- #1
yellowcakepie
Homework Statement
A scale is adjusted so that when a large, shallow pan is placed on it, it reads zero. A water faucet at height h = 4.0 m above is turned on and water falls into the pan at a rate R = 0.20 kg/s.
A) Determine a formula for the scale reading as a function of time t if at the moment t=0 first drops of water reach the pan.
B) Determine the reading for t = 9.4 s.
C) Repeat part B, but replace the shallow pan with a tall, narrow cylindrical container of area A = 18 cm^2 (the level rises in this case).
Homework Equations
Δx = 0.5gt^2
v = gt
I = R*v
F(t) = I + Rgt
The Attempt at a Solution
I have already solved parts A and B, but I am having trouble with part C.
A) F(t) = R√(2h/g)*g + Rgt (force due to change of momentum of the water plus weight of water in the container)
B) F(9.4 s) = 20 N
C) I have A = 0.0018 m^2 area for the cylindrical container, and density of water (D) is 1000 kg/m^3, so I got the fill rate by dividing D/R, and then divided A by D/R to get the change in height per second, which is 0.11 m/s.
I have no clue how to incorporate this height change rate into my answer.
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