A scale is adjusted so that when a large, shallow pan is placed on it, it reads

Question

A scale is adjusted so that when a large, shallow pan is placed on it, it reads zero. A water faucet at height h = 3.2m above is turned on at t=0 and water falls into the pan at a rate R = 0.20kg/s .

A)

Determine a formula for the scale reading as a function of time t for t > sqrt(2h/g)

Express your answer in terms of some or all of the variables h, R, t, and appropriate constants.

B)

Determine the reading for t = 9.0s .

C)

Repeat part B, but replace the shallow pan with a tall, narrow cylindrical container of area A = 11cm2(the level rises in this case).

Explanation / Answer

The first drop of water falss in the shallow pan only after t= sqrt(2h/g)= 0.808s

A) The formula for scale reading is proportional to the rate of fall of water and is expressed as,

m= 0.2*(t-0.808)

B) Hence, at t=9s, the reading of scale is, m= 0.2*(9-0.808)=1.6384kg

C) In case of the cyllindrical container, the height of water rises per second.

volume of 0.2kg water= 0.2/1000=2*10^-4 m^3

Hence, height raised per second= volume/area= 2/11=0.182m

Height of water at t=9 is,

h= 0.182*(9-0.808)=1.49m

volume of water= 1.49*11*10^-4= 0.001639 m^3

Mass of water= volume*density= 1.639kg

Hence, the mass recorded by the scale wil lbe same in both the cases.

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