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When objects slide or move on an inclined plane, the coefficient of friction plays a crucial role in determining the resistance to motion. The coefficient of friction is a measure of the interaction between two surfaces and determines the frictional force between them. In this blog post, we will explore how to find the coefficient of friction on an inclined plane.
We will cover the necessary tools and materials, the step-by-step procedure, and provide worked-out examples. We will also differentiate between the coefficients of static and kinetic friction on an inclined plane to gain a deeper understanding of their differences.
Determining the Coefficient of Friction on an Inclined Plane
Required Tools and Materials
Before we dive into the procedure, let’s gather the tools and materials we need. Here’s a list of what you’ll require: – Inclined plane – Object to slide – Protractor or angle measuring device – Weighing scale – Measuring tape or ruler
Step-by-step Procedure
Now, let’s walk through the step-by-step procedure to find the coefficient of friction on an inclined plane:
1. Set up the inclined plane at the desired angle of inclination. Make sure it is stable and secure.
2. Measure the angle of inclination using a protractor or angle measuring device. This angle will be denoted as θ.
3. Place the object on the inclined plane and adjust its position until it remains stationary without any external force acting on it.
4. Measure the weight of the object using a weighing scale. This weight will be denoted as W.
5. Calculate the normal force acting on the object, which is the component of the weight perpendicular to the inclined plane. The normal force (N) can be calculated using the formula N = W * cos(θ).
6. Gradually increase the inclination of the plane until the object starts sliding. Note down the angle of inclination at which the object begins to slide. This angle will be denoted as θs.
7. Measure the sliding distance of the object along the inclined plane.
8. Calculate the coefficient of static friction (μs) using the formula μs = tan(θs).
9. Calculate the coefficient of kinetic friction (μk) using the formula μk = tan(θ).
Worked-out Example
To illustrate the procedure, let’s consider an example:
1. The inclined plane has an angle of inclination (θ) of 30 degrees.
2. The object on the inclined plane has a weight (W) of 20 N.
3. The object begins to slide at an angle of inclination (θs) of 20 degrees.
4. The sliding distance of the object is measured to be 2 meters.
Using the given values, we can calculate the coefficients of static and kinetic friction: – Normal force (N) = W * cos(θ) = 20 N * cos(30 degrees) = 17.32 N – Coefficient of static friction (μs) = tan(θs) = tan(20 degrees) ≈ 0.364 – Coefficient of kinetic friction (μk) = tan(θ) = tan(30 degrees) ≈ 0.577
Therefore, the coefficient of static friction on the inclined plane is approximately 0.364, while the coefficient of kinetic friction is approximately 0.577.
Finding the Coefficient of Friction on an Inclined Plane without Mass
Theoretical Background
Now, let’s explore how to find the coefficient of friction on an inclined plane without knowing the mass of the object. This method utilizes the relationship between the angle of inclination and the coefficient of friction.
Detailed Procedure
Here’s a detailed procedure to find the coefficient of friction on an inclined plane without mass:
1. Set up the inclined plane at the desired angle of inclination and ensure its stability.
2. Measure the angle of inclination using a protractor or angle measuring device. Let’s denote this angle as θ.
3. Place the object on the inclined plane and adjust its position until it remains stationary without any external force acting on it.
4. Gradually increase the inclination of the plane until the object starts sliding. Note down the angle of inclination at which the object begins to slide. This angle will be denoted as θs.
5. Calculate the coefficient of static friction (μs) using the formula μs = tan(θs).
6. Calculate the coefficient of kinetic friction (μk) using the formula μk = tan(θ).
Practical Example
Let’s consider a practical example to understand this method better:
1. The inclined plane has an angle of inclination (θ) of 45 degrees.
2. The object begins to slide at an angle of inclination (θs) of 30 degrees.
Using the formulas mentioned above, we can calculate the coefficients of static and kinetic friction:
Hence, the coefficient of static friction on the inclined plane is approximately 0.577, and the coefficient of kinetic friction is approximately 1.
Differentiating Between Coefficient of Static and Kinetic Friction on an Inclined Plane
Defining Static and Kinetic Friction
Before understanding how to calculate each coefficient, let’s define static and kinetic friction.
– Static friction occurs when two surfaces are in contact but not sliding relative to each other. It prevents the object from moving until a certain force is applied.
– Kinetic friction, on the other hand, occurs when two surfaces are sliding relative to each other. It opposes the motion of the object.
How to Calculate Each Coefficient
To calculate the coefficient of static friction (μs) and the coefficient of kinetic friction (μk) on an inclined plane, we use the following formulas:
– Coefficient of static friction (μs) = tan(θs), where θs is the angle of inclination at which the object begins to slide.
– Coefficient of kinetic friction (μk) = tan(θ), where θ is the angle of inclination of the inclined plane.
Examples for Better Understanding
Let’s consider an example to differentiate between the coefficients of static and kinetic friction: – The inclined plane has an angle of inclination (θ) of 20 degrees. – The object begins to slide at an angle of inclination (θs) of 15 degrees.
Using the formulas mentioned earlier, we can calculate the coefficients of static and kinetic friction: – Coefficient of static friction (μs) = tan(θs) = tan(15 degrees) ≈ 0.268 – Coefficient of kinetic friction (μk) = tan(θ) = tan(20 degrees) ≈ 0.364
In this example, the coefficient of static friction is approximately 0.268, while the coefficient of kinetic friction is approximately 0.364.
By understanding the distinction between static and kinetic friction, we can better comprehend the nature of the forces at play on an inclined plane.
Numerical Problems on how to find coefficient of friction on an inclined plane
Problem 1
A block of mass 5 kg is placed on an inclined plane with an angle of 30 degrees. The block is on the verge of sliding down the plane, and the force required to just prevent the block from sliding is 30 N. Find the coefficient of friction between the block and the plane.
Solution:
Given:
Mass of the block, m = 5 kg
Angle of the inclined plane, θ = 30 degrees
Force required to prevent sliding, F = 30 N
The force required to prevent sliding can be calculated using the equation:
where g is the acceleration due to gravity and μ is the coefficient of friction.
Rearranging the equation to solve for μ:
Substituting the given values:
Simplifying the equation gives:
Therefore, the coefficient of friction between the block and the inclined plane is approximately 0.232.
Problem 2
A box of mass 10 kg slides down an inclined plane with a constant acceleration of 2 m/s². The angle of the inclined plane is 45 degrees. Calculate the coefficient of friction between the box and the plane.
Solution:
Given:
Mass of the box, m = 10 kg
Acceleration of the box, a = 2 m/s²
Angle of the inclined plane, θ = 45 degrees
The acceleration of the box can be related to the force of friction using the equation:
where g is the acceleration due to gravity and μ is the coefficient of friction.
Rearranging the equation to solve for μ:
Substituting the given values:
Simplifying the equation gives:
Therefore, the coefficient of friction between the box and the inclined plane is approximately 0.414.
Problem 3
A block of mass 2 kg is placed on an inclined plane with an angle of 60 degrees. The block is at rest and requires a force of 7 N to start sliding down the plane. Determine the coefficient of static friction between the block and the plane.
