A cable weighing 0.8 pounds per foot is attached to a small

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A cable weighing 0.8 pounds per foot is attached to a small 80-pound robot,and then the robot is lowered into a 50-foot deep well to retrieve a 7 pound wrench.The robot gets out of the well (carrying the wrench) by climbing up the cable with one end of the cable still attached to the robot.How much work does the robot do in climbing to the top of the well?
请看清楚哦，机器人是沿着绳子往上爬的，也就是说每时每刻它本身的重量在变化（绳子挂在它身上的部分随着它往上爬也在增加）所以不是单纯的物理题目我肯定是微积分的题目因为它就是在我书上这一个chapter的内容啊。

为什么要用微积分?就是简单的做功问题吧?（80+7）*50,我们国内的物理教材上功的单位是牛·米,这里的单位是磅·英尺,必要的话换算下

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