Calculating Apparent Weight A Metal Cube In Methylated Spirit A Physics Problem
This article delves into the fascinating world of buoyancy and Archimedes' principle. We'll explore how to calculate the apparent weight of an object immersed in a fluid, specifically focusing on a metal cube submerged in methylated spirit. This exploration involves understanding concepts like density, weight, buoyant force, and how they interplay to determine an object's apparent weight in a fluid. We will solve a numerical problem by applying these physics principles, step by step, to find a practical solution. Understanding the principles governing buoyant force and apparent weight is not only essential in physics but also has real-world applications, from designing ships and submarines to understanding the behavior of objects in various fluids. This article aims to provide a clear and concise explanation, making it accessible to students and anyone interested in the topic.
A metal cube with sides measuring 2 cm weighs 0.56 N in air. Our objective is to determine the apparent weight of this cube when it is fully immersed in methylated spirit, which has a density of 0.585 g/cm³.
Understanding the Concepts
Before we dive into the calculations, let's clarify the key concepts involved:
- Weight in Air: The weight of an object in air is the force exerted on it due to gravity. It is calculated using the formula W = mg, where 'm' is the mass of the object and 'g' is the acceleration due to gravity (approximately 9.8 m/s²).
- Density: Density is a measure of how much mass is contained in a given volume. It is defined as mass per unit volume (ρ = m/V). In this problem, we are given the density of the methylated spirit.
- Buoyant Force: When an object is immersed in a fluid, it experiences an upward force called the buoyant force. This force is equal to the weight of the fluid displaced by the object. This is Archimedes' principle. The buoyant force (Fb) can be calculated as Fb = Vρg, where 'V' is the volume of the fluid displaced (which is equal to the volume of the submerged object), 'ρ' is the density of the fluid, and 'g' is the acceleration due to gravity.
- Apparent Weight: The apparent weight of an object immersed in a fluid is the difference between its weight in air and the buoyant force acting on it. It is the net force experienced by the object in the fluid. In simpler terms, it's what the object seems to weigh when submerged. Mathematically, Apparent Weight = Weight in Air - Buoyant Force.
Step-by-Step Solution
Now, let's break down the problem and calculate the apparent weight step by step:
1. Calculate the Volume of the Cube
The cube has sides of 2 cm each. Therefore, the volume (V) of the cube can be calculated as:
V = side × side × side = 2 cm × 2 cm × 2 cm = 8 cm³
It is crucial to maintain consistent units throughout the calculation. Let's convert the volume from cm³ to m³ since the standard unit for density is kg/m³ and for acceleration due to gravity is m/s². We know that 1 m = 100 cm, so 1 m³ = (100 cm)³ = 1,000,000 cm³. Therefore:
V = 8 cm³ × (1 m³ / 1,000,000 cm³) = 8 × 10⁻⁶ m³
2. Convert the Density of Methylated Spirit to kg/m³
The density of the methylated spirit is given as 0.585 g/cm³. We need to convert this to kg/m³. We know that 1 kg = 1000 g and 1 m³ = 1,000,000 cm³.
ρ = 0.585 g/cm³ × (1 kg / 1000 g) × (1,000,000 cm³ / 1 m³) = 585 kg/m³
3. Calculate the Buoyant Force
The buoyant force (Fb) is the weight of the fluid displaced by the cube. We can calculate this using the formula:
Fb = Vρg
Where:
V = Volume of the cube = 8 × 10⁻⁶ m³
ρ = Density of methylated spirit = 585 kg/m³
g = Acceleration due to gravity = 9.8 m/s²
Substituting the values, we get:
Fb = (8 × 10⁻⁶ m³) × (585 kg/m³) × (9.8 m/s²)
Fb = 0.045864 N (approximately)
4. Calculate the Apparent Weight
The apparent weight is the difference between the weight in air and the buoyant force:
Apparent Weight = Weight in Air - Buoyant Force
Apparent Weight = 0.56 N - 0.045864 N
Apparent Weight = 0.514136 N
Therefore, the apparent weight of the metal cube when immersed in methylated spirit is approximately 0.514 N.
Summary of Calculations
- Volume of the cube: 8 × 10⁻⁶ m³
- Density of methylated spirit: 585 kg/m³
- Buoyant force: 0.045864 N
- Apparent weight: 0.514 N
Practical Implications and Real-World Applications
Understanding the principles behind buoyancy and apparent weight is crucial in various practical applications. For example, the design of ships and submarines heavily relies on these concepts. Ships are designed to displace a volume of water equal to their weight, allowing them to float. Submarines, on the other hand, can control their buoyancy to submerge or surface by adjusting the amount of water in their ballast tanks. This precisely controls the submarine's displacement and, consequently, its buoyancy.
The concept of buoyancy also plays a significant role in meteorology. Hot air balloons rise because the hot air inside the balloon is less dense than the surrounding cooler air, creating a buoyant force that lifts the balloon. Similarly, the movement of air masses in the atmosphere is influenced by density differences, which in turn affect weather patterns.
In engineering, understanding buoyant forces is essential in designing structures that are partially or fully submerged in water, such as bridges and offshore platforms. Engineers must consider the buoyant forces acting on these structures to ensure their stability and safety. The principles of buoyancy are also used in the design of life jackets and other flotation devices, which rely on materials that are less dense than water to provide an upward force and keep a person afloat.
Additionally, buoyancy is a critical factor in the oil and gas industry, particularly in offshore drilling operations. Floating platforms and drilling rigs must be designed to withstand the forces exerted by the water, including buoyant forces. The stability and safety of these structures depend on a thorough understanding of buoyancy principles. Moreover, the transportation of heavy equipment and materials often involves using buoyancy to reduce the effective weight of the items being moved, making the process more manageable and efficient.
The study of buoyancy also extends into the realm of scientific research. In oceanography, for instance, scientists use buoyant instruments and devices to collect data from different depths of the ocean. These instruments, such as floats and gliders, are designed to maintain specific buoyancy characteristics, allowing them to operate autonomously and gather valuable information about ocean currents, temperature, and salinity.
In the field of medicine, buoyancy principles are applied in hydrotherapy, where patients perform exercises in water to reduce the load on their joints and muscles. The buoyant force of the water assists in movement and provides support, making it easier for patients to rehabilitate from injuries or manage chronic conditions.
These are just a few examples of how the principles of buoyancy and apparent weight are applied in various fields. The fundamental understanding of these concepts allows for the development of innovative solutions and technologies that benefit society in numerous ways.
In this article, we successfully calculated the apparent weight of a metal cube immersed in methylated spirit by applying the principles of buoyancy and Archimedes' principle. We demonstrated how to calculate the volume of the cube, convert units, determine the buoyant force, and finally, compute the apparent weight. This exercise highlights the importance of understanding these fundamental physics concepts in solving practical problems. Mastering these concepts not only enhances our understanding of the physical world but also equips us with the tools to tackle a wide range of engineering and scientific challenges. The applications of buoyancy extend far beyond simple calculations, influencing the design and operation of various technologies and systems that impact our daily lives. From marine engineering to atmospheric science, the principles of buoyancy remain a cornerstone of scientific and engineering endeavors, underscoring the significance of a thorough grasp of these concepts for students and professionals alike. The ability to apply these principles effectively ensures the development of safer, more efficient, and innovative solutions in diverse fields. This article serves as a stepping stone for further exploration and application of these principles in more complex scenarios, fostering a deeper appreciation for the role of physics in our world.