Solution:
Given:
Mass of the block, m = 2 kg
Angle of the inclined plane, θ = 60 degrees
Force required to start sliding, F = 7 N
The force required to start sliding can be calculated using the equation:
where g is the acceleration due to gravity and μ_s is the coefficient of static friction.
Rearranging the equation to solve for μ_s:
Substituting the given values:
Simplifying the equation gives:
Therefore, the coefficient of static friction between the block and the inclined plane is approximately 0.577.
The back work ratio is a crucial parameter in the field of thermodynamics, specifically in the study of gas and steam turbines. It provides valuable insights into the efficiency and performance of these machines. In this section, we will delve into the definition of the back work ratio and explore the formula used to calculate it.
Definition of Back Work Ratio
The back work ratio is a measure of the amount of work required to operate a turbine compared to the work it produces. It is expressed as a ratio and is an essential factor in determining the overall efficiency of a turbine.
In a gas or steam turbine, the back work ratio represents the portion of the work output that is used to drive the compressor or pump. This work is necessary to maintain the required pressure ratio and ensure the continuous operation of the turbine.
A high back work ratio indicates that a significant portion of the turbine’s power output is used to drive the compressor or pump, resulting in lower overall efficiency. Conversely, a low back work ratio signifies that a smaller proportion of the power output is consumed by these components, leading to higher efficiency.
Formula for Back Work Ratio
The back work ratio can be calculated using the following formula:
Back Work Ratio = (Work Input - Work Output) / Work Output
To understand this formula better, let’s break it down:
Work Input: This refers to the amount of work required to operate the turbine. It includes the work needed to drive the compressor or pump, as well as any other external work input.
Work Output: This represents the actual work produced by the turbine. It is the net power output available for useful work, such as generating electricity or driving machinery.
By subtracting the work output from the work input and dividing it by the work output, we obtain the back work ratio. This ratio provides a quantitative measure of the energy losses within the turbine system.
It is important to note that the back work ratio is influenced by various factors, including turbine efficiency, compressor efficiency, pressure ratio, and isentropic efficiency. These parameters play a significant role in determining the overall performance and effectiveness of the thermodynamic cycle.
In the next sections, we will explore each of these factors in more detail and understand their impact on the back work ratio.
Back Work Ratio in Gas Turbine Engines
The back work ratio is an important parameter that measures the efficiency of a gas turbine engine. It represents the amount of work required to drive the compressor compared to the work produced by the turbine. In other words, it quantifies the energy losses within the engine.
Reasons for Relatively High Back Work Ratio
There are several factors that contribute to a relatively high back work ratio in gas turbine engines. Understanding these reasons is crucial for optimizing the performance of these engines.
Compressor Efficiency: The efficiency of the compressor plays a significant role in determining the back work ratio. A less efficient compressor requires more work to achieve the desired pressure ratio, resulting in a higher back work ratio.
Pressure Ratio: The pressure ratio, which is the ratio of the compressor outlet pressure to the inlet pressure, also affects the back work ratio. Higher pressure ratios generally lead to higher back work ratios.
Isentropic Efficiency: The isentropic efficiency of the compressor and turbine stages impacts the back work ratio. Lower isentropic efficiencies result in higher back work ratios, as more work is required to compensate for the energy losses.
Typical Back Work Ratio Values for Gas Turbine Engines
The back work ratio values for gas turbine engines can vary depending on various factors such as engine design, operating conditions, and specific applications. However, there are some typical ranges that can be observed.
Aircraft Gas Turbines: In aircraft gas turbines, the back work ratio is usually in the range of 0.3 to 0.5. These engines are designed to prioritize power output and fuel efficiency, which leads to relatively lower back work ratios.
Industrial Gas Turbines: Industrial gas turbines, used in power generation and other industrial applications, tend to have higher back work ratios. Typical values for these engines range from 0.5 to 0.8. The higher back work ratios are often a result of the need for higher power output and efficiency.
Combined Cycle Power Plants: Gas turbines used in combined cycle power plants, where the exhaust gases are used to generate steam for a steam turbine, have lower back work ratios compared to standalone gas turbines. The back work ratio for these systems can range from 0.2 to 0.4.
It’s important to note that these values are general guidelines and can vary depending on specific engine configurations and operating conditions.
In conclusion, the back work ratio is a critical parameter in gas turbine engines that measures the efficiency of the engine. Understanding the reasons for a relatively high back work ratio and typical values for different types of gas turbines can help engineers and operators optimize the performance of these engines. By focusing on improving compressor efficiency, pressure ratio, and isentropic efficiency, it is possible to reduce the back work ratio and enhance the overall efficiency of gas turbine engines.
Back Work Ratio in Brayton Cycle
The back work ratio is an important parameter in the Brayton cycle, which is a thermodynamic cycle commonly used in gas turbine engines. It quantifies the amount of work required to drive the compressor compared to the work output of the turbine. In this section, we will explore the explanation of the Brayton cycle and the formula used to calculate the back work ratio.
Explanation of Brayton Cycle
The Brayton cycle is a thermodynamic cycle that describes the operation of a gas turbine engine. It consists of four main processes: compression, combustion, expansion, and exhaust. Let’s take a closer look at each of these processes:
Compression: In this process, the air is drawn into the compressor and compressed to a higher pressure. The compressor plays a crucial role in increasing the pressure of the air before it enters the combustion chamber.
Combustion: Once the air is compressed, it is mixed with fuel and ignited in the combustion chamber. The combustion process releases a large amount of heat, which increases the temperature and pressure of the working fluid.
Expansion:The high-pressure, high-temperature gas from the combustion chamber is expanded in the turbine. As the gas expands, it loses energy, which is converted into mechanical work to drive the turbine and any attached load, such as an aircraft engine or a power generator.
Exhaust: After the expansion process, the gas is exhausted from the turbine. It may still contain some energy, but it is typically at a lower pressure and temperature compared to the gas entering the turbine.
The Brayton cycle is often referred to as an ideal cycle, assuming certain ideal conditions such as no losses due to friction or heat transfer. However, in real-world applications, these losses are inevitable and can impact the overall efficiency of the cycle.
Back Work Ratio Formula in Brayton Cycle
The back work ratio (BWR) is defined as the ratio of the work required to drive the compressor to the work output of the turbine. It is an essential parameter in determining the overall efficiency of the gas turbine engine. The formula to calculate the back work ratio is as follows:
BWR = (Work Input to Compressor) / (Work Output of Turbine)
The work input to the compressor is the energy required to compress the air, while the work output of the turbine is the energy produced by the expansion of the high-pressure gas. By comparing these two values, we can determine the efficiency of the Brayton cycle.
A high back work ratio indicates that a significant portion of the turbine’s output work is used to drive the compressor, resulting in lower net power output. Conversely, a low back work ratio implies that the turbine is more efficient, as less work is required to drive the compressor.
It is important to note that the back work ratio is influenced by various factors, including the efficiency of the compressor and turbine, the pressure ratio across the compressor and turbine, and the isentropic efficiencies of these components. Optimizing these factors can help improve the overall efficiency of the Brayton cycle.
In conclusion, the back work ratio is a crucial parameter in the Brayton cycle, as it quantifies the efficiency of the gas turbine engine. By understanding the explanation of the Brayton cycle and the formula to calculate the back work ratio, engineers and designers can make informed decisions to optimize the performance of gas turbine systems.
