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Chapter 3: Problem 110

In the "Cartesian diver" child's toy, a miniature "diver" is immersed in a column of liquid. When a diaphragm at the top of the column is pushed down, the diver sinks to the bottom. When the diaphragm is released, the diver again rises. Explain how the toy might work.

Short Answer

Expert verified
The 'Cartesian diver' toy operates based on the principles of pressure and buoyancy. When the diaphragm is pushed, it increases the water pressure, which compresses the air inside the diver, making it heavier than water and thus, it sinks. When the diaphragm is released, the pressure decreases, the air inside the diver expands, reducing its density, and making it lighter than water and thus, it rises.

Step by step solution

01

Understanding the Toy Mechanics

The primary mechanics behind a 'Cartesian diver' toy relies on principles of pressure and buoyancy. It involves a container filled with water and a small 'diver' that can float and sink based on whether or not pressure is applied to the system.
02

Pushing Down the Diaphragm

When the diaphragm at the top of the column is pushed down, it increases the pressure of the water column. This increased pressure compresses the air inside the diver, reducing its volume. The decrease in volume increases the density of the diver (Density = mass / volume), making it heavier than the water around it and thus, it sinks.
03

Releasing the Diaphragm

When the diaphragm is released, the pressure of the water column decreases. This allows the air inside the diver to expand and increase in volume. As the volume of the diver increases, its density decreases, making it lighter than the water around it. Therefore, it floats or rises to the surface. This process leverages the principles of buoyancy, a force exerted by a fluid that opposes an object's weight.

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