Introduction:

Perhaps you've inflated a balloon or a ball until it was fully inflated; this inflation is a result of the movement of air particles inside the object, as depicted in Figure 14. These particles move, colliding with each other and the inner walls of the object. Each time a particle collides with the inner wall, it exerts a force either pushing or pulling. As previously studied, the sum of these forces creates air pressure. Pressure, denoted as P, equals the force applied on a surface divided by the total area it acts upon.

Force and Area:

From the equation above, it's evident that pressure depends on both the force and the area it affects. Increasing the force on a specific area increases pressure, while decreasing it reduces pressure. The relationship between pressure and force is direct, whereas with area, it's inverse, as illustrated in Figure 15.

Factors Influencing Pressure:

Air Pressure:

The atmospheric air exerts significant force on us, known as air pressure. At sea level, the standard atmospheric pressure is 101.3 kilopascals, equivalent to the force of approximately 101,300 newtons per square meter. Despite its strength, we don't feel or see this pressure. Pascal explained this by demonstrating that when ascending to higher altitudes, where there are fewer air particles, the external air pressure decreases, allowing the object to expand.

Pressure Equilibrium:

The body can withstand the external air pressure due to the internal pressure of fluids inside it, creating equilibrium. This is exemplified by the athlete in Figure 17, whose body withstands external and internal pressures, preventing it from collapsing.

Changes in Air Pressure:

Air pressure changes with altitude. As elevation increases, air pressure decreases due to the lower density of air particles, leading to fewer collisions and, consequently, reduced pressure. Pascal demonstrated this concept by ascending a partially inflated balloon to a mountain top, causing it to expand.

Air Travel and Pressure:

During air travel, changes in air pressure can cause discomfort, such as ear blockage. The pressure inside the ears becomes greater than outside, trapping air, which eventually releases, creating a popping sound. Aircraft are designed to mitigate sudden pressure changes, ensuring a more comfortable journey.

Changes in Gas Pressure:

The pressure of confined gases also changes with alterations in conditions, including changes in volume and temperature. Pressing on part of a gas-filled balloon increases pressure, while expanding the balloon decreases pressure, assuming constant temperature.

Pressure and Volume:

Pressing on a portion of an air-filled balloon causes another part to inflate further. This is because the compressed particles occupy a smaller space, resulting in more collisions with the inner walls, generating increased pressure. This relationship is inversely proportional – an increase in volume reduces pressure, assuming constant temperature. See Figure 19 for a visualization of particle movement.

In conclusion, Pascal's principle illustrates the intricate relationship between force, area, and pressure, highlighting how changes in these factors affect the physical properties of gases and fluids.

Pressure and Temperature:

When the volume of a confined gas remains constant, its pressure changes with a change in temperature. An increase in the gas temperature leads to an increase in the kinetic energy of its particles, causing them to move faster and collide more frequently. As a result, the pressure increases. The relationship between pressure and temperature is known as an inverse relationship. In other words, as the temperature of a confined gas increases, its pressure increases at constant volume, as shown in Figure 20.

Why does a tightly sealed container with air shrink or break after freezing?

Buoyancy or Submersion:

You may have noticed that you feel lighter when in water. When immersed in water, the pressure of the water affects you and pushes you in all directions. The deeper you go into the water, the higher the water pressure, as water pressure increases with depth. The pressure pushing the lower surface of a submerged object upward is greater than the pressure acting on the upper surface downward. This difference in pressure creates a force called buoyant force, as shown in Figure 21. An object floats if the buoyant force equals its weight and sinks if the buoyant force is less than its weight.

Archimedes' Principle:

What determines buoyant force? Archimedes' Principle states that the buoyant force acting on a body immersed in a fluid is equal to the weight of the fluid displaced by that body. Placing an object in a container filled to the brim with water, as in Figure 22, causes some water to spill. By weighing the spilled water (displaced water), you can determine the buoyant force acting on the object. Density helps understand whether an object will float or sink. Density, defined as mass divided by volume, plays a crucial role in buoyancy.

Pascal's Principle:

What happens when you step on a tightly sealed plastic container filled with water? The additional pressure is evenly distributed throughout the water inside the container due to the absence of an outlet. Pascal's Principle states that an increase in pressure on a confined fluid, resulting from an external force, is transmitted equally to all parts of the fluid. Hydraulic systems, such as hydraulic lifts and dental chairs, operate based on Pascal's Principle, as shown in Figure 23. Figure 24 illustrates hydraulic pistons; the force applied to the left piston generates additional pressure on the confined fluid, which is then transmitted to the right piston. If the piston areas are equal, the forces are also equal. If the area of the right piston is relatively larger, a greater force is generated, allowing hydraulic pistons to lift heavy objects with relatively small forces.

Power Pumps:

A forceful stream of water emerges when pressure is applied to a container filled with fluid, known as a power pump. Examples include toothpaste tubes, mustard bottles, and some ketchup bottles. In the human heart, there are two power pumps—one propels blood from the heart to the lungs for oxygenation, and the other propels oxygen-rich blood from the heart to the rest of the body, as shown in Figure 25.

Conclusion:

Understanding the significance of forces and pressures in our daily lives and their impact on various phenomena around us is crucial. We've explored how the movement of air particles inside a ball or balloon can lead to inflation and how pressure is influenced by force and area, whether in the context of the human body or in the case of liquids and gases. Additionally, we've delved into Archimedes' Principle, explaining the phenomena of buoyancy and submersion, and how Pascal's Principle is utilized in hydraulic systems to lift heavy loads efficiently. Finally, we've discussed power pumps and their ability to generate low forces to lift liquids.

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