28.
(2023八下·永年期末)
图甲是某卫生间马桶水箱的进水调节装置,图乙为其结构示意图,浮臂AB可视为绕
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EO%3C%2Fmi%3E%3C%2Fmath%3E)
点转动的杠杆,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EO%3C%2Fmi%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmn%3Ec%3C%2Fmn%3E%3Cmn%3Em%3C%2Fmn%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EO%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3Ec%3C%2Fmn%3E%3Cmn%3Em%3C%2Fmn%3E%3C%2Fmath%3E)
, A端通过细连接杆AC与柱状浮筒连接,浮筒质量为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3Eg%3C%2Fmn%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
端通过细连接杆BD与圆饼状止水阀连接,止水阀上下表面积与进水管口面积均为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3Ec%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3Em%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
。当水箱中无水或水量较少时,止水阀打开,水从进水管流进水箱。水位达到一定高度时,浮筒推动杠杆,使止水阀刚好堵住进水管,停止进水,此时AB处于水平位置,连接杆竖直,大气压强
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmi%3Ep%3C%2Fmi%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmsup%3E%3Cmn%3E10%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmn%3EP%3C%2Fmn%3E%3Cmn%3Ea%3C%2Fmn%3E%3C%2Fmath%3E)
, 进水管中水压
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ep%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3E%E6%B0%B4%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmn%3EP%3C%2Fmn%3E%3Cmn%3Ea%3C%2Fmn%3E%3C%2Fmath%3E)
。除浮筒外其它装置所受重力不计,忽略所有摩擦,g取
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3EN%3C%2Fmn%3E%3Cmn%3E%2F%3C%2Fmn%3E%3Cmn%3Ek%3C%2Fmn%3E%3Cmn%3Eg%3C%2Fmn%3E%3C%2Fmath%3E)
, 水的密度
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmtext%3E%CF%81%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3E%E6%B0%B4%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmn%3Ek%3C%2Fmn%3E%3Cmn%3Eg%3C%2Fmn%3E%3Cmn%3E%2F%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3Em%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E)
。刚停止进水时,求:
![](//tikupic.21cnjy.com/2023/07/27/30/d6/30d62aaa4d65f59eb8b18ef257ab06c9_188x131.png)
![](//tikupic.21cnjy.com/2023/07/27/66/db/66db52fe21a84cc8c271e7dcef9d265e_236x136.png)
甲 乙