I'm blind, but I can see

Classical Mechanics Level 4

Salim is in a dark room, his friend Moustafa teases him by challenging him to measure a length:" there is a cylinder filled with water and oil, so obviously the water will separate from the oil because the oil is hydrophobic, Moustafa needs Salim to figure what is the oil layer thickness" …

In order to know the thickness of the oil layer you drop a tiny iron ball onto the surface, so the ball sink.

what is the thickness of oil in centimeters?

Details and Assumptions :

The ball reach the limit speed immediately after being dropped, and when it transfer between layers.
The ball reach the bottom of the cylinder in 30 second.
The mix is 1 meter high.
The limit speed for water, oil is 4cm/s, 3 cm/s respectively.

The answer is 60.

1 solution

Jafar Badour
Dec 30, 2015

let h be the water thickness and l be the oil thickness so the sum of them will be the high of the mix ,

$h+l=100$

let $t_1$ be the time required the ball to pass the oil and $t_2$ the time for the ball to pass the water and hit the bottom of the cylinder so salim can stop his watch and obtain a time he can use in his calculations!

$v_{oil}t_1=l$

$v_{water} t_2=h$

so $t_1 +t_2 =30$

$\frac{l}{ v_{oil}}+\frac{h}{v_{water}} =30$

$\frac{l}{3}+\frac{h}{4} =30$

and $h=100-l$ so

$\frac{l}{3}+\frac{100-l}{4} =30$

$\frac{l}{3}-\frac{l}{4} =30-25$

$\frac{l}{12} =5$

$l=60cm$

I'm blind, but I can see

The answer is 60.

1 solution

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