Work is distance times force, not time times force. Also, to get work in Joules, you need to multiply the mass in kilograms by g = 9.8 m/s^2.
A bucket that weighs 3kg and a rope of negligible weight are used to draw water from a well that is 100m deep. The bucket is filled with 40 liters of water and is pulled up at a rate of 2m/s, but water leaks out of a hole in the bucket at a rate of 0.2 m/s (I think the question is supposed to say 0.2 liters/s ?). Find the work done in pulling the bucket to the top of the well.
I came across a more basic physics type problem recently and it made me interested so I have been looking into it as a side project lately. I came across this random problem which I don't have a solution for and gave it a go. Sorry if I am missing gaps in my knowledge, I just started with them
I assume that 40 liters means 40kg of weight/force.
Weight of the bucket at any given time
Am I way off?
Any help/direction is much appreciated.
Let denote time and denote height. Then . As was said above, , so . By definition of work, . Since and , using integration by substitution, this is the same as .
Edit: corrected formula for work.
1 liter of water has a mass of 1 kg
initial mass = 43 kg
initial weight = 43g = 421.4 Newtons
lifting the bucket at a rate of 2 m/s takes 50 seconds. in that time, (50 sec)(0.2 L/sec) = 10 L leak out, ending with a final weight of 33g = 323.4 N
Work done is the area of the trapezoid in the Force vs. displacement graph shown.
To be honest, I wasn't sure why the timing was even given for the question initially.