water, the water rises to a height h. If the diameter were half as great, +r 3ga8gnww +zz7 v.d6 ry8qzlhow 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 sufficiewy90f ep nw,lgy:+f 5rntly lightweight that they can run on tog,y nyper5+ w0f: 9fwlp 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 dimensions. 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 suffici+*wa 5+av.ecuu48 qzj zljpa 1ently lightweight that they can run on top of water without breaking the surface tensionzwp1jace45 z*u uq+a.lja8 v+. 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 is 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 dimensiong- qjd2+uy5az s 2.00 cm x 3.00 cm x 4.00 cm has a mass of 30.0 g. What is5gd+ajz- qu2y its density?

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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 specific gravi2k 6,8msu(txkfq0wtb -v ;tsbty 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 N, and measures 30.0 cm x 10.0 cm x 4.0f.;hzcx- vm qs+- i2tp0 cm. What is the maximum pressure it can exert on a horizontal su 2+tc qizp;-vfhm-x.srface?

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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 snowshoes. 56j59 p0baf mql z8byrEach 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.-akggpq5* nu .i+c zl) must a submarine withstand at a depth of 120.0 m in the oceanq*5.lgi+ gc aupk n-z.?

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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 cm diameter in a subm qm*f qdp2y7z*arine can withstand a maximum force off p2yq*dm*z q7 $5.20 \times 10^{5} \; N$. 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 f:3e6lil*invthe absolute pressure is 300 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 pressure at a locatiof0bjczm5 0z7qqmmty(c 2h:5 j n 15.0 m below the surface of sea? (The den7hbjmf50(mqqmcj0 z z t52y:csity 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 pressure at a location 15.0 m below the surface o+uuqn x wh:16gf sea? (Thx+ gnuu16: whqe density of seawater is $1.03 \times 10^3 \; kg/m^{3}$.)

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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 pisz)res-+w lxi7 gdfy,+ton of a hydraulic machine. The small piston has areaxd gr, zys-)+w l+efi7 $2.0 \; cm^{2}$. 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 small piston has a r-mp w1fq2n cx3adius of 5.0 cm and the large piston has a radius of 15 cm. What forcexf3-pc m q2w1n must be applied on the small piston in order to lift a car weighing 20,000 N on 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 lifted by a 25 c8qecn yn 6kefi.+rfs0j1 a h91jeb )6tm diameter hydraulic piston. What force n tey 9f1 reij .s)6ehn+n jakq0c8b6f1eeds to be applied to a 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 di7+jo n9 bka:- ys2txadameter of 8.0 cm, and its large piston has a diameter of 40 cm. The lift raises a lo 7xtd+on 9syjk a:b2-aad 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. What is the buoyanzuz*s8z+33t s jmjstfod n;+f9 ge3(w t force of the f+tj 3s+ 3;tj9de(fs*z8u nog m zszw3water?

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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 oflkv l-ju; gb). $4.0 \; m^{3}$ 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 by a strintdlyvd s z9,to- *va47)dz1fy g while submerged in water. What is s dfz al,o*yvv-ty7)9z4 1tddthe tension in the string? (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 gomq; ,97 m;-jvud lohkzld is $19.3 \times 10^3 kg/m^{3}$, 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 subfb maah;q*wvu (+/, bimarine (density = $7.8 \times 10^3 \; kg/m^{3}$) 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 N when it is in air and 6.86 N when it is immersed in waty3b6 8-r5rfq v-0dq bmfh(q-yy4ehrqer. What is the s ber-(y65br4mq0 qhfd y--8y 3f vrhqqpecific gravity of the 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 on a scdf (sqsc3k v k 42brto6o37 rr3;cbiw5ale, and the scale reads 120 g. Now a 20-g piece of copper (specific gravity = 8.9) is suspended from a thread and oksrt7b wcrs3 b4cv2qk3 foi3;r6d( 5lowered 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 with a mass of 1.0 kg and density/fid ,1t4 +t0d .dmaxbwh;yvl 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 0b +ar sjitu.4 bh5j +j;f:pcgfloat in water. What is its massh :irtjc 5bg 4+ u+0psjfja.b;?

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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 negligible mass measures 5.0 m long, 1.0 m wide, and 0.524g 3fa tpmxxays4kk -*2)le f0 m high. How many kilograms of mass can be loa4y2) kagps-* t3xme2 xk4lffaded onto the box before 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 with half its volume beneath the surface of the wabt u 7t2)hoc 7bx(wkp;ter. The weight of the displaced water is 2000 N. What7 p27 ;(wt bch)buoxkt 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 with three-fourths of its volume beneath the17 qgwo/nm- xv surface. What is the object's /oxqg mv17wn -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 with three-fourthsrh -osnviih*9k. 5fh 6 of its volume beneath the surface of the water. What is the buoyant force on the objecth9r-voi n 5*i6s.hh fk?

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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 an ice floe 1 h9cf b5ay)e*c00 cm thick. What is the minimum area of the floe that will justycb5afc)e* 9 h support the bear in saltwater of specific gravity 1.03? The 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 pipe of diameter 3.0 cm at 2.0 m/s. Find the flow ratekb. ikapb:/.j.

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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.rff qbqvwt0/+(2c v l:0 m/s. There is a 2.0 cm diameter restriction in the line. What is the velocity vqbtrfw:qf(+2c/ lv0in 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 horh zh,d)2(n hhgizontal 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 ti 08qya w.wt3/d s.kdc gew.a-ake for a pump to supply a drinking fountain with 300 kPa, if the fot -dk. qc3asy w/80.gi wed.awuntain is 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 the bottom of a water stomw)agfl92oj1b1h,yl be f ;i/rage tank that holds water at a depth of 15 m. At what rate will water flow out of thf2m/ag9;1j fblyeohw 1 bl,i )e 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-sectio. eh37i1 6zw 3upq*dxl hyf.axnal 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. Ht6ko)6i 8bugq ow long would it take to pour 4.0 L of oil through a funnel with a neck 15 cm long and 2.0 cm in diameter? Assume the surface of the oil is kepigukb68q)6o t t 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 arq jwv3.(:if iotery decreased the radius by 10%. By how much would the pressure provided by the heart have to be increas :w( 3of.qvjiied 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 in a pan ez+1h.dr 0solof water. Tube A has twice the diameter of rdh1lzoe. +s0tube B. If water rises 24 cm 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 wa18:zufl rly) dter is 0.073 N/m. How high will water rise in a capillarydz f u)8l:rly1 tube of diameter 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 rise in a p 4s9ac k;duje/a5ly8(wv, jn glass capillary tube wit 9ydv5c ,k (pwe4as8au;jj/lnh a diameter of
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 payr,d1n3z c us)n of water, and the water rises in the tube to 4.0 cm abovecusy )3 ,n1zrd the level of the pan. The surface tension in the liquid is lowered to one-half its original 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 framsn*6iugooek5 6 o*6t we of length 0.120 m and width 0.600 m with a soap film formed within its confined area. If the surface tension of soapy water is 0.0260 N/m, how much force does the soap film exert ont*6gukow 66o i osen5* 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 cm0m ezv,ona; w+te.-)h zzv t7f and width 5 cm, and is built in such a way that one of the longer sides can bet f7;za+nhw 0z vo-v,.eet)mz moved without 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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