题目内容
(12分)某电视台娱乐节目在游乐园举行家庭搬运砖块比赛活动.比赛规则是:如图甲所示向滑动行驶的小车上搬放砖块,且每次只能将一块砖无初速度(相对地面)地放到车上,车停止时立即停止搬放,以车上砖块多少决定胜负.已知每块砖的质量m=0.8 kg,小车的上表面光滑且足够长,比赛过程中车始终受到恒定牵引力F=20 N的作用,未放砖块时车以v0=3 m/s的速度匀速前进.获得冠军的家庭上场比赛时每隔T=0.8 s搬放一块砖,从放上第一块砖开始计时,图中仅画出了0~0.8 s内车运动的v-t图象,如图乙所示,g取10 m/s2.求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250030498493320.png)
(1)小车的质量及车与地面间的动摩擦因数;
(2)车停止时,车上放有多少块砖.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250030498493320.png)
(1)小车的质量及车与地面间的动摩擦因数;
(2)车停止时,车上放有多少块砖.
(1)8 kg 0.25 (2)5块
试题分析:(1)开始比赛前车匀速运动,由
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003049864628.png)
放上第一块砖后车减速运动,加速度大小
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003049880315.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003049896996.png)
对小车由牛顿第二定律
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003049911867.png)
由①②③式联立解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003049927643.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003049942522.png)
(2)放上第一块砖后1s,车的速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003049974298.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003049880315.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050098532.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050130789.png)
放上第二块砖后1 s车的速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050161330.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050192533.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050208877.png)
同理
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050223597.png)
放上第n块砖作用1s后车速为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050254336.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050270348.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050286619.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050317878.png)
由以上各式可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050332906.png)
将
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050348534.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250030503641375.png)
故
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250030503951287.png)
令
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050410428.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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