Back Work Ratio in Rankine Cycle
Explanation of Rankine Cycle
The Rankine Cycle is a thermodynamic cycle commonly used in power plants to generate electricity. It is a closed-loop cycle that utilizes both a heat source and a heat sink to convert heat energy into mechanical work. The cycle consists of four main components: a boiler, a turbine, a condenser, and a pump.
The process begins in the boiler, where heat is added to the working fluid, typically water, to convert it into high-pressure steam. This high-pressure steam then enters the turbine, where it expands and does work by driving the turbine blades. As the steam expands, its pressure and temperature decrease.
After leaving the turbine, the low-pressure steam enters the condenser, where it is cooled and condensed back into liquid form. This condensation process releases heat, which is transferred to a cooling medium, such as water from a nearby river or ocean. The condensed liquid is then pumped back to the boiler to repeat the cycle.
Back Work Ratio Formula in Rankine Cycle
The back work ratio (BWR) is a parameter used to evaluate the performance of a Rankine Cycle. It represents the ratio of the work required to operate the pump to the net work output of the turbine. Mathematically, it can be expressed as:
BWR = (Work input to pump) / (Net work output of turbine)
The work input to the pump is the energy required to increase the pressure of the working fluid from the condenser pressure to the boiler pressure. This work input is typically expressed in terms of kilojoules per kilogram (kJ/kg) of the working fluid.
On the other hand, the net work output of the turbine is the difference between the work done by the turbine and the work done by the pump. The work done by the turbine is the energy extracted from the steam as it expands in the turbine, while the work done by the pump is the energy required to increase the pressure of the working fluid.
The back work ratio is an important parameter because it indicates the efficiency of the Rankine Cycle. A lower back work ratio implies a more efficient cycle, as less work is required to operate the pump relative to the work output of the turbine. Conversely, a higher back work ratio indicates a less efficient cycle, as more work is needed to operate the pump.
In practice, engineers strive to minimize the back work ratio by optimizing the design and operation of the Rankine Cycle. This can be achieved by using efficient pumps and turbines, maximizing the temperature difference between the heat source and heat sink, and reducing losses due to friction and heat transfer.
By carefully considering the back work ratio, engineers can improve the overall efficiency and performance of power plants that utilize the Rankine Cycle. This, in turn, leads to reduced energy consumption and lower environmental impact.
Back Work Ratio in Otto Cycle
The back work ratio is an important parameter in the Otto cycle, which is a thermodynamic cycle commonly used in internal combustion engines. It helps us understand the efficiency of the cycle and the amount of work required to operate the engine. In this section, we will explain the Otto cycle and discuss the formula for calculating the back work ratio.
Explanation of Otto Cycle
The Otto cycle is a theoretical thermodynamic cycle that describes the operation of a typical gasoline engine. It consists of four processes: intake, compression, combustion, and exhaust. During the intake process, the fuel-air mixture is drawn into the cylinder. In the compression process, the mixture is compressed to increase its temperature and pressure. The combustion process involves the ignition of the compressed mixture, resulting in a rapid expansion of gases and the generation of power. Finally, in the exhaust process, the burned gases are expelled from the cylinder.
The Otto cycle is an idealized representation of the actual engine operation, assuming certain ideal conditions such as perfect combustion, no heat loss, and ideal gas behavior. Despite these simplifications, the Otto cycle provides a useful framework for analyzing engine performance.
Back Work Ratio Formula in Otto Cycle
The back work ratio (BWR) is defined as the ratio of the work required to operate the engine’s auxiliaries (such as the compressor and the pump) to the net work output of the engine. It is an indicator of the efficiency of the cycle and is typically expressed as a percentage.
The formula for calculating the back work ratio in the Otto cycle is:
BWR = (Work Input to Compressor + Work Input to Pump) / Work Output of Engine * 100
The work input to the compressor is the work required to compress the air-fuel mixture during the compression process. It is influenced by factors such as the compression ratio and the efficiency of the compressor. The work input to the pump is the work required to circulate the coolant or lubricant in the engine. It depends on the flow rate and the pressure difference across the pump.
The work output of the engine is the net work produced during the power stroke of the combustion process. It is influenced by factors such as the pressure ratio, the isentropic efficiency of the combustion process, and the mechanical efficiency of the engine.
By calculating the back work ratio, engineers can assess the efficiency of the engine’s auxiliaries and identify areas for improvement. A high back work ratio indicates that a significant portion of the engine’s power is consumed by the auxiliaries, reducing the overall efficiency of the system. On the other hand, a low back work ratio suggests that the auxiliaries are operating efficiently, allowing more power to be delivered to the output.
In conclusion, the back work ratio is an important parameter in the Otto cycle, providing insights into the efficiency of the engine’s auxiliaries. By understanding and optimizing the back work ratio, engineers can enhance the overall performance of internal combustion engines.
Significance of Back Work Ratio
The back work ratio is an important parameter in the field of thermodynamics, specifically in the study of gas turbines and steam turbines. It plays a crucial role in determining the overall efficiency and performance of these power generation systems. In this section, we will explore the importance of the back work ratio and how it is calculated.
Importance of Back Work Ratio
The back work ratio is a measure of the energy required to drive the compressor or the pump in a thermodynamic cycle. It represents the fraction of the work output that is used to overcome the losses in the turbine or the compressor. A low back work ratio indicates that a significant portion of the work output is consumed by these losses, resulting in reduced overall efficiency.
One of the key reasons why the back work ratio is significant is its direct impact on the efficiency of the turbine. The back work ratio affects both the turbine efficiency and the overall power output of the system. A higher back work ratio means that more energy is required to drive the compressor or the pump, resulting in a decrease in the net power output of the turbine.
Additionally, the back work ratio also influences the pressure ratio and the isentropic efficiency of the compressor or the pump. These parameters are crucial in determining the performance of the entire thermodynamic cycle. A higher back work ratio leads to an increase in the pressure ratio, which can have a positive effect on the overall efficiency of the system.
Furthermore, the back work ratio is closely related to the efficiency of the turbine. By minimizing the losses in the turbine or the compressor, the back work ratio can significantly improve the overall efficiency of the system. This is particularly important in power generation applications, where even a small increase in efficiency can result in substantial cost savings and environmental benefits.
Calculation of Back Work Ratio
The back work ratio can be calculated using the following formula:
Back Work Ratio = (Work Input - Work Output) / Work Output
To calculate the back work ratio, we need to determine the work input and the work output of the system. The work input represents the energy required to drive the compressor or the pump, while the work output represents the useful work produced by the turbine.
In a gas turbine, the work input is typically calculated by measuring the power input to the compressor, while the work output is determined by measuring the power output from the turbine. Similarly, in a steam turbine, the work input is calculated based on the enthalpy change of the steam, while the work output is determined by measuring the power output from the turbine.
Once we have the values for the work input and the work output, we can substitute them into the formula to calculate the back work ratio. The resulting value provides us with a quantitative measure of the energy losses in the turbine or the compressor.
