Question : \" You have a vacation cabin that has a nearbysolar (black) water con

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Question : " You have a vacation cabin that has a nearbysolar (black) water container used to provide a warm outdoorshower. For a few days last summer, your pump went out and you hadto personally haul the water up the 4.0m from the pond to the tank.Suppose your bucket has a mass of 5.0 kg and holds 15.0 kg of waterwhen it is full. However, your bucket has a hole in it, and as youmoved it vertically at a constant spped v, waterleaked out at a constant rate. By the time you reached the top,only 5.0kg of water remained. (a) Write an expression for the mass of teh bucket plus wateras a function of the height abouve the pond surface. (b) Find the work done by you on the bucket for each 5.0 kg ofwater delivered to the tank."
I figured out (a) and came up with the equation mass= 20kg - (2.5(kg/m))(x); where x = meters
I'm having a difficult time with (b). I've tried usingv, but to no avail. I do understand that I will needto manipulate the above equation to calculate an equation for Forceand find the integral from 0 to 4, and the result is Work, but I'mjust having a tough time deriving the equation


(a) Write an expression for the mass of teh bucket plus wateras a function of the height abouve the pond surface. (b) Find the work done by you on the bucket for each 5.0 kg ofwater delivered to the tank."
I figured out (a) and came up with the equation mass= 20kg - (2.5(kg/m))(x); where x = meters
I'm having a difficult time with (b). I've tried usingv, but to no avail. I do understand that I will needto manipulate the above equation to calculate an equation for Forceand find the integral from 0 to 4, and the result is Work, but I'mjust having a tough time deriving the equation

Explanation / Answer

Rate of loss is = 10 kg/ 4m = 2.5 kg/m then m(x)= Mb + Mw - x m(x)= 5 + 15 - 2.5x m(x)= 20 - 2.5x . . b)Work is force time distance, so W= m(x)gy since in this case y=x we have W(x)= [20 - 10x]gx W(x)= [20x - 2.5x2 ] g . Let me know if you have any problems. . Let me know if you have any problems.

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