滑轮组机械效率计算中的问题
在滑轮组机械效率计算的学习中，多数同学存在下列两个问题：
（一）有用功、额外功的概念含糊不清
由于课本中的例题、习题及课外练习题，大都以滑轮组匀速提升重物来计算机械效率，因而许多同学不加思索，以为克服重力所做的功Gh就是有用功，一但题型变化，便束手无策。
有用功：是为了某种目的需要，无论采取哪种方法都必须做的功。
额外功：是并非需要，但不得不做的功。
因此，在确定有用功、额外功（或总功）时，要看是哪种目的，不能盲目照仿。
例1. 如图1所示，用一滑轮组拉着重![](https://wkrtcs.bdimg.com/rtcs/image?w=64&md5sum=fecbabcfbabcd89b33cd83e0696144cc&sign=dc1203f235&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"64","h":"20","dataType":"png","c":"word/media/image1.png","imgOriW":63,"imgOriH":19})
的汽车沿水平方向匀速移动，汽车所受阻力是车重的0.03倍，绳自由端的拉力为1000N，当汽车前进1m时，求：
![](https://wkrtcs.bdimg.com/rtcs/image?w=334&md5sum=fecbabcfbabcd89b33cd83e0696144cc&sign=dc1203f235&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"334","h":"131","dataType":"png","c":"word/media/image2.png","imgOriW":334,"imgOriH":131})
图1
（1）滑轮组的机械效率；
（2）额外功的大小。
解析：（1）目的：是拉汽车匀速前进。无论采用什么方法，都必须克服汽车阻力做功，因而克服汽车阻力做的功是有用功。
![](https://wkrtcs.bdimg.com/rtcs/image?w=82&md5sum=fecbabcfbabcd89b33cd83e0696144cc&sign=dc1203f235&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"82","h":"34","dataType":"png","c":"word/media/image3.png","imgOriW":82,"imgOriH":24})
F拉绳的自由端做的功，是采用机械（滑轮组）时所做的功，是总功
![](https://wkrtcs.bdimg.com/rtcs/image?w=253&md5sum=fecbabcfbabcd89b33cd83e0696144cc&sign=dc1203f235&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"253","h":"78","dataType":"png","c":"word/media/image5.png","imgOriW":253,"imgOriH":78})
（2）![](https://wkrtcs.bdimg.com/rtcs/image?w=123&md5sum=fecbabcfbabcd89b33cd83e0696144cc&sign=dc1203f235&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"123","h":"24","dataType":"png","c":"word/media/image6.png","imgOriW":123,"imgOriH":24})
![](https://wkrtcs.bdimg.com/rtcs/image?w=227&md5sum=fecbabcfbabcd89b33cd83e0696144cc&sign=dc1203f235&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"227","h":"20","dataType":"png","c":"word/media/image7.png","imgOriW":227,"imgOriH":19})
这个功是克服滑轮摩擦所做的功，不需要，但只要采用滑轮组，就不得不做的功。
（二）误以为同一滑轮组的机械效率不变
用同一滑轮拉不同的物体，由于有用功和总功的比例不同，因而机械效率就不同。
例2. 用如图2所示的滑轮组匀速提升重120N的重物，绳自由端的拉力F为50N（绳重不计，滑轮间摩擦不计）。
求：（1）滑轮组机械效率；
![](https://wkrtcs.bdimg.com/rtcs/image?w=114.66666666667&md5sum=fecbabcfbabcd89b33cd83e0696144cc&sign=dc1203f235&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"114.66666666667","h":"241.33333333333","dataType":"png","c":"word/media/image8.png","imgOriW":150,"imgOriH":230})
（2）若用此滑轮组匀速提升270N的重物时，绳自由端的拉力应为多大？
解析：（1）目的：提升重物，设重物匀速升高hm，则有用功为![](https://wkrtcs.bdimg.com/rtcs/image?w=84&md5sum=fecbabcfbabcd89b33cd83e0696144cc&sign=dc1203f235&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"84","h":"24","dataType":"png","c":"word/media/image10.png","imgOriW":83,"imgOriH":24})
。
![](https://wkrtcs.bdimg.com/rtcs/image?w=269&md5sum=fecbabcfbabcd89b33cd83e0696144cc&sign=dc1203f235&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"269","h":"99","dataType":"png","c":"word/media/image11.png","imgOriW":210,"imgOriH":77})
图2 （2）错解：![](https://wkrtcs.bdimg.com/rtcs/image?w=189&md5sum=fecbabcfbabcd89b33cd83e0696144cc&sign=dc1203f235&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"189","h":"50","dataType":"png","c":"word/media/image12.png","imgOriW":189,"imgOriH":50})
由![](https://wkrtcs.bdimg.com/rtcs/image?w=164&md5sum=fecbabcfbabcd89b33cd83e0696144cc&sign=dc1203f235&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"164","h":"86","dataType":"png","c":"word/media/image13.png","imgOriW":83,"imgOriH":43})
即： ![](https://wkrtcs.bdimg.com/rtcs/image?w=271&md5sum=fecbabcfbabcd89b33cd83e0696144cc&sign=dc1203f235&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"271","h":"44","dataType":"png","c":"word/media/image14.png","imgOriW":271,"imgOriH":43})
认为机械效率不变的原因，仍是没有弄清哪是有用功，哪是额外功。
目的：提升270N的重物。
本例中由于滑轮的摩擦、绳重不计，额外功只有克服滑轮重所做的功，前后两次提升重物不同，有用功不同，但额外功相同，因而总功不同。
（2）正解1：
![](https://wkrtcs.bdimg.com/rtcs/image?w=169.33333333333&md5sum=fecbabcfbabcd89b33cd83e0696144cc&sign=dc1203f235&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"169.33333333333","h":"98.666666666667","dataType":"gif","c":"word/media/image15.png"})
当用此滑轮组提升的重物时，三段绳承担的总重为。
所以绳自由端拉力![](https://wkrtcs.bdimg.com/rtcs/image?w=131&md5sum=fecbabcfbabcd89b33cd83e0696144cc&sign=dc1203f235&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"131","h":"41","dataType":"png","c":"word/media/image18.png","imgOriW":131,"imgOriH":41})
（2）正解2：
当用此滑轮组提升![](https://wkrtcs.bdimg.com/rtcs/image?w=73&md5sum=fecbabcfbabcd89b33cd83e0696144cc&sign=dc1203f235&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"73","h":"16","dataType":"png","c":"word/media/image16.png","imgOriW":73,"imgOriH":15})
的重物时
![](https://wkrtcs.bdimg.com/rtcs/image?w=246&md5sum=fecbabcfbabcd89b33cd83e0696144cc&sign=dc1203f235&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"246","h":"197","dataType":"png","c":"word/media/image19.png","imgOriW":246,"imgOriH":197})
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