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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: 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 matt9p e/x9uvbioke8 -8vq1 c2xkxer 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 densij an61:c40uelk jon g.+uw wcybr9g-)ty 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 a unit of45 8n qpfxzg1mzj1i5lp .aq5 o 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 base, anv ow:0 shyg2l-d 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 -: w02yo hvglsso 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 t(vmgq: +t :qjk/(wm ciire 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 jb22y)uqh e2 tto the absolute pressure at the ejyq2bh)2 2utbottom 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. If you dive to 2yj 8c8.n.- 9 e -q0hp/dre+ab9exhujqow- upn.0 m benjppuueeq8d c qx9jyn+ar-8h--0.. eb9hno / weath 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 principle.tkdah k2 e8 )eo9f5(nc
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11#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
State Archimedes' princ-cgpw sf /p6s4iple.
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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 water0 ,sjmcave +4l8mj /ft*: gljd of constant density, what happens to the buoyant for gtsf8ld*me:,4c/ l v0aj+jm jce on 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 water. A boat flog*(uh2;qk eap ats in both fresh water and in salt water. Where is the buoyapk ;(aq*geh 2unt 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)/ry sy4op k2w 77c ;ynh,jvpy floats in both fresh water and saltc 7 j;y,/w4vphy7yo2nk pys r) water. Compared to the 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. Where ibh:yjq 8ip g1vx+i3v 5s the buoyant force on the ball greate18g5 qh3y + i:pvixbjvr?

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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, rigpqbb0th -gbkl.+0y :/cr ,yxuxdv3 u -ht next to a 10-kg piece of lead.vhgd0br+u-y b-x b , 3/0uqpltk:xcy. Which 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 of a piece of wood floatin/-x iw f9lyp;9 lo(0jol dzx,vg in a bathtub. If the iron is removed from the wood, what happens to the lv-0wxjo/lpl ;( 9z 9ixd,yofwater 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. A second piece of woodpq9prkc2 h9 e0 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 level p9ecrqp h 9k02in 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 p5.:xfod-dpkaqi2cm u: m3d)u ipe at point B is larger than at point A. Where is the i)5 du :qm :pfod-.umca2kx3dspeed 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 pipkm/1u(x 5kklje widens to twice its original radius, what is the flow speed in the wider sectio5m1l(jk/ xukkn?

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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 th8,hyoanh/s(a8z jemu0i, .ho e pipe narrows to half its original rajh0.h(yoo nz,8saih,um 8/ eadius, 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--dz6h;j p2so e9l 5em2-.yaqr zmfsu e.
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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 consery5;tji2byzu.qu sl(8 mo hsg3 .( cz(qvation of energy in futhq(35yq ; jc zl2u(zs. 8s.mb(g ioyluids?

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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 pressure in the fluz kyrm;i21x-pf;h o0bid

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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 ps:1q*g cwwj -r3jybm8ipe at point B is larger than at point w gy183b -j:*rsqcmjw 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, the paper rises. This is bqd1 yek 9o)jv0ecause

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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 re6f(ucwy ikc 7)sistance on hicc(fu7yk i6)w m 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 oaf iplgqv1hpv1 )/,+ radii R and 2R, are released simultaneously from a tall tower. Which will reach thepg/q + ov,h)1i apfv1l 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 exper;keis*e iji6+ wr))uf iences a drag force+ i i;ijesuerw))* 6fk $F=arv$, 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 dsb) cndagv4*j jpe;1-p ye81*nd6it the flow of fluid through a narrow pipe? That is, if you made a 10% change in each of the quannp btg-)*deje8641p;s y*ddija nvc 1tities 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 leng4) vvxtf5;4v dd6xnmrth, but pipe B has twice the diameter of pipe A. x5fv 64d);nrv mx4tvdWater 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 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 pipe B is twice as long asfpi4( d6hpr8 0qvc. zvcbu23m pipe A. Water undeuv3mbchf. irpvz2 dp c486q0 (rgoes viscous flow in both pipes, subject to the same 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" tas7m: v t5j7z vclu0sc+ute seems to be associated with oil spreading out all over the surface of the soup, instead of staying in little globules. To us "physikers", ttlv5cjvmc 7s7u u:z0+ his 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 water ris li-i(ghv+5)kx sxhn ,bhu -u5es to a height h. If the diameter were half as gre-u5 i n(gx5s hhbi+,)uk- lvxhat, 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 suffici 28tdx+yt +,gd6sngpsently lightweight that they can run on top of wx2dt,gy nsts8+ 6+pdg ater 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 sufficiently lightw um005zjc3z wnz/)i mweight 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 dimensi zwnwc53 0)/muz0jm zion. 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 2.00 cm x 3.00 azrm(c 7pxkz)3z b(8d cm x 4.00 cm has a mass of 30.0 g. What is its den zrmc(b3 zz k7px8ad)(sity?

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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 gravity of 0.357. What is its density pe7+8t5iaamw?

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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 +nsqsy /y./ qhk3)vdo.0 cm x 10.0 cm x 4.00 cm. What is the maximum pressure it can e/+vyy)dq k3 q noh/.ssxert on a horizontal 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 sta r3e) jktowb-1nding on snowshoes. 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-5+-0s, qktopghqbz i a depth of 120.0 m in the oceaop +i 5g,-qsht- bkqz0n?

