解:(1)∵ρ=

,
∴水的體積:
V=
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=
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=2×10
-3m
3;
(2)∵是圓柱形容器,
∴水對(duì)容器底的壓力:
F
乙=G
水=m
水g=2kg×9.8N/kg=19.6N,
水對(duì)容器底的壓強(qiáng):
p
乙=

=

=1960Pa;
(3)酒精對(duì)容器底的壓力:
F
甲=G
酒精=m
酒精g=1.8kg×9.8N/kg=17.64N,
酒精對(duì)容器底的壓強(qiáng):
p
甲=

=

=1102.5Pa;
∴p
甲<p
乙,
抽出相同質(zhì)量的酒精和水,△F=△G=△mg,因?yàn)镾
甲>S
乙,由壓強(qiáng)公式可知

<

,即甲容器減小的壓強(qiáng)小于乙容器減小的壓強(qiáng),會(huì)使容器底受到的壓強(qiáng)相等;
抽出相同體積的酒精和水,因?yàn)椤鱂=△G=△mg=ρ△Vg,酒精的密度小于水的密度,所以△F
甲<△F
乙,而S
甲>S
乙,
由壓強(qiáng)公式可知

<

,即甲容器減小的壓強(qiáng)小于乙容器減小的壓強(qiáng),會(huì)使容器底受到的壓強(qiáng)相等;
倒入相同質(zhì)量的酒精和水,△F=△G=△mg,因?yàn)镾
甲>S
乙,由壓強(qiáng)公式可知

<

,即△p
甲<△p
乙,即甲容器增加的壓強(qiáng)小于乙容器增加的壓強(qiáng),會(huì)使乙容器底受到的壓強(qiáng)更大,不會(huì)使容器底受到的壓強(qiáng)相等;
倒入相同體積的酒精和水,因?yàn)椤鱂=△G=△mg=ρ△Vg,酒精的密度小于水的密度,所以△F
甲>△F
乙,而S
甲>S
乙,不好確定

和

的大小,不能確定△p
甲與△p
乙的大小關(guān)系,不一定使容器底受到的壓強(qiáng)相等;
由上述分析可知小明和小紅的設(shè)計(jì)可行.
小明同學(xué)的設(shè)計(jì):
∵p
甲=p
乙,
∴1102.5Pa-

=1960Pa-

,
即:1102.5Pa-

=1960Pa-

,
解得:△F≈22.9N,
∵△F=△G=△mg,
∴抽出液體的質(zhì)量:
△m=

=2.3kg;
小紅同學(xué)的設(shè)計(jì):
∵p
甲=p
乙,
∴1102.5Pa-

=1960Pa-

,
∵△F
甲=△G
甲=△m
甲g=△ρ
酒精Vg,△F
乙=△G
乙=△m
乙g=△ρ
水Vg,
∴1102.5Pa-

=1960Pa-

,
1102.5Pa-

=1960Pa-

,
解得:
△V=1.75×10
-3m
3.
答:(1)水的體積為2×10
-3m
3;
(2)水對(duì)容器底部的壓力為19.6N、壓強(qiáng)為1960Pa;
(3)小明和小紅同學(xué)的設(shè)計(jì)可行;抽出酒精和水的質(zhì)量為2.3kg、抽出酒精和水的體積為1.75×10
-3m
3.
分析:(1)知道水的質(zhì)量、水的密度,利用密度公式求水的體積;
(2)知道水的質(zhì)量,利用重力公式求水重,因?yàn)槭菆A柱形容器,水對(duì)容器底面的壓力等于水重,又知道底面積,利用壓強(qiáng)公式求水對(duì)容器底的壓強(qiáng);
(3)同理求出水對(duì)容器底的壓強(qiáng),可知水對(duì)容器底的壓強(qiáng)大于酒精對(duì)容器底的壓強(qiáng);要想使水和酒精對(duì)容器底部的壓強(qiáng)相等,采取的辦法就是倒入水和酒精產(chǎn)生的△p
水<△p
酒或抽出水和酒精產(chǎn)生的△p
水>△p
酒,據(jù)此判斷哪個(gè)設(shè)計(jì)可行,再利用壓強(qiáng)相等列方程求解.
點(diǎn)評(píng):本題考查了學(xué)生對(duì)密度公式、重力公式、壓強(qiáng)公式的掌握和運(yùn)用,知識(shí)點(diǎn)多、綜合性強(qiáng),分析時(shí)要求靈活選用公式,注意液體對(duì)直壁容器(圓柱形、方形)底的壓力等于液體重.