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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: 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 mabc/ p3d3s/w s5wegz6btter 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 density 92ibr(o mi)qh8mzo ed)lj ( 4yof $3.0 \; g/cm^{3}$ 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 followi2r2mgy d959ak4 ytzw xng is not 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 nzq-x+ mu8 7 1o0ogqrq0bji1da*fr3a area base, and all thre31bo qar008x zg fmo1rauji qn7*-qd+e 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 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 outside a tire called?;gw h-ej dw3:e

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8#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  When atmospheric pressb 69c q;7rrw, klyob j-(f-vwcure changes, what happens to the absolute pressure at the bot; r rb-cj6qyl-,vwfwcko(b 97tom of 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 of a pool. Ihiu* ld;t(i k6p0)jhqf you dive to 2.0 m be p;0lh u*ki(j)6qih tdneath the surface, what 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 principbr evfc x7 hew:2.(f8ble.
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11#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
State Archimedes' princiy/ra5uuz62 fw(xhu awi e,5: kple.
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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 water 7rw5 38nk1h/otu d nxry8 b6deof constant density, what happens to the buoyant force oenox 6t8urnwr5dd h3k/ b81y7n 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 than5l e6.wmkz y,e fresh water. A boat floats in both fresh water and in salt water. Where is the buoyaemlwy 5.6ek, znt 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 both freswe7u t gurzyd;0 1by)3-tuhp :h water and salt water. Compared to the fresh water, the volume of water displaced in the sal)ghbyu -e 7: ;3rdy utu1wptz0t 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 merc5y5 w/ch 15y/ ;b jq)dlnbyqriury. Where is the buoyant forcqy d r5iqhbljb//n)cwy1 5y;5e 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 sits at the bottom of a lake, right nexdty (o0em f2y,c3 y;xlzg6-pst to a 10-kg piece of lead. Which has the greater buoyan d,cf my2yg0eyst -36(pzo ;xlt 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 f9rvo m 4) z3nyt,zpk,in a bathtub. If the iron is removed from the wood, what happens to the water level in )yn4 r9mtfz,pzk3v, o 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. A second piece of wooymh6z -1 s3jgm)raliub1 22jhd sits on top of the first piece, and does not touch the water. If the top piece is taken off and placed in the water, what happens to the water levej 326us 1 r z1yhmh-abmli)j2gl 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 diamecc b4n+/vj w55syyo, eter of the pipe at point B is larger than at poin wcs5yv+n/b 5y,4ojcet A. Where is the speed 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 hor;17qavc ylhl-* x.jap izontal pipe. If the pipe widens to twice its original radius, what is the flxjp lhq7lav.*y 1a ;c-ow speed 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 horizontaz.ie0b4yxn h)oh ,(ro l pipe. If the pipe narrows to half its original radius, what is the flow speed in the narro ye)on h4z(box.ihr, 0wer 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 prinykys w90 /ikdehcd ,+9wxt0+pciple.
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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 ene, (7v0quzmqm giqs w+3rgy in fluids?+gq3m,0 suwv iqmq7 (z

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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 fixmb qd + 7c3;g kgai:35svsa;luid increases, 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 a pipe. The diameter of the pipe at point B is larger tg qyw-4w:gracyitn j-hl.,3f o6 7b3jhan at poin63: obry,wf-gcn7-q 3jw.lj4 gih tyat A. Where 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, z -w3v w9x0sevthe 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 the n, w4lcwks- n;air at terminal velocity. The force of air resistance on himwkn s4 -nwc,l; 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, of5dm-zjyylxwyk;9 k 2* radii R and 2R, are released simultaneously from a tall tower. Which w;kkj2*d5-m 9wyzl yyxill 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 fallsy 88ys54s sctj through water, it experiences a dry48c5 t ss8syjag force $F=arv$, 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 through a narrow pipe? rj pp+z0mg k*-That im-+gp *pj0krz s, if you made a 10% change in each 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,l(gtl 6k-r2tbug/, tf but pipe B has twice the diameter of pipe A. Water undergoes viscous flow in both pipes, subject to the same pressure difference across the lengths of the pipes. It2 fb rllk( -t/ug,t6gf the flow rate in pipe A is Q, what is the flow 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, bc i+4*+oyfg4 )z o:whifd oyo.ut pipe B is twice as long as pipe A. Water undergoes viscous flow in both pipes, subject to the same pressure differenodc)4gz o ++*fi4 h .wf:oyioyce 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 "greas-v3 ez:0z1sxb7soq yr y" taste seems to be associated with oil spreading out all over the surface of the soup, instead of staying in little globules. To us "physikers", this is readily explained in terms o0bxezs13 rysq v7z-:o f

