ECH 141
Problem Set #2
(Due 1/25/17)
1.
A rectangular tank that is 7 m wide is layered with 8 m of oil (
ρ
= 880 kg/m
3
), 6 m of water, and
4 m of mercury (
ρ
= 13,600 kg/m
3
).
The tank is surrounded by air at atmospheric pressure and the
top is open.
Calculate the total force on the side of the tank.
2.
Some claim that Archimedes discovered the buoyancy laws when asked by King Hiero of
Syracuse to determine whether or not his crown was pure gold (specific gravity = 19.3).
Archimedes found the weight of the crown in air to be 13.0 N and in water to be 11.8 N.
Was the crown made of gold?
Explain your reasoning.
3.
One possible way to measure surface tension is to monitor the force on a frictionless "slide wire" that
forms one boundary of a liquid film. The liquid/air interfaces of the film are approximately flat, and
the film is bounded on three other sides by a stationary, U-shaped wire:
L
Liquid
film
Slide
wire
F
If the surface tension in the film is
γ
and the applied force is
F
, derive a relation between

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