Calculating Pressure A 7.5 Kg Block On A Table Physics Problem Solved

In the realm of physics, understanding pressure is crucial for comprehending how forces are distributed over surfaces. Pressure, defined as the force applied perpendicularly to a surface per unit area, plays a vital role in various phenomena, from the simple act of a block resting on a table to complex engineering applications. This article delves into a specific scenario: calculating the pressure exerted by a 7.5 kg block placed on a tabletop with a bottom surface area of 0.6 m². We will explore the fundamental concepts of pressure, force, and area, and apply them to determine the pressure exerted by the block. By understanding the relationship between these factors, we can gain insights into the mechanics of how objects interact with surfaces and the forces they exert upon them. This knowledge is not only essential for physics students but also for anyone interested in the mechanics of everyday objects and structures.

Before diving into the calculation, let's establish a clear understanding of the key concepts involved: pressure, force, and area. Pressure, denoted by P, is the measure of force applied perpendicularly to a surface per unit area. It is mathematically expressed as P = F/A, where F represents the force and A represents the area over which the force is distributed. The standard unit of pressure in the International System of Units (SI) is Pascal (Pa), which is equivalent to one Newton per square meter (N/m²). Force, in the context of this problem, is the gravitational force acting on the block, commonly known as weight. Weight is the product of an object's mass (m) and the acceleration due to gravity (g), approximately 9.8 m/s² on the Earth's surface. Therefore, the force exerted by the block on the tabletop is its weight, calculated as F = mg. Area, in this scenario, refers to the bottom surface area of the block in contact with the tabletop. It is the area over which the block's weight is distributed. Understanding these concepts and their interrelationship is fundamental to calculating pressure accurately.

Consider a scenario where a block with a mass of 7.5 kg rests on a table. The bottom surface of this block, which is in contact with the tabletop, has an area of 0.6 m². Our objective is to determine the pressure exerted by this block on the tabletop. This problem exemplifies a common physics question that requires applying the principles of pressure, force, and area. By solving this problem, we can gain practical experience in calculating pressure and understand how the weight of an object and its contact area influence the pressure it exerts on a surface. The problem provides a clear context for applying the formula P = F/A and reinforces the importance of understanding the units involved. The mass of the block determines the force it exerts due to gravity, and the surface area determines how this force is distributed, ultimately affecting the pressure. This type of problem is crucial for students learning about mechanics and for anyone interested in understanding the physical forces at play in everyday situations.

To determine the pressure exerted by the block, we will follow a step-by-step approach, applying the concepts we have discussed. First, we need to calculate the force exerted by the block on the tabletop. As mentioned earlier, this force is the weight of the block, which can be calculated using the formula F = mg. Here, m is the mass of the block (7.5 kg) and g is the acceleration due to gravity (9.8 m/s²). Substituting these values, we get F = 7.5 kg * 9.8 m/s² = 73.5 N. This force represents the total gravitational pull acting on the block. Next, we calculate the pressure using the formula P = F/A, where F is the force we just calculated (73.5 N) and A is the bottom surface area of the block (0.6 m²). Plugging in these values, we get P = 73.5 N / 0.6 m² = 122.5 N/m². Since 1 N/m² is equal to 1 Pascal (Pa), the pressure exerted by the block on the tabletop is 122.5 Pa. This step-by-step solution demonstrates how the fundamental principles of physics can be applied to solve practical problems, providing a clear understanding of the relationship between force, area, and pressure.

To ensure clarity and understanding, let's break down the calculation into even more detail. We begin with the fundamental formula for pressure: Pressure (P) = Force (F) / Area (A). The force in this scenario is the weight of the block, which we calculate using Force (F) = mass (m) × acceleration due to gravity (g). The mass of the block is given as 7.5 kg, and the acceleration due to gravity is approximately 9.8 m/s². Therefore, F = 7.5 kg × 9.8 m/s² = 73.5 kg⋅m/s². Note that 1 kg⋅m/s² is equivalent to 1 Newton (N), so the force is 73.5 N. The area in this problem is the bottom surface area of the block, given as 0.6 m². Now we can substitute these values into the pressure formula: P = 73.5 N / 0.6 m² = 122.5 N/m². As we established earlier, 1 N/m² is equal to 1 Pascal (Pa), so the pressure exerted by the block is 122.5 Pa. This detailed breakdown emphasizes each step of the calculation, ensuring a thorough understanding of the process. By understanding the conversion of units and the application of the formulas, one can confidently calculate pressure in various scenarios. This level of detail is crucial for students learning the fundamental principles of physics and for professionals who need to apply these concepts in practical applications.

