In the movie Once Upon a Time in America, set in the Prohibition era, a clever p

Question

In the movie Once Upon a Time in America, set in the Prohibition era, a clever ploy is used by bootleggers transporting liquor by boat. Attached to each case of liquor is a balloon of negligible weight and a cloth bag filled with salt as shown in the figure below. When police approach, the liquor is dumped overboard. Initially the cases sink, but after a time the salt dissolves and the balloons float to the surface. Suppose that a liquor case weighs 175 N and displaces 137 N of water and that, when the balloon floats, it is half submerged. Find the volume of the balloon and the required weight of salt.

volume of the balloon = ? weight of the salt = ?

Explanation / Answer

first lets concentrate on the liquor
weight =175N
displacement = 137N
due to buoyancy when the liquor is fully submerged it experiences a force of 137 upward
so the effective weight of liquor inside water = 175-137 = 38 N
so the balloon must balance this weight when the salt has melted,
so water displaced by half of balloon = 38N
total balloon = 76N
(taking g=10 m/s^2 , density of water = 1000m3 / kg)

we get the volume of balloon as , 7.6 *10^-3 m3

but initially the whole ballon and liquor together with salt will sink ,

in this case salt must balance the force of another half of balloon

therefore the salt must be greater than 38N

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