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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 wg * s3qq9lt.laater rises to a height h. If the diameter were half as great,.lqltq3a 9s *g 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, abzg26abz o-nzfy*r:hcf4 z s xpq +(8)re sufficiently lightweight that they carxyzzbsq-n82ff:p zz6)* ( 4ahc bg+o n 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 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 x 6.n.m,srhf5 vzr:qe bug, are sufficiently lightweight that they can run on top of water without breaking the surface tension. This is possible because the water, due to surface tensiqn:ve.x5z r,s6mr hf.on, 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 dimensions 2vzz6qyeh;: g)l gy7o5.00 cm x 3.00 cm x 4.00 cm has a mass of 30.0 g. What ;g:yv 7zhgqy z o5)6leis 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 specir(o ;b;6mpgu efic 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 N, and meas25z1f.9jmk b gisp/z 6kbilz- ures 30.0 cm x 10.0 cm x 4.00 cm. What is the maximum pressure it can exert on a horizo i2kl19jgmb zsf .-/b z6ik5pzntal 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 sns+xnf.3t kskhez,vi 9yi2w1;1zjn 5 wowshoes. 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 an (dcpb6pb*75q:d y m in the ocean?pbbq76cpndady* (:5 a

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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 submarine can withstand a maximum forc h) .1sxycm*dzuvnv 20e o.zs m)ux0 *1nhcvvd 2yf $5.20 \times 10^{5} \; N$. 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 1jlld l /g8;f(o3sovuthe 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 location 15.0 / va96;cs qtprq-o h1sm below the surface of sea? (The density of seawvq-pth 9rqo; 6sas/1c ater 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 of sea? py)3/z b0 doms(The density of/3py) s0 zdobm 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 piston of a hydraulic machine. si a(nps9+.th0ufbo 8 The small piston has ar9f0 s(p +ohs t.uniba8ea $2.0 \; cm^{2}$. 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 l-(bo it rw .w/wa6owi)ift, the small 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 on the large pisto/w -irbo)6(www itao.n?