Based on our calculations, the pressure exerted by the 7.5 kg block on the tabletop is 122.5 Pa. Therefore, the correct answer is D. 122.5 Pa. This result signifies that the weight of the block, which is 73.5 N, is distributed over the contact area of 0.6 m², resulting in a pressure of 122.5 Pascals. The pressure is a measure of how concentrated the force is; a smaller area would result in a higher pressure, while a larger area would result in a lower pressure for the same force. This understanding is crucial in various real-world applications, such as designing structures that can withstand certain pressures or understanding how different materials distribute weight. The correct answer reaffirms the importance of accurately applying the pressure formula and understanding the relationship between force, area, and pressure. Furthermore, it demonstrates how a simple physics problem can provide valuable insights into the mechanics of everyday objects and the forces they exert.

Understanding pressure is of paramount importance in numerous scientific, engineering, and everyday contexts. In physics, pressure is a fundamental concept that helps explain a wide range of phenomena, from fluid dynamics to thermodynamics. Engineers rely on pressure calculations to design structures, machines, and systems that can withstand various loads and stresses. For instance, civil engineers must consider the pressure exerted by soil and water on foundations and retaining walls to ensure structural integrity. Mechanical engineers need to understand pressure in hydraulic and pneumatic systems, where fluids are used to transmit force. In everyday life, we encounter pressure in various situations, such as the pressure in car tires, the pressure exerted by our bodies on the ground, and the atmospheric pressure that surrounds us. A grasp of pressure concepts allows us to make informed decisions and understand the world around us better. Understanding pressure also has significant implications for safety; for example, understanding pressure limits in containers and pipelines is crucial to preventing accidents. Therefore, the principles of pressure are not only academically valuable but also practically relevant in various professional fields and daily life.

The application of pressure calculation extends far beyond academic exercises and into various real-world scenarios. In civil engineering, calculating the pressure exerted by soil and water on structures like dams, bridges, and tunnels is crucial for ensuring their stability and safety. In mechanical engineering, pressure calculations are essential in the design of hydraulic systems, which are used in heavy machinery, braking systems, and aircraft control systems. Medical professionals use pressure measurements to monitor blood pressure, which is a vital indicator of cardiovascular health. In the field of meteorology, atmospheric pressure is a key factor in weather forecasting. The design of airplanes and submarines relies heavily on pressure calculations to ensure they can withstand the forces exerted by the surrounding fluids (air and water, respectively). Divers need to understand pressure to safely explore underwater environments. The food industry uses pressure in processes like pasteurization and sterilization. Even in everyday life, understanding pressure helps us make informed decisions, such as inflating tires to the correct pressure for optimal performance and fuel efficiency. These examples highlight the broad applicability of pressure calculations and underscore their importance in various aspects of our lives and industries. Mastering these calculations provides a valuable tool for problem-solving and decision-making in a wide range of fields.

In conclusion, calculating the pressure exerted by the 7.5 kg block on the tabletop provides a practical illustration of the fundamental principles of physics. By applying the formula P = F/A, we were able to determine that the block exerts a pressure of 122.5 Pa on the table. This calculation highlights the relationship between force, area, and pressure, and underscores the importance of understanding these concepts in various scientific, engineering, and everyday contexts. The step-by-step solution presented in this article demonstrates how to approach similar problems systematically, ensuring accuracy and clarity. The real-world applications of pressure calculations, ranging from structural engineering to medical diagnostics, further emphasize the significance of mastering these concepts. Whether you are a student learning the basics of physics or a professional working in a technical field, a solid understanding of pressure is essential for problem-solving and decision-making. This exercise not only reinforces the specific calculation but also promotes a deeper appreciation of the underlying physical principles and their relevance in the world around us.