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<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">在缺水地区，需要时刻储备生活用水。图示为一种具有自动蓄水功能的长方形水池，A是一个底面积为100cm<sup>2</sup>的方形塑料盒，与塑料盒连接的直杆可绕固定点O转动，当蓄水量达到2.4m<sup>3</sup>时，活塞B堵住进水管，注水结束，水位为H．（水的密度是1.0×10<sup>3</sup>kg/m<sup>3</sup>，g取10N/kg）</span></span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（1）注水的过程中，随着水位上升，水对水池底部的压强逐渐<u>　</u></span></span></span><u> </u><u>　</u><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">。</span></span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（2）注水结束时，水池中水的质量是多少？此时塑料盒浸入水中的深度是10cm，塑料盒所受的浮力是多大？</span></span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（3）若在塑料盒内放入质量为0.3kg的物体，注水结束时的水位H高了多少？</span></span></span></span></span></span><br />
<img src="/uploads/meth/20210528/6b8b4b296939425ed608d680431ace06.png" style="float: right; width: 144px; height: 90px;" /><br />

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<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">解：（1）底部受到水的压强：p=ρgh，随着水位上升，水对水池底部的压强逐渐变大；</span></span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（2）水池中水的质量是m=ρV=1.0×10<sup>3</sup>kg/m<sup>3</sup>×2.4m<sup>3</sup>=2.4×10<sup>3</sup>kg；</span></span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">塑料盒排开水的体积：V<sub>排</sub>=Sh=100cm<sup>2</sup>×10cm=10<sup>3</sup>cm<sup>3</sup>=10<sup>﹣3</sup>m<sup>3</sup>；</span></span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">塑料盒受到的浮力：F<sub>浮</sub>=ρ<sub>水</sub>gV<sub>排</sub>=1.0×10<sup>3</sup>kg/m<sup>3</sup>×10N/kg×10<sup>﹣3</sup>m<sup>3</sup>=10N；</span></span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（3）物体重力G=mg=0.3kg×10N/kg=3N；</span></span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">注水结束时，塑料盒受到的浮力应增加3N，</span></span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">塑料盒排开水的体积增加值：</span></span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">V′=</span></span></span></span></span></span><img height="53" src="/uploads/meth/20210528/e281bff8926f35c0de147f5e646b77e2.png" width="46" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">=</span></span></span></span></span></span><img height="41" src="/uploads/meth/20210528/1e0f89baf5c487386ca7fe0670bbaeb3.png" width="182" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">=3×10<sup>﹣4</sup>m<sup>3</sup>；</span></span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">水位变化：h′=</span></span></span></span></span></span><img height="41" src="/uploads/meth/20210528/f38ba5ae73f218440ee3e6b94e297387.png" width="28" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">=</span></span></span></span></span></span><img height="46" src="/uploads/meth/20210528/7593650f7339672e4e1681efe65e92b5.png" width="81" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">=0.03m；</span></span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">故答案为：</span></span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（1）变大；</span></span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（2）注水结束时，水池中水的质量是2.4×10<sup>3</sup>kg；塑料盒所受的浮力是10N；</span></span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（3）若在塑料盒内放入质量为0.3kg的物体，注水结束时的水位H高了0.03m。</span></span></span></span></span></span><br />

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