In conclusion, the back work ratio is a significant parameter in the study of gas turbines and steam turbines. It directly influences the efficiency and performance of these power generation systems. By understanding the importance of the back work ratio and how to calculate it, engineers and researchers can optimize the design and operation of turbines to achieve higher efficiency and improved performance. Conclusion
In conclusion, the back work ratio is a crucial metric that helps measure the efficiency of a heat engine or a refrigeration system. It indicates the amount of useful work output obtained from a system compared to the amount of work input required to operate it. A higher back work ratio signifies a more efficient system, as it indicates that a larger proportion of the input energy is converted into useful work. On the other hand, a lower back work ratio suggests that a significant portion of the input energy is lost as waste or used to operate auxiliary components. By optimizing the back work ratio, engineers and designers can improve the overall performance and energy efficiency of various systems, including power plants, engines, and refrigeration units. It is important to consider the back work ratio when evaluating and comparing different systems, as it provides valuable insights into their energy conversion capabilities. By understanding and optimizing the back work ratio, we can strive towards more sustainable and energy-efficient technologies that minimize waste and maximize the utilization of available resources.
Frequently Asked Questions
Q: Why are the back work ratio relatively high in gas turbine engines?
A: Gas turbine engines have relatively high back work ratios because a significant portion of the work produced by the turbine is used to drive the compressor, resulting in a higher energy requirement for the overall operation of the engine.
Q: What are typical back work ratio values for gas-turbine engines?
A: Typical back work ratio values for gas turbine engines can vary depending on the specific design and operating conditions. However, values between 0.3 and 0.5 are commonly observed in practice.
Q: What is back work ratio?
A: Back work ratio is a thermodynamic parameter that represents the ratio of work required to drive the compressor to the work produced by the turbine in a thermodynamic cycle. It is an indicator of the efficiency of the overall cycle.
Q: What is the back work ratio of this cycle?
A: The back work ratio of a specific cycle depends on the design and operating conditions of the system. It can be calculated by dividing the work required to drive the compressor by the work produced by the turbine.
Q: What is back work ratio in Brayton cycle?
A: In the Brayton cycle, the back work ratio represents the ratio of work required to drive the compressor to the work produced by the turbine. It is an important parameter that affects the overall efficiency of the cycle.
Q: What is back work ratio formula?
A: The formula to calculate the back work ratio is: Back Work Ratio = Work Required to Drive Compressor / Work Produced by Turbine.
Q: What is back work ratio of gas turbine?
A: The back work ratio of a gas turbine represents the ratio of work required to drive the compressor to the work produced by the turbine. It is an important parameter that affects the efficiency and performance of the gas turbine.
Q: What is back work ratio in thermodynamics?
A: In thermodynamics, back work ratio is a parameter that measures the efficiency of a thermodynamic cycle. It represents the ratio of work required to drive the compressor to the work produced by the turbine.
Q: What is turbine efficiency?
A: Turbine efficiency is a measure of how effectively a turbine converts the energy of a fluid (such as gas or steam) into mechanical work. It is typically expressed as a percentage and is influenced by factors such as design, operating conditions, and losses.
Q: What is compressor efficiency?
A: Compressor efficiency is a measure of how effectively a compressor increases the pressure of a fluid. It is typically expressed as a percentage and is influenced by factors such as design, operating conditions, and losses.
Static and kinetic friction are fundamental concepts in the field of physics, governing the motion of objects and the forces that act upon them. Understanding the nuances of these two types of friction is crucial for students studying mechanics, engineering, and related disciplines. This comprehensive guide will delve into the technical details, formulas, and practical applications of static and kinetic friction, providing a valuable resource for physics students.
Understanding Static Friction
Static friction is the force that opposes the relative motion between two surfaces in contact when they are at rest. This force arises due to the adhesive and interlocking forces between the microscopic irregularities on the surfaces. The coefficient of static friction, denoted as μ_s, is a dimensionless quantity that describes the magnitude of this force.
The maximum static friction force, F_s,max, can be calculated using the following formula:
F_s,max = μ_s * N
Where:
– F_s,max is the maximum static friction force (in Newtons)
– μ_s is the coefficient of static friction (dimensionless)
– N is the normal force acting on the object (in Newtons)
The coefficient of static friction can be determined experimentally by gradually increasing the applied force on an object until it just begins to move. The ratio of the maximum static friction force to the normal force is the coefficient of static friction.
Factors Affecting Static Friction
The coefficient of static friction can be influenced by several factors, including:
Surface Roughness: Rougher surfaces generally have a higher coefficient of static friction, as the microscopic irregularities on the surfaces create more interlocking and adhesive forces.
Surface Cleanliness: Contaminants or lubricants on the surfaces can reduce the coefficient of static friction by decreasing the adhesive forces between the surfaces.
Temperature: The coefficient of static friction may decrease at higher temperatures due to the increased thermal energy and reduced adhesion between the surfaces.
Normal Force: The coefficient of static friction is generally independent of the normal force, as long as the surfaces remain in contact.
Examples and Numerical Problems
Example 1: A 5 kg box is resting on a horizontal surface. The coefficient of static friction between the box and the surface is 0.4. Calculate the maximum static friction force acting on the box.
Given:
– Mass of the box, m = 5 kg
– Coefficient of static friction, μ_s = 0.4
– Normal force, N = m × g = 5 kg × 9.8 m/s^2 = 49 N
Calculation:
F_s,max = μ_s × N
F_s,max = 0.4 × 49 N = 19.6 N
Numerical Problem: A 10 kg object is placed on a horizontal surface. The coefficient of static friction between the object and the surface is 0.3. Determine the minimum force required to start the object moving.
Given:
– Mass of the object, m = 10 kg
– Coefficient of static friction, μ_s = 0.3
– Normal force, N = m × g = 10 kg × 9.8 m/s^2 = 98 N
Calculation:
F_s,max = μ_s × N
F_s,max = 0.3 × 98 N = 29.4 N
The minimum force required to start the object moving is 29.4 N.
Understanding Kinetic Friction
Kinetic friction, also known as dynamic friction, is the force that opposes the relative motion between two surfaces that are already in motion. This force is generally lower than the maximum static friction force and is more constant in nature. The coefficient of kinetic friction, denoted as μ_k, is a dimensionless quantity that describes the magnitude of this force.
The kinetic friction force, F_k, can be calculated using the following formula:
F_k = μ_k × N
Where:
– F_k is the kinetic friction force (in Newtons)
– μ_k is the coefficient of kinetic friction (dimensionless)
– N is the normal force acting on the object (in Newtons)
The coefficient of kinetic friction can be determined experimentally by measuring the force required to maintain a constant velocity of an object sliding on a surface.
Factors Affecting Kinetic Friction
The coefficient of kinetic friction can be influenced by several factors, including:
Surface Roughness: Rougher surfaces generally have a higher coefficient of kinetic friction, as the microscopic irregularities on the surfaces create more resistance to motion.
Surface Cleanliness: Contaminants or lubricants on the surfaces can reduce the coefficient of kinetic friction by decreasing the adhesive forces between the surfaces.
Temperature: The coefficient of kinetic friction may decrease at higher temperatures due to the increased thermal energy and reduced adhesion between the surfaces.
Sliding Velocity: The coefficient of kinetic friction may slightly decrease as the sliding velocity increases, due to the reduced time for adhesion to occur.
