为了将放置在水平地面上、重G=100 N的重物提升到高处。小明同学设

为了将放置在水平地面上、重G=100 N的重物提升到高处。小明同学设计了图24(甲)所示的滑轮组装置。当小明用图24(乙)所示随时间变化的竖直向下拉力F拉绳时,重物的速度υ和上升的高度h随时间t变化的关系图像分别如图24(丙)和(丁)所示。不计摩擦,绳对滑轮的拉力方向均可看成在竖直方向。求:

(1)在2~3s内,拉力F的功率P及滑轮组的机械效率η。

(2)在1~2s内,拉力F做的功W。

 

 

 

答案

(1)在2~3s内,重物做匀速运动,υ3=2.50 m/s,拉力F3=40N,因为连接动滑轮的绳子有三根,所以拉力F的作用点下降的距离是重物上升高度h3的三倍。

P= F3υ3=100W                                                   (1分)

η=(W有用/W)×100%=[Gh3/(3F3h3)] ×100% =83.33%              (1分)

(2)在1~2s内,拉力F2=50 N,重物上升高度h2=1.25 m

W=3F2h2                                                                                      (2分)

代入数据解得W=187.5J 

解析:略

 

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