Video: Determining Changes in the Pressure Exerted by a Fluid on Its Container

A cubic container holds water. The lid of the container can be pushed downward, exerting pressure on the water in the container. Which of the following statements most correctly describes how the pressure exerted by the water is changed when the lid is pushed downward? [A] The pressure exerted on the cube’s horizontal sides is increased. [B] The pressure exerted on the base of the cube and its horizontal sides is increased. [C] The pressure exerted on the base of the cube and its lid is increased. [D] The pressure exerted on the base of the cube is increased. [E] The pressure exerted on the base of the cube, its horizontal sides, and its lid is increased.

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Video Transcript

A cubic container holds water. The lid of the container can be pushed downward, exerting pressure on the water in the container. Which of the following statements most correctly describes how the pressure exerted by the water is changed when the lid is pushed downward? Number one: The pressure exerted on the cube’s horizontal sides is increased. Number two: The pressure exerted on the base of the cube and its horizontal sides is increased. Number three: The pressure exerted on the base of the cube and its lid is increased. Number four: The pressure exerted on the base of the cube is increased. Or number five: The pressure exerted on the base of the cube, its horizontal sides, and its lid is increased.

To answer this question, we need to recall something known as Pascal’s principle. This is also known as Pascal’s law. And it states that the pressure of a liquid is equally transmitted in all directions. So we know we’ve got this cubic container. And it’s filled up with water, which we then compress with a lid, which of course results in an increase in pressure of the water. This is because we’re trying to compress it. We’re trying to squeeze the water into a smaller space.

But we also know that water is an incompressible fluid. Basically, we cannot compress it or squeeze it into a smaller space like we’re trying to do. So if we’re exerting a force from above with the lid, then the water must exert a force back so that it count as the force that we’re putting on it. And now since the lid has a certain area, that force is being transmitted all over the area of the lid. And this is basically what a pressure is. It’s a force distributed over an area.

Hence, the pressure in the water increases when we try to squeeze it with the lid. However, Pascal’s principle tells us that the pressure of a liquid is equally transmitted in all directions. So when we try to squeeze the water with the lid, not only is it putting an increased pressure on the lid itself, but it’s also putting an extra pressure on the sides of the cube and the base of the cube. Which means that our final answer is statement number five: The pressure exerted on the base of the cube, its horizontal sides, and its lid is increased.

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