Examples and Numerical Problems
Example 2: A 2 kg object is sliding on a horizontal surface with a constant velocity. The coefficient of kinetic friction between the object and the surface is 0.25. Calculate the kinetic friction force acting on the object.
Given:
– Mass of the object, m = 2 kg
– Coefficient of kinetic friction, μ_k = 0.25
– Normal force, N = m × g = 2 kg × 9.8 m/s^2 = 19.6 N
Calculation:
F_k = μ_k × N
F_k = 0.25 × 19.6 N = 4.9 N
Numerical Problem: A 5 kg object is sliding on a horizontal surface with an initial velocity of 10 m/s. The coefficient of kinetic friction between the object and the surface is 0.3. Determine the distance the object travels before coming to a complete stop.
Given:
– Mass of the object, m = 5 kg
– Initial velocity, v_0 = 10 m/s
– Coefficient of kinetic friction, μ_k = 0.3
– Normal force, N = m × g = 5 kg × 9.8 m/s^2 = 49 N
Calculation:
F_k = μ_k × N
F_k = 0.3 × 49 N = 14.7 N
Using the kinematic equation:
v^2 = v_0^2 – 2 × a × d
0 = (10 m/s)^2 – 2 × (F_k / m) × d
d = v_0^2 / (2 × a)
d = (10 m/s)^2 / (2 × 14.7 N / 5 kg)
d = 50 m / 2.94 m/s^2
d = 17 m
The object will travel a distance of 17 meters before coming to a complete stop.
Comparison of Static and Kinetic Friction
The key differences between static and kinetic friction are:
Property
Static Friction
Kinetic Friction
Definition
Force that opposes the initiation of motion
Force that opposes the continued motion
Coefficient
Coefficient of static friction (μ_s)
Coefficient of kinetic friction (μ_k)
Magnitude
Generally higher than kinetic friction
Generally lower than static friction
Variability
Can vary depending on surface conditions
Relatively constant for a given pair of surfaces
Dependence on Normal Force
Generally independent of normal force
Directly proportional to normal force
Dependence on Sliding Velocity
Independent of sliding velocity
May slightly decrease with increasing velocity
It is important to note that in certain cases, the coefficient of static friction can be less than the coefficient of kinetic friction. This can occur when the surfaces are very smooth and have a low level of adhesion between them. In such situations, the force required to initiate motion may be less than the force required to maintain motion.
Practical Applications of Static and Kinetic Friction
Static and kinetic friction play a crucial role in various real-world applications, including:
Braking Systems: The coefficient of kinetic friction between the brake pads and the brake discs or drums determines the braking force and the stopping distance of a vehicle.
Traction and Locomotion: The coefficient of static friction between the tires and the road surface is essential for the traction and acceleration of vehicles, as well as the stability and control of the vehicle.
Mechanical Devices: Static and kinetic friction are important in the design and operation of mechanical devices, such as gears, bearings, and clutches, where they can affect the efficiency and performance of the system.
Climbing and Gripping: The coefficient of static friction between the soles of shoes and the surface being walked on determines the ability to climb and grip surfaces, which is important in activities like rock climbing and mountaineering.
Sliding and Pushing: The coefficient of kinetic friction between two surfaces determines the force required to slide or push an object across a surface, which is relevant in various industrial and everyday applications.
Understanding the principles of static and kinetic friction, as well as their practical applications, is essential for physics students to develop a comprehensive understanding of mechanics and its real-world implications.
Conclusion
Static and kinetic friction are fundamental concepts in physics that govern the motion of objects and the forces acting upon them. This comprehensive guide has provided a detailed exploration of these two types of friction, including their definitions, formulas, factors affecting them, and practical applications. By understanding the nuances of static and kinetic friction, physics students can better analyze and solve problems related to mechanics, engineering, and various other fields. The examples and numerical problems presented in this guide serve as valuable resources for students to apply the concepts and deepen their understanding of this crucial topic.
References
Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers with Modern Physics (10th ed.). Cengage Learning.
Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics (10th ed.). Wiley.
Giancoli, D. C. (2014). Physics for Scientists and Engineers with Modern Physics (4th ed.). Pearson.
Tipler, P. A., & Mosca, G. (2008). Physics for Scientists and Engineers (6th ed.). W. H. Freeman.
Young, H. D., & Freedman, R. A. (2016). University Physics with Modern Physics (14th ed.). Pearson.
This article discusses about angular momentum examples. The term angular simply adds a rotational component in the motion. This article discusses about angular momentum and its examples.
First we shall discuss about linear momentum and its true meaning. Then a simple addition of rotational component in the motion will make it angular momentum. This article will focus more on angular momentum and its examples.
Linear momentum is defined as the product of mass of an object with its velocity. It is essential to find the force exerted by the oject’s motion.
We can say that the rate of change of linear momentum will give us the value of force that will be exerted by that object when it crashes into another object or the force that will be needed to stop it from moving. Linear momentum takes place in a linear motion. Let us study about angular momentum in the next section.
What is angular momentum?
The analog of linear momentum in rotational motion is called as angular momentum. The magnitude of angular momentum can be found using three quantities.
These three quantities are- mass of the object, velocity of the object, radius of the trajectory traced by the object in rotational motion. These three quantities are multiplied by each other as a result of which we get the value of angular momentum. We shall see examples of angular momentum in the next section.
The angular momentum is the analog of linear momentum in rotational motion. The radius factor peeps in when we deal with objects following rotational motion.
Let us see some of the examples of angular momentum that are given below-
Ice skater
An ice skater spreads his/her hands to maintain stability while rotating on ice, then he/she come closer in order to increase the rotational speed. This is a clear example of conservation of momentum.
Helicopter propellers
The helicopter propellers are so arranged that effect of one propellers cancels out effect of other propeller. This effect is the net centrifugal force which acts outside due to the action of angular momentum.
Gyroscope
Gyroscopes are used for controlling the orientation of the spacecraft/aircrafts. They spin so fast that the force generated out of this angular momentum makes the gyroscopes stand straight on its axis, any deviation in this axis will mean that the aircraft or spacecraft is making a turn.
Fan blades
Similar to the helicopter blades, fan blades are also arranged in such a manner that they will cancel each other’s effect. We should note that the blades with smaller length rotate faster and the blades with greater length move slower. But the net angular momentum remains conserved.
Rotation of Earth
Earth has an angular momentum of magnitude mvr. Where m is the mass of Earth, V is the velocity of Earth and R the radius of Earth.
A rotating chair is an example of angular momentum. Here we can also note that momentum will be conserved if the person sitting on the chair tries to spreads his legs or joins his legs. The speed of the chair will be increased or decreased according to the legs position implying that the momentum is conserved.
Rotating a luggage bag
We often get bored while waiting for our flights. Sometimes we start rotating our bags to pass our time. These bags will gain angular momentum once we start rotating it.
Toys
Some toys have rotating elements in them or they themselves rotate. Their rotational motion is possible mainly due to angular momentum that they have gained.
Rolling in flight
When an aircraft performs rolling maneuver, it is supposed to have angular momentum. The direction of the momentum is perpendicular to the motion of the aircraft.