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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 ck1bjq1ju17is5m a3 ja maximum force o j1 1j7jcmqk51biusa 3f $5.20 \times 10^{5} \; N$. 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 prelr-m+3y -ifkb z2ls.ossure if the 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 m below the surface of sea? 87ithh *d- hh2qw-chn(The densit7dh2h-ih-*wht 8 hncqy 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 of a 30em+ c bl8bi5b+3btczc1wq7cy7nn sea? (The density of seawater z0cc83+niq c7ye+cawb bm 17b3ntbl5 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. The small pistohmg c.d,7d b7, zgvq3hn h,c,d dbv37mq. zghh g7as 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 small piston has a radius of 5.0 cm and the ln o0c20v 6q gjz xu/59on 8k(cercizx1arge piurc1g2ok6(xe 0 nz90 oc5 q jzc/8nvxiston 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 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 k0kl+4 axh/ly 25 cm diameter hydraulic piston. What force needs to be applied to a 5.0 cm diameter piston to accomplish thax + 0l/ky4klhis?

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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 cm, and isqm1w(q9q6qi2)x n su ts large piston has a q1sxwm n9squq) 2i(6qdiameter 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 )qe7yy7 bhiokjzsy ,*7bvb* +30 N in water. What is the buoyant force of +jqyes7)bz7i*b k , *y 7vhoybthe 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 of gx (6m-71m3alyal esvlz3h)i$4.0 \; m^{3}$ 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 4.u d1xwfyf6s while submerged in water. What is the tension in the strin46f fxsyd1wu.g? (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 goldi( ,n6hji 1mnn 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 submarine (ocvv *3q7mbx9density = $7.8 \times 10^3 \; kg/m^{3}$) 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 6pj 0b+2zkx.mcdc (a pimmersed in water. What is theb6m0 c z2k +paj(p.cxd specific 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 waterqbys3) xno3d(atibrlsy;. : 4zgo, a 9 is placed 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 lowered 4saz)r,(id3 a 9obn;t .x :lyy3obgqsinto 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.w d9hi+bcus 8,0 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 wilbg) flttsdz+jipu,4 gp26 4)cl just barely float in tj2+)bp i ,dtc46szlf4u g p)gwater. What 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 measurxwim9 xb ,r0.)goua -ses 5.0 m long, 1.0 m wide, and 0.50 m high. How many kil w9),a0bgiuor-x.x msograms of mass can be loaded 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 6lf5:qk ne ul 9vdmi* lk7zcru80p(y*its volume beneath the surface of the water. The weight of the displaced water is 2000 N. What is the ull:kln *0qup6fek (9 *5i zrcvmd8y7weight 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 ben n jd(z*(sxud99h9 mtdeath the surface. What inu(xm htdj 9zd9 9(*dss 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 with three-fourths of itstf :13hw n99:ytov yk)m vafu. volume beneath the surface of the water. What is the buoyant forcttw1)3:vkuo vm a9y 9ynhf.f:e 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. Whato8h rsd 7- z.)1qekgre is the minimum area of the floe that will just support the ohkz .s-rq deer817g) 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 ra*4nxq hvr- -bv(zae,+dfe *ndte.

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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 1.0 m/s. There;jf zkj9u1jq( l+ov bh9pn)* b is a 2.0 cm diameter restriction in tu n9h(pjvkbqz +1;* f9jo j)lbhe 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 horizontal pipe woew m4 ,nt-6nbith 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 az+zc 3o id y5;x;sy5ka pump to supply a drinking fountain with 300 kPa, if the fountain is 30.0 m above the cazsxyk+3 iyzd 5o5;;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 bocbb2(y;5ycp cx-xw i84fwu8*ijdz,er. g 3g w ttom of a water storage tank that holds water at a depth of 15 m. At what rate wili -cby4fijw8x8eugy 2cw;(5 .zgd ,*cbpw 3xr l 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 cro5c.qqpui/ s -c:+mus bru03e hss-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 Pbq6lk tx, bo,)a-s. How long would it take to pour 4.0 L of oil thro , l)qb6,kxotbugh 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 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 tissuhma-u713v la we on the wall of an artery decreased the radius by 10%. By how much would the pressure provided by the heart have to be inw1ama 3v-u 7lhcreased 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 pa 3a y3xp7.evs /4modmq in2+kbn of water. Tube A has twice the diameter of tube B. If wm3 eq+ s7pkay24 inv. dxob/m3ater 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 wat9qjf , co5wmv d,y9q/ver is 0.073 N/m. How high will water rise in a capillary tube of diametermcvo vfj ,q,qd5/9 y9w 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 Celsun5h 84qgn) qxog8p 5rius rise in a glass capillary tube with a diameter88n h5 go)x54qr uqnpg 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 6j1 ojz+ql4sfvertically in a pan of water, and the water rises in the tube to 4.0 cm above 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 hz6j+1 oqls4 jfappens 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 widyv1:+e)9 klbd7aaj d69shj d o5-gdtnth 0.600 m with a soap film formed within its confined ars+ao5h9galdy d-)19ebd7j vdktn : 6jea. If the surface tension 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 rectangul9rm 94fr;gil- rqgx3o ar frame has length 12 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 gr4 mr lx39q-of9ri;g0.026 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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