题目内容
(14分)一小石块从空中自由下落h=5m后,掉入淤泥,落到淤泥底时速度恰好为零,全过程共用时t=1.2s。假设石块在淤泥中做匀减速直线运动,且g=10m/s2,则:
(1)小石块掉入淤泥前的瞬时速度
大小为多少;
(2)石块陷入淤泥的深度d及此过程石块的加速度
的大小
(1)小石块掉入淤泥前的瞬时速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144829219265.png)
(2)石块陷入淤泥的深度d及此过程石块的加速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144829282283.png)
(1)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144829469685.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144829360597.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144829438497.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144829469685.png)
试题分析:(1)设石块落入淤泥前速度速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144829219265.png)
此前石块做自由落体,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144829594585.png)
代入相关数据得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241448296721153.png)
2)由自由落体运动规律
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144829719456.png)
得石块自由落体运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144829765599.png)
因此石块在淤泥中匀减速的时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144829812719.png)
则此过程石块加速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144829875954.png)
又由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144829937577.png)
代入相关数据得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144829438497.png)
(或由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241448300461070.png)
或
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241448301091804.png)
点评:本题学生清楚石块调入淤泥前做自由落体运动,在淤泥中做匀减速直线运动,解决此题的关键是分析清物体在每个过程的运动性质。
![](http://thumb2018.1010pic.com/images/loading.gif)
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