Mixer grinder blades
The blades of mixer grinder rotate to cut the vegetables or fruits placed inside the grinder. These blades move as a result of angular momentum gained by them.
Spinning a cricket ball
When we spin a cricket ball, the ball gains some angular momentum. This way the ball turns when it has impact on the ground, this happens due to force generated due to angular momentum.
Swinging a bat
When we swing a bat to hit the ball, the bat gains angular momentum. The momentum is then transferred to the ball which after impacts goes far away from the batsman.
Ballerina
A ballerina rotates on her toes. The hand positions decide the rotational speed of ballerina. If her hands are spread across then the speed is less and if the hands are closer to her body then she rotates faster.
Stone ties with a thread and rotating it
This is the most common example of rotational motion. Once the thread is subject to rotation, the stone tied with it gains angular momentum.
Spinning a basketball
Some basketball players rotate basketball on their fingers. The basketball rotates as a result of angular momentum gained by it.
Discuss throw
A discuss throw player rotates his/her hand in such a way that the discuss also gains some angular momentum. This angular momentum is then transferred to a linear motion after getting released from hand.
Hammer throw
Similar to discuss throw, hammer also gains angular momentum after the player rotates his hands with hammer in it. The hammer attains linear momentum once it is released from the hands of hammer throw player.
Cycling
The wheels of cycles attain angular momentum which is converted to linear momentum of the cycle itself. This way the momentum is also conserved.
Divers making a 360 degree dive
While diving, sometimes, the divers make 360 degrees loop before entering the water body. This is an example angular momentum gained by the diver while jumping of the diving board.
This article answers the question why does ionization energy increase across a period? We will study basics of periodic table first.
Then carry our discussion to trends followed by ionisation energy of different elements in the periodic table. It is important to know the meaning of ionisation energy first, so we shall discuss about ionisation energy and then continue with our discussion.
What is ionisation energy?
If we want to remove an electron from an atom, it is logical to remove the most loosely packed electron of that atom.
Ionisation energy is the name given to this energy that is required to remove the loosely packed electron. Without this energy, we won’t be able to remove the electron from the influence of nuclear force of attraction.
Periodic table is a table which represents different chemical elements found on Earth. These elements are given a specific atomic number and are then arranged in ascending order of atomic number.
Periodic table has many divisions in it. These divisions are called as blocks. With all the rows being called as period and all the columns being called as groups. We shall study about the trends of ionisation energy across both periods and groups.
What is atomic number?
Atomic number is considered as the fingerprint of the chemical element. It is simply the total number of protons present inside the atom.
Number of protons for every chemical element is unique hence it is considered as the fingerprint of that particular chemical element. The arrangement of chemical elements in the periodic table is done in increasing values of atomic numbers.
What is a period?
A period is simply a row in periodic table. Horizontal arrangement of chemical elements in periodic table is termed as period.
The atomic number increases by 1 as we move ahead in a period. The last element of any period is a noble gas. Noble gases have no free electron revolving around the nucleus. Noble gases are considered as the most stable elements in the periodic table.
What is a group?
As discussed above, rows of periodic table are called as period. Similarly, the columns are called as groups.
Here as we move down the group, the atomic number increases but not by 1. These groups divide metals from non metals and noble gases and alkali metals. Even the groups follow a trend for different properties. We shall discuss about them in later sections of this article.
Periodic trends
Different properties follow different trends as we move from left to right in a period. There are certain exceptions as well which don’t fit inside the trend.
We shall discuss about different trends in a period in the section given below-
Atomic radius– The atomic radius or the size of an atom generally decreases as we move across a period from left to right. This is due to the fact that the magnitude of nuclear charge is same but number of electrons keep increasing in the shell.
Ionsiation energy- Ionisation energy depends on the atomic radius. As the radius decreases acrosss a period, the ionisation energy keeps on increasing as we move across a period. It is maximum for nobel gases.
Electorn affinity– This property is exactly opposite to ionisation energy. Energy is released when an electron is stuffed into an atom meaning it is added to an atom. Electron affinity will increase while moving towards right in the periodic table.
Electronegativity – This property increases its value when we move towards right in the period. Metallicity- The metals are situated at the left hand side of the periodic table and non metals are situated at the right hand side of the periodic table. We can conclude that the metallicity value decreases when we move towards right in a period.
Group trends
A column of periodic table is called as group. The properties exhibited by these elements follow different trends along the group. We shall discuss about these trends in section given below-
Atomic radius- As we move down the group, an extra shell is added in the elements. We can say that due to addition of an extra shell, the atomic radius increases as we go down along the group.
Ionisation energy – The minimum value of energy required to pull out an electron from the influence of nucleus is called as ionisation energy. As the atomic radius increases as we move down the group, the influence of nucleus decreases on the electron and hence it becomes easier to remove electron. So we can conclude that the value of ionisation energy decreases as we go down along the group.
Electron affinity– Its meaning is right opposite to that of ionisation energy. Atom will release energy if an electron is plucked from it or stuffed into it. Similar to the trend of ionisation energy, electron affinity decreases while moving towards bottom in a group.
Electronegativity– While going towards the bottom of group, electronegativity keeps decreasing.
Metallicity- Metallicity can becompared to the tendency of an atom to lose electron. Metallicity increases while going towards the bottom of group in periodic table.
Why does ionization energy increase across a period?
Coming to the most important question in this article that is why does ionization energy increase across a period? The answer is already discussed n above sections, but we shall discuss it again.
Atomic radius is a deciding factor behind the energy required to remove the loosely packed electron. This is because smaller the radius, closer the electron will be to the nucleus. Hence greater will be the attractive force of nucleus towards electron. Hence ionisation energies of Hydrogen is low and keeps on increasing as we move towards right in the period. Only Oxygen has an exception because it forms electron pairs, due to repulsive forces, the electron is easily removed.
Why is second ionisation energy greater than first ionisation energy?
The name itself suggests that first ionisation energy is related to the first electron. It is the energy required to pluck out the first electron from the atom.
Similarly the second ionisation energy is used to remove second electron from the already electron deficit atom. The influence of nucleus on electron increases as and when we dig deeper into the atom. Hence it becomes difficult to remove that electron from the influence of nucleus thus justifying the fact that second ionisation energy is more than first ionisation energy.
Magnetic materials can be broadly classified into three categories: ferromagnetic, paramagnetic, and diamagnetic materials. Each type of magnetic material has unique properties and can be characterized by various measurable and quantifiable parameters. This comprehensive guide will delve into the intricate details of these magnetic materials, providing a thorough understanding for physics students.
Ferromagnetic Materials
Ferromagnetic materials are the most widely studied and utilized magnetic materials due to their strong magnetic properties and ability to be easily magnetized. These materials exhibit a spontaneous magnetization even in the absence of an external magnetic field, and their magnetic moments align in the same direction, resulting in a net magnetic moment.
Saturation Magnetization (Ms)
The saturation magnetization, denoted as Ms, is the maximum magnetization that a ferromagnetic material can achieve when it is fully magnetized. This parameter is a crucial characteristic of ferromagnetic materials and is measured in units of Tesla (T). The saturation magnetization is directly related to the magnetic moment of the atoms or ions within the material and can be calculated using the following formula:
Ms = Nμ / V
Where:
– N is the number of magnetic atoms or ions per unit volume
– μ is the magnetic moment of each atom or ion
– V is the volume of the material
The saturation magnetization of common ferromagnetic materials, such as iron (Fe), nickel (Ni), and cobalt (Co), can range from 1.6 T to 2.4 T, depending on the specific material composition and microstructure.
