题目内容
右图是小敏同学在控究甲、乙两种不同的固体物质的质量和体积的关系时得出的图象.如果用上述两种物质做成甲、乙两个质量相同的实心正方体,把它们放在水平面上,则根据图象可知,甲、乙两种物体对水平面的压强之比P甲:P乙为( )![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_ST/images0.png)
A.8:1
B.4:1
C.2:1
D.1:1
【答案】分析:平面上静止的物体,对水平面的压力等于其自身的重力,两个物块质量相同,重力相同,对水平面的压力也相同.
先根据图象给出的数据求出甲.乙两物质的密度之比,从而推出其体积之比,边长之比,底面积之比,然后利用压强公式即可得出答案.
解答:解:从物质的质量和体积的关系图可知,横坐标为条体积,纵坐标为质量,
则甲、乙两种物质的密度为:
ρ甲=
=
=8g/cm3,ρ乙=
=
=1g/cm3,
∴
=
=
,
因为A,B两个正方体质量相等,即m甲=m乙,
所以
=
=
×
=
×
=
,
又因为都是正方体,
=
=
所以它们的边长之比为:
=
,
则底面积之比为
=
=
,
平面上静止的物体,对水平面的压力等于其自身的重力,两个物块的质量相同,所以两个物块的重力相同,对水平面的压力也相同,即此时F相等,
则甲、乙两种物体对水平面的压强之比为:
=
=
×
=
=
.
故选B.
点评:许多物理量之间的变化关系可以用数学上的图象来形象直观的表示出来,反过来,如果画出了相应的物理量变化图象,我们也能根据数学知识从中分析出物理量之间的变化及其关系.
先根据图象给出的数据求出甲.乙两物质的密度之比,从而推出其体积之比,边长之比,底面积之比,然后利用压强公式即可得出答案.
解答:解:从物质的质量和体积的关系图可知,横坐标为条体积,纵坐标为质量,
则甲、乙两种物质的密度为:
ρ甲=
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/0.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/1.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/2.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/3.png)
∴
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/4.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/5.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/6.png)
因为A,B两个正方体质量相等,即m甲=m乙,
所以
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/7.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/8.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/9.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/10.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/11.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/12.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/13.png)
又因为都是正方体,
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/14.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/15.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/16.png)
所以它们的边长之比为:
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/17.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/18.png)
则底面积之比为
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/19.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/20.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/21.png)
平面上静止的物体,对水平面的压力等于其自身的重力,两个物块的质量相同,所以两个物块的重力相同,对水平面的压力也相同,即此时F相等,
则甲、乙两种物体对水平面的压强之比为:
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/22.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/23.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/24.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/25.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/26.png)
![](http://thumb.1010pic.com/pic6/res/czwl/web/STSource/20131024153540861072852/SYS201310241535408610728013_DA/27.png)
故选B.
点评:许多物理量之间的变化关系可以用数学上的图象来形象直观的表示出来,反过来,如果画出了相应的物理量变化图象,我们也能根据数学知识从中分析出物理量之间的变化及其关系.
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目