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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 cm diameter ib .5 bff696s sdze+h*8k odlzhydraulic piston. What force needs to be applied to a 5.0 cm diameter piston to accompl.zk6*of fs 6ed5+8bdbh zsil9ish 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 hy r 14iku iou.9qg54gutdraulic lift has a diameter of 8.0 cm, and its large piston has a diameter of 40 cm. The lift raises a load of 15,04rk5ut iiu49u 1ogg.q 00 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 watehb k e6nd0qtps- 3qf; lkjp-(,r. What is the buoyant force k kbq0; f-t(6d3pp-l hjqne ,sof the 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 volujx3gw:eyh6 va:pw4 /f 2ar7tvme of $4.0 \; m^{3}$ 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 string while submerbb)-vm 1ago f(lbv ;b8ged in water. What is v- ba vgob)bb;8(lf1mthe 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 gold 4x 9evu-dfdva4 m(+ro 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 submarinetq;6p+jtrp9p -k,a5 4 ivowrt (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 ai iytbxst9 t9,iq,,b*q)loq x- r and 6.86 N when it is immersed in water. What is the specific gravity of th,bl),x,9si*qt q qt y-9itob xe 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 scale, and the scale reads 120 g. cekeg-) u0zvx3g2imad 4oe5; Now a 20-g piece of copper (specific gravity = 8.9) is suspended from a thread and lowered into the wage k54dzc)go2ui3 xa0ve-;em ter, 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 it 9 uk 5i2gq5ayh1n7xwith 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 d lxj s6k2z;w)ciameter 2.0 cm will just barely float in water. Whatlwk z x6cs;2)j is 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 negligible mass measures 5.0 m l3;bmn 5yoze7khr8 +-*a:l4 eo inuumtong, 1.0 m wide, and 0.50 m high. How many kilograms of mass can be loaded onto mu 7 lr-e5khe8 o3ibnunta;+mz4:oy*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 b a-d:tk)p- v txe 7wv6v,il9uqeneath the surface of the water. The weight of the dispad9qt7,6wtvp: e x- vluk)iv-laced 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 with three-fourths of its vo1-wl 5c--bj.0boqd9t iwei9qem 9f gflume beneath the surface. What is the object's debmdqbfigi f -o5t9.c 0-el1ej 9-9wwqnsity?

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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-fourths of i0fh9 nf l-bs*yts volume beneath the surface of the water. What is the buobf s0fyln-9*hyant 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 an ice floe 100 cm thick. What 0h :.2rwbileveq9ebmr3l2* h w y.h*iis the minimum area of the floe that will just support the bear in saltwater of specific gravity 1.03? Theibhir3e 2 ql.*r0*veeh:myw 9lwhb.2 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 dity1yzj)c/wktngf 5 i.w ww/al zqo r 49*16q0cameter 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 1.08(hk vl/acy 6nubww j+1;cix0 m/s. There is a 2.0 cm diameter restriction in the line. What is the velocity in this restri y8vbl; /a w+wni1xjcu6(k0hcction?

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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 hori jcw9flaqfoa6 6oj+ ;8zontal 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 drinkisz .(ff- 0mok3qmhdxt 6kf-z)ng fountain with 300 kPa, if thkt- 3mfxf6zkhfm-0q) o d.z(s e fountain 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 thd z7m-* +xr(my/fjbqoe bottom of a water storage tank that holds water m7 z/yofbjmqx+d -(r*at a depth 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 r;0p j5.ex ,(ba6lird ebx.d+bx umt;cross-sectional 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 mrk/t czga4(* 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 kept 6 cm above the top of the neck, and negl*mg a ztk4cr(/ect 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 the2 gz2drdu 13ek wall of an artery decreased the radius by 10%. By how much would the pressure provided by the heart have to be increased to mage23u1d2krz dintain 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 6hz )fp) o2u(rb8wlnra pan of water. Tube A has twice the diameter of tun)hp r) fwr 86uobzl(2be 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 water is 0.073 N/m. How high will water rise bd: o,2za;pey in a capillary tu;pe2 obad:y ,zbe 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 - eig.gru;sy, 0 degree Celsius rise in a glass capillary tube witi yge;-,g.r suh 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 pan of water, and the water rises in j)2d*ha fit q-s7 9fefthe tube to 4.0 cm above the level of the pan. The surfaceaj9fse2*if)d-t 7 f hq 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 frame of length 0.120 m and width 0.600 m with f+zf7p; :u9*vcqelu 8*jrxtcoq.t)i a soap film formed within its confined area. If the surface tension of soapy water is 0).*te9qut oc ;7vp if*j+cuqr:8x flz.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 1.k, x6+eqqz ovu29 obucrfc 9l ;k1k6i2 cm and width 5 cm, and is built in such a way that one of the longer sides can be moved without bursting the soap film contained in the frame. Soapy water has surface tension 0.026 N/m. How mukle6cciv+ .96 o2z,;rxqk9uuq bfo1 kch work is required to move the adjustable long side so that the frame is 12 cm square?

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