Remanence (Br)
Remanence, denoted as Br, is the magnetization that remains in a ferromagnetic material after the removal of an external magnetic field. This parameter is crucial for the design of permanent magnets and is measured in units of Tesla (T). The remanence of a ferromagnetic material is influenced by its microstructure, composition, and the strength of the applied magnetic field during magnetization.
The remanence of a ferromagnetic material can be calculated using the following formula:
Br = Ms (1 - e^(-t/τ))
Where:
– Ms is the saturation magnetization
– t is the time for which the external magnetic field is applied
– τ is the characteristic time constant of the material
The remanence of common ferromagnetic materials can range from 0.5 T to 1.4 T, depending on the specific material composition and processing conditions.
Coercivity (Hc)
Coercivity, denoted as Hc, is a measure of the resistance of a ferromagnetic material to becoming demagnetized. It is the magnetic field required to reduce the magnetization of the material to zero after it has been fully magnetized. Coercivity is measured in units of Oersted (Oe) or Ampere per meter (A/m).
The coercivity of a ferromagnetic material can be calculated using the following formula:
Hc = (6K1 / Ms) + (Nz Ms)
Where:
– K1 is the first-order anisotropy constant of the material
– Ms is the saturation magnetization
– Nz is the demagnetizing factor in the direction of magnetization
The coercivity of common ferromagnetic materials can range from 10 Oe to 2000 Oe, depending on the specific material composition and microstructure.
Curie Temperature (Tc)
The Curie temperature, denoted as Tc, is the temperature at which a ferromagnetic material transitions to a paramagnetic state. At this temperature, the material loses its spontaneous magnetization, and its magnetic moments become randomly oriented. The Curie temperature is a fundamental property of ferromagnetic materials and is measured in units of Kelvin (K).
The Curie temperature of common ferromagnetic materials can range from 600 K to 1400 K, depending on the specific material composition and structure.
Paramagnetic Materials
Paramagnetic materials exhibit weak magnetic properties and become magnetized only in the presence of an external magnetic field. Unlike ferromagnetic materials, paramagnetic materials do not possess a spontaneous magnetization, and their magnetic moments are randomly oriented in the absence of an external magnetic field.
Magnetic Susceptibility (χ)
The magnetic susceptibility, denoted as χ, is a measure of the degree of magnetization of a paramagnetic material in response to an external magnetic field. It is a dimensionless quantity that represents the ratio of the induced magnetization to the applied magnetic field. The magnetic susceptibility of paramagnetic materials is typically positive and small, ranging from 10^-5 to 10^-3.
The magnetic susceptibility of a paramagnetic material can be calculated using the following formula:
χ = C / (T - Tc)
Where:
– C is the Curie constant, a material-specific parameter
– T is the absolute temperature
– Tc is the Curie temperature of the material
The Curie constant, C, is a measure of the strength of the magnetic interactions within the paramagnetic material and is related to the magnetic moment of the atoms or ions. The Curie constant can be calculated using the following formula:
C = (Nμ^2) / (3kB)
Where:
– N is the number of magnetic atoms or ions per unit volume
– μ is the magnetic moment of each atom or ion
– kB is the Boltzmann constant
The magnetic susceptibility of paramagnetic materials is strongly dependent on temperature, and it decreases as the temperature increases, as described by the Curie-Weiss law.
Diamagnetic Materials
Diamagnetic materials exhibit no magnetic properties and become slightly magnetized in the presence of an external magnetic field. Unlike ferromagnetic and paramagnetic materials, diamagnetic materials do not possess any permanent magnetic moments, and their magnetic moments are induced by the applied magnetic field.
Magnetic Susceptibility (χ)
The magnetic susceptibility, denoted as χ, is a measure of the degree of magnetization of a diamagnetic material in response to an external magnetic field. It is a dimensionless quantity that represents the ratio of the induced magnetization to the applied magnetic field. The magnetic susceptibility of diamagnetic materials is typically negative and very small, ranging from -10^-6 to -10^-9.
The magnetic susceptibility of a diamagnetic material can be calculated using the following formula:
χ = -2μ0μB^2 / (3kBT)
Where:
– μ0 is the permeability of free space
– μB is the Bohr magneton, a fundamental unit of magnetic moment
– kB is the Boltzmann constant
– T is the absolute temperature
The negative value of the magnetic susceptibility indicates that diamagnetic materials are repelled by an external magnetic field, in contrast to ferromagnetic and paramagnetic materials, which are attracted to the field.
The magnetic susceptibility of diamagnetic materials is independent of temperature and the strength of the applied magnetic field, making them useful for various applications, such as magnetic shielding and the detection of small magnetic fields.
Hysteresis Loops
In addition to the parameters discussed above, the magnetic properties of magnetic materials can also be characterized by hysteresis loops, which describe the relationship between the magnetization and the magnetic field. The hysteresis loop is a graphical representation of the magnetization process, and it provides information about the energy required to magnetize the material.
The area inside the hysteresis loop is a measure of the energy required to magnetize the material, and it is known as the hysteresis loss. Ferromagnetic materials typically exhibit a larger hysteresis loop compared to paramagnetic and diamagnetic materials, indicating a higher energy requirement for magnetization.
The shape and size of the hysteresis loop are influenced by the material’s composition, microstructure, and processing conditions, making it a valuable tool for the characterization and optimization of magnetic materials.
Conclusion
In this comprehensive guide, we have explored the intricate details of the three main types of magnetic materials: ferromagnetic, paramagnetic, and diamagnetic. Each type of material exhibits unique magnetic properties that can be quantified and characterized using various parameters, such as saturation magnetization, remanence, coercivity, Curie temperature, and magnetic susceptibility.
By understanding the fundamental principles and characteristics of these magnetic materials, physics students can gain a deeper insight into the behavior and applications of these materials in various fields, including electronics, energy storage, and magnetic sensing.
References
Jiles, D. C. (1998). Introduction to magnetism and magnetic materials. CRC Press.
Spaldin, N. A. (2011). Magnetic materials: fundamentals and applications. Cambridge University Press.
Tumanski, S. (2011). Handbook of magnetic materials. CRC Press.
Mass is a fundamental physical quantity that is widely recognized as an extensive property. Extensive properties are those that depend on the amount of matter or substance present in a system, and mass is a direct measure of the quantity of matter. In this comprehensive blog post, we will delve into the intricacies of mass as an extensive property, exploring its characteristics, applications, and the underlying principles that govern its behavior.
Understanding Extensive Properties
Extensive properties are physical quantities that scale with the size or amount of a system. In other words, the value of an extensive property is directly proportional to the quantity of matter or substance present. Some common examples of extensive properties include:
Mass
Volume
Energy
Charge
Amount of substance (moles)
Extensive properties are in contrast to intensive properties, which do not depend on the size or amount of a system. Intensive properties, such as temperature, pressure, and density, remain constant regardless of the quantity of matter present.
