题目内容
如图所示,长l的轻杆OA的左端O点为固定转动轴,杆上B点处垂直固定着一个轻杆BC,已知OB=![](http://thumb.1010pic.com/pic6/res/gzwl/web/STSource/20131028201147324588181/SYS201310282011473245881023_ST/0.png)
![](http://thumb.1010pic.com/pic6/res/gzwl/web/STSource/20131028201147324588181/SYS201310282011473245881023_ST/1.png)
![](http://thumb.1010pic.com/pic6/res/gzwl/web/STSource/20131028201147324588181/SYS201310282011473245881023_ST/images2.png)
【答案】分析:以O支点,缓慢地将杆从图示位置提起的过程中,杆的力矩平衡,由力矩平衡条件得出F与θ的关系式,由数学知识求解F的最大值及θ的值.
解答:解:设OA转过的角度为θ.
以O支点,缓慢地将杆从图示位置提起的过程中,由力矩平衡条件得
Fl=mg(
+
)
得F=mg(
+
)=
sin(α+θ),式中,tanα=
=
,得α=53°
则根据数学知识得:当θ=37°,α+θ=90°,sin(α+θ)最大,F有最大值,最大值Fm=![](http://thumb.1010pic.com/pic6/res/gzwl/web/STSource/20131028201147324588181/SYS201310282011473245881023_DA/7.png)
故答案为:37°,![](http://thumb.1010pic.com/pic6/res/gzwl/web/STSource/20131028201147324588181/SYS201310282011473245881023_DA/8.png)
点评:本题采用数学上函数法求解F的最大值,考查运用数学知识解决物理问题的能力.
解答:解:设OA转过的角度为θ.
以O支点,缓慢地将杆从图示位置提起的过程中,由力矩平衡条件得
Fl=mg(
![](http://thumb.1010pic.com/pic6/res/gzwl/web/STSource/20131028201147324588181/SYS201310282011473245881023_DA/0.png)
![](http://thumb.1010pic.com/pic6/res/gzwl/web/STSource/20131028201147324588181/SYS201310282011473245881023_DA/1.png)
得F=mg(
![](http://thumb.1010pic.com/pic6/res/gzwl/web/STSource/20131028201147324588181/SYS201310282011473245881023_DA/2.png)
![](http://thumb.1010pic.com/pic6/res/gzwl/web/STSource/20131028201147324588181/SYS201310282011473245881023_DA/3.png)
![](http://thumb.1010pic.com/pic6/res/gzwl/web/STSource/20131028201147324588181/SYS201310282011473245881023_DA/4.png)
![](http://thumb.1010pic.com/pic6/res/gzwl/web/STSource/20131028201147324588181/SYS201310282011473245881023_DA/5.png)
![](http://thumb.1010pic.com/pic6/res/gzwl/web/STSource/20131028201147324588181/SYS201310282011473245881023_DA/6.png)
则根据数学知识得:当θ=37°,α+θ=90°,sin(α+θ)最大,F有最大值,最大值Fm=
![](http://thumb.1010pic.com/pic6/res/gzwl/web/STSource/20131028201147324588181/SYS201310282011473245881023_DA/7.png)
故答案为:37°,
![](http://thumb.1010pic.com/pic6/res/gzwl/web/STSource/20131028201147324588181/SYS201310282011473245881023_DA/8.png)
点评:本题采用数学上函数法求解F的最大值,考查运用数学知识解决物理问题的能力.
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目