SOLUTION: 1. A rectangular water tank is 3m long, 6m wide, and 2m deep. Water exits the tank by pouring over the sides. Assume that depth is measured from the top of the tank (i.e. depth =

Question 120167: 1. A rectangular water tank is 3m long, 6m wide, and 2m deep. Water exits the tank by pouring over the sides. Assume that depth is measured from the top of the tank (i.e. depth = 0 at the top of the tank)
a) If the tank is initially full of water, find the work required to empty the tank.
b) If the tank is initially full of water, find the work required to pump out half of the water
c)If the tank is initially half-full of water, find the work required to empty the tank.
d)Why isn’t the answer to parts b) and c) the same?
e)If the tank is initially full of water, find the work F(y) required to pump out the water until the depth of water in the tank is y. Plot F(y)
f)If your goal is to pump out all of the water, at which water level y0 will half of the work be done?
Thankz to anyone in advance who even attempts this question !
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
work is force times distance ___ using the MKS system

it is a linear relationship, so the work done in moving a "section" of water
___ is the average depth [(top+bottom)/2] multiplied by the mass of the water
___ [(area)*(bottom-top)*(density)] and the gravitational acceleration (g)

a) w=mgh __ w=((3m*6m*2m)*1000kg/m^3)(9.8nt/kg)(1m) __ w=352.8kJ

b) the average depth is 1/2 and so is the mass of water __ 352.8*.5*.5=88.2kJ

c) the average depth is 3/2 and the mass is 1/2 __ 352.8*1.5*.5=264.6kJ

d) the water in c) has to be lifted 3 times as high (on average)

e) F(y)=(y)(y/2)(176.4kJ) __ F(y)=(88.2nt/m)y^2m^2

f) 176.4kJ=88.2y^2 __ 2m^2=y^2m^2 __ y=sqrt(2)m
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