3.
起重船的工作就是将重物起吊移至指定位置。为了防止起重船吊装重物时发生倾斜,在起重船的船体两侧建造了由许多小舱室组成的水舱。起重船吊起重物后,就通过抽水机将一侧水舱里的水抽向另一侧水舱来保持起重船平衡,示意图如图乙所示。小海设计了一种用力传感器感知抽水量的长方体水舱模型,其底面积为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmsup%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 示意图如图丙所示,其中A是固定的力传感器,能够显示B对它的压力或拉力的大小;B是质量和体积均可忽略的细直杆,B的上端固定在A上,下端固定在物体C上;物体C是质量为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmn%3E20%3C%2Fmn%3E%3Cmtext%3Ekg%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
、高度为2m的圆柱体。水舱中装有
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmn%3E4.2%3C%2Fmn%3E%3Cmsup%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的水,抽水机将水抽出的过程中,力传感器示数F的大小随抽出水的体积V变化的图像如图丁所示,已知水的密度
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3E%CF%81%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3E%E6%B0%B4%3C%2Fmi%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1.0%3C%2Fmn%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E10%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmtext%3Ekg%3C%2Fmtext%3E%3Cmo%3E%2F%3C%2Fmo%3E%3Cmsup%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 求:
![](http://tikupic.21cnjy.com/ct20241o/63/e2/63e2575e49f16980721bdb16a4d040ad.png)