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

for the balloon to support the case of liquor when floating, the half of the submerged balloon must displace a weight of water equal to

175 - 137 = 38 N

(this is so that the case and balloon together displace a weight of water equal to the weight of the case).

this amount of water has a volume of...

weight = density * volume* g

38 = 1000 * V * 9.80

V = 0.003878 m^3

This is HALF the volume of the balloon, so

volume of balloon = 2*0.003878 = 0.007755 m^3 = 7.755 liters = 7755 cubic cm

now for the weight of the salt...

weight of case + weight of salt = weight of water displaced by case + balloon + salt

175 + weight of salt = 137 + 38+38 + weight of salt * density of water / density of salt

weight of salt = 38 + weight of salt * 1000/density of salt

Now... we have a problem. What is the density of salt? I found a value of 2165. But you might have something different. If your density for salt is different, you'll have to recalculate by using your value in place of the 2165 here:

weight of salt = 38 / (1 - 1000/2165) = 70.62 N

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