The Concept of Pressure

Introduction

Pressure is a fundamental concept in physics that plays a crucial role in understanding how forces interact with surfaces. It helps us quantify how much force is distributed over a given area, and it is a vital aspect of various everyday scenarios, from standing on solid ground to the mechanics of fluids. In this discussion, we will explore the concept of pressure and apply it to a real-world example: calculating the pressure exerted by a person on the floor when standing on both feet and then on one foot.

Imagine we apply a force F perpendicular on an area A of a wall, we say that a pressure P is exerted on the wall by the force.

Thus, force and area are involved in the definition of pressure but that force must act perpendicularly to the area under consideration.

Pressure is defined as the perpendicular force per unit area acting on a surface. It is a scalar quantity which means that it has only magnitude but no direction.

Or

Pressure is a fundamental concept in physics , defined as the force applied perpendicular to a given surface divided by the area over which the force is applied.

It is a measure of how much force is distributed over a specific area. Mathematically, pressure (P) is defined as: P= ^F/_A

Force (F) is a measure of how strongly something pushes or pulls. It's measured in units called Newtons (N).

Area (A) represents the amount of space or surface. It's measured in square meters (m²).

Pressure (P) is a measure of how much force is applied over a given area. It's like how hard you press on something relative to the size of what you're pressing on. Pressure is measured in Newtons per square meter (N/m²), which is also known as Pascals (Pa).

So, in simpler terms, pressure (P) is a way to describe how much force (F) is spread out over a certain amount of space or area (A). The unit for pressure can be expressed as N/m² or Pa, and they both mean the same thing - how much force is applied per square meter of area.

Example:1

Calculate the pressure exerted on the floor by a person weighing 80kg whose two feet covers an area of 400cm². If the one stands on one foot what is the new pressure he exerts on the floor?

Solution

P= ^F/_A

First, calculate the force due to the weight of the person (F):

Force due to the weight of the person is given: by F= mg (N)

F represents the force due to gravity (weight) in newtons (N).

m is the mass of the body in kilograms (kg) which is given as 80kg from the question.

g is the acceleration due to gravity. the acceleration due to gravity (g) is approximately a constant value of 9.81 meters per second squared (m/s²) on the surface of the Earth.

F = m X g
F = 80 kg X 9.81 m/s²
F = 784.8 N

Note

When calculating pressure, it's important to ensure that the units are consistent. Pressure is defined as force per unit area. In the International System of Units (SI), the standard unit of pressure is the Pascal (Pa), which is equal to one Newton per square meter (N/m²).

To calculate pressure using the formula P = F / A:

F represents the force in Newtons (N).

A represents the area in square meters (m²).

Therefore, it's necessary to ensure that both the force and the area have consistent units in the SI system. If you have an area in square centimeters (cm²), it should be converted to square meters (m²) to match the SI unit of area.

To convert square centimeters (cm²) to square meters (m²), you need to divide the number of square centimeters by 10,000 because there are 10,000 square centimeters in 1 square meter.

So, to convert 400 square centimeters to square meters:

400 cm² / 10,000 = 0.04 m²

Therefore, 400 square centimeters is equal to 0.04 square meters.

Given:

Force = 784.8 N
Area (A) covered by both feet = 400 cm² = 0.04 m²

Now, calculating the pressure (P) exerted on the floor by the person using the formula: P = F / A, we have

P = 784.8 N / 0.04 m²
P ≈ 19620 N/m² (Pascals or Pa)

So, the pressure exerted on the floor by the person when standing on both feet is approximately 19620 Pascals (Pa).

Now, let's calculate the new pressure when the person stands on one foot. The mass and the force remains the same. but the area of contact is reduced to half (200 cm² = 0.02 m²) because the person is now standing on one foot.

Therefore new pressure represented as P (new) = Force F / the new area represented as A (new)

P (new) = F / A (new)
P (new) = 784.8 N / 0.02 m²
P (new) ≈ 39240 N/m² (Pascals or Pa)

It is important to note that when area is less, pressure increases as seen from the above example. When area was 0.04, pressure was 19620 but when area was reduced to 0.02, pressure increased to 39240 Pa.

Conclusion

In summary, pressure is a fundamental concept that helps us understand how forces interact with surfaces, and it plays a significant role in various aspects of physics and engineering. Our example of calculating the pressure exerted on the floor by an 80kg individual showcased how pressure is affected by both force and area. When standing on both feet, the pressure was approximately 19620 Pascals (Pa), but when the person shifted their weight to one foot, the pressure increased to about 39240 Pascals (Pa) due to the reduced contact area.

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