Topic 8

Objectives and Conceptual Overview of Pressure

The primary focus of this study unit is to clarify the distinction between weight and pressure and establish a foundational ability to calculate pressure given specific variables. Conceptually, pressure is linked directly to the relationship between force and surface area. When a force is applied to a smaller area, it results in more pressure. Conversely, when the same force is applied over a larger area, it results in less pressure. This principle explains various physical phenomena, such as the difficulty of traversing soft surfaces like mud or sand without sinking.

Earthmover Mechanics and Ground Interaction

A practical application of pressure distribution is seen in earthmovers. These machines are massive and exceptionally heavy, possessing a weight of approximately $1,000,000\,N$ , which is equivalent to the weight of about $15,000$ people. Despite this extreme weight, an earthmover does not sink into muddy ground where a single person might. This is because earthmovers utilize wide tracks instead of ordinary tyres. By using wide tracks, the earthmover's weight is spread out over a significantly larger area, which produces a much smaller pressure on the mud than the pressure produced by a person’s footprint.

The Scientific Definition and Formula for Pressure

Pressure is scientifically defined as a measure of how much force is applied over a certain area. To calculate this value, one must use the following standard equation:

$\text{Pressure} = \frac{\text{force}}{\text{area}}$

In this formula, force is consistently measured in newtons ( $N$ ). The units used for area determine the final units for pressure. Standard measurements for area include metres squared ( $m^2$ ) and centimetres squared ( $cm^2$ ).

Measurement Units and the Pascal

The specific units of pressure are derived from the units used for force and area. When area is measured in metres squared ( $m^2$ ), pressure is expressed in newtons per metre squared ( $N/m^2$ ). A standard convention in physics is that $1\,N/m^2$ is also referred to as $1\, \text{pascal}$ ( $Pa$ ). In many practical scenarios, it is more convenient to measure smaller surface areas in centimetres squared ( $cm^2$ ). If the area is measured in $cm^2$ and the force remains in $N$ , then the resulting pressure is measured in newtons per centimetre squared ( $N/cm^2$ ). It is essential during calculations to explicitly write the units next to the numbers in the equation to ensure the correct unit of pressure is identified.

Worked Examples of Pressure Calculations

To illustrate the application of the pressure formula, consider the following instructional examples:

Example A: A force of $100\,N$ is spread over an area of $2\,m^2$ . $\text{Pressure} = \frac{100\,N}{2\,m^2} = 50\,N/m^2$ This value can also be stated as $50\,Pa$ .

Example B: A force of $20\,N$ is spread over an area of $4\,cm^2$ . $\text{Pressure} = \frac{20\,N}{4\,cm^2} = 5\,N/cm^2$

Fragmentary Earthmover Data: The transcript implies a calculation for an earthmover where a weight is divided by a total area. The visible calculation steps are: $\text{Pressure} = \frac{\text{force}}{\text{area}} = \frac{1,000,000\,N}{\text{area}} = 500\,N/m^2$ This illustrates how the immense weight is mitigated by a large area, resulting in a manageable pressure level.

Sports Science Applications: The Footballer Example

Pressure principles are vital in the design of athletic equipment. Consider a footballer with a weight of $800\,N$ . The total surface area of his two feet is $200\,cm^2$ . Under normal conditions, the pressure he exerts is: $\text{Pressure} = \frac{800\,N}{200\,cm^2} = 4\,N/cm^2$

However, football boots utilize studs. These studs serve to drastically reduce the surface area in contact with the ground. Because the same force (his weight) is concentrated over a much smaller area, the studs produce a bigger pressure. This increased pressure allows the studs to penetrate and grip the ground, providing the footballer with the necessary traction for movement and stability.

Exercises and Fragmentary Practice Problems

The following section outlines practice items and conceptual checks found within the text:

Copy and complete definitions or tables as provided in the source material, ensuring not to forget the appropriate units throughout.
Analyze a scenario involving pressure when an object is placed on a surface (details regarding the specific object/body are partially obscured in the transcript).
Calculate the pressure exerted by a brick where the area is given as $0.5$ (unit obscured, likely $m^2$ or $cm^2$ ).
Evaluate a case study regarding a hippopotamus standing on a specific area, likely involving a force related to its weight and a resulting pressure value around $40$ .