Mass as an Extensive Property
Mass is a fundamental extensive property that quantifies the amount of matter in an object or system. It is a measure of the inertia of an object, which is the resistance to changes in its motion. The mass of an object or system is directly proportional to the amount of matter it contains.
Characteristics of Mass as an Extensive Property
Additive Nature: The mass of a system is the sum of the masses of its individual components. If you combine two objects with masses m1 and m2, the total mass of the combined system is m1 + m2.
Proportionality: The mass of an object or system is proportional to the amount of matter it contains. If you double the amount of matter in a system, the mass of the system will also double.
Invariance: Mass is an invariant property, meaning it does not change with the location or state of the object. The mass of an object remains the same regardless of its position, temperature, or other physical conditions.
Measuring Mass
Mass is typically measured using a balance or scale, which compares the gravitational force acting on the object to the force acting on a known standard mass. The SI unit of mass is the kilogram (kg), and common smaller units include the gram (g) and the milligram (mg).
Relationship with Other Extensive Properties
Mass is closely related to other extensive properties, such as volume and weight. The volume of an object is the amount of space it occupies, and it is also an extensive property. The weight of an object is the force exerted on it by gravity, which is proportional to its mass and the acceleration due to gravity.
The relationship between mass, volume, and density (an intensive property) can be expressed as:
Density = Mass / Volume
This equation shows that mass and volume are both extensive properties, while density is an intensive property that does not depend on the amount of matter present.
Applications of Mass as an Extensive Property
The extensive nature of mass has numerous applications in various fields of science and engineering. Some of the key applications include:
Measurement and Quantification: Mass is used to measure and quantify the amount of matter in objects, substances, and systems. This is essential for various scientific and industrial processes, such as chemical reactions, material processing, and product manufacturing.
Conservation of Mass: The principle of conservation of mass states that the total mass of a closed system remains constant during any physical or chemical process. This principle is fundamental to many laws and theories in physics and chemistry.
Density Calculations: As mentioned earlier, the relationship between mass and volume can be used to calculate the density of a substance, which is an important property in fields like materials science, engineering, and geology.
Gravitational Interactions: The mass of an object determines its gravitational attraction to other objects, which is crucial in understanding celestial mechanics, orbital dynamics, and the behavior of massive objects in the universe.
Inertia and Momentum: Mass is a measure of an object’s inertia, which is its resistance to changes in motion. This property is essential in understanding the dynamics of moving objects, such as in mechanics, engineering, and transportation.
Atomic and Subatomic Particles: In the realm of particle physics, the mass of subatomic particles, such as protons, neutrons, and electrons, is a fundamental property that governs their behavior and interactions.
Numerical Examples and Calculations
To further illustrate the extensive nature of mass, let’s consider some numerical examples and calculations:
Mass of a Substance: Suppose you have a sample of pure copper with a mass of 50 grams. If you double the amount of copper, the mass of the new sample will be 100 grams.
Mass and Volume Relationship: A cube-shaped block of aluminum has a mass of 500 grams and a volume of 200 cubic centimeters. The density of the aluminum can be calculated as: Density = Mass / Volume
Density = 500 g / 200 cm^3 = 2.5 g/cm^3
If the volume of the block is doubled, the mass will also double to 1000 grams, while the density remains the same.
Mass and Weight Relationship: The weight of an object is the force exerted on it by gravity, which is proportional to its mass. If an object has a mass of 10 kilograms and the acceleration due to gravity is 9.8 m/s^2, the weight of the object can be calculated as: Weight = Mass × Acceleration due to gravity
Weight = 10 kg × 9.8 m/s^2 = 98 N
If the mass of the object is doubled, its weight will also double to 196 N.
These examples demonstrate how the extensive nature of mass allows for the calculation and prediction of various physical properties and relationships.
Conclusion
In summary, mass is an extensive property that depends on the amount of matter present in a system. The mass of an object or substance is directly proportional to the quantity of matter it contains, and this property has numerous applications in various fields of science and engineering. Understanding the characteristics and behavior of mass as an extensive property is crucial for understanding and analyzing a wide range of physical phenomena.
References:
Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers with Modern Physics (10th ed.). Cengage Learning.
Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics (10th ed.). Wiley.
Tipler, P. A., & Mosca, G. (2008). Physics for Scientists and Engineers (6th ed.). W. H. Freeman.
Young, H. D., & Freedman, R. A. (2016). University Physics with Modern Physics (14th ed.). Pearson.
This article discusses about thermal radiation example. Radiation is nothing but a mode of heat transfer which does not need any medium for the transfer to take place.
It is notable fact that for radiation heat transfer to take place, even physical contact is not required. The heat gets transferred without any medium in between or physical contact between the two systems. We shall discuss more about different examples of radiation heat transfer.
Heat transfer is the process in which thermal energy and entropy is transferred from one system to another.
Major factor which affects the heat transfer is the temperature difference between the two systems. The heat will flow always in the direction from high temperature to low temperature system. Although there are multiple modes of heat transfer but we shall limit our discussion to only radiation heat transfer.
In simple words, radiation heat transfer is the type of heat transfer in which the system at lower temperature absorbs, reflects or transmits the heat that is being emitted by system at higher temperature.
It is a notable fact that radiation heat transfer does not need any medium or physical contact. The best example of radiation heat transfer is Earth getting heated by the heat being emitted by sun. This transfer of heat takes place through radiation heat transfer. We shall study more examples of radiation heat transfer in the later sections of this article.
Example of radiation heat transfer
Radiation heat transfer takes place around us but we usually ignore it. If we look around, there are many examples where we can see radiation heat transfer taking place.
Let us see some common examples of radiation heat transfer. They are given below-
Heat transfer taking place inside microwave oven
Microwave oven is used to heat food. The microwave oven sends out electromagnetic waves which penetrate the food and makes it warm. This way the heat transfer takes place.
Earth getting heated by Sun
Sun sends out electromagnetic waves to the vacuum of space. These waves are collected by Earth as a result of which the planet gets heated up. This is the most common example of heat transfer done by radiation.
Heat being emitted by a radiator
A radiator in vehicle sends out heat to the surroundings. If we are standing near the radiator, we are bale to feel the heat due to radiation.
Light being emitted by an incandescent lamp
An incandescent lamp becomes hot after being lit for some while. This heat is transferred to the surroundings with the help of radiation heat transfer. If we are standing near this lamp, we will be able to feel the heat. This is due to Radiation heat transfer.
Gamma ray emission from a nucleus
Gamma rays are an example of electromagnetic waves. These waves don’t need any medium to travel hence we can say that these waves travel with the help of radiation. When gamma rays are emitted by nucleus, they travel with the help of radiation. Any object coming in its close vicinity may experience radiation effects.
Feeling warm when standing beside a car whose engine is hot
When a car is used for long period, the engine becomes hot due to its long operation duration. The engine surface is hot but we can feel the heat without even touching the engine itself. This happens as a result of radiation heat transfer from the surface of engine to its surroundings.
Heat coming out of hot food
We feel the heat from warm food without even touching it. The plate becomes hot due to conduction taking place. But when we feel the heat without touching the plate or food, it is because of radiation heat transfer.
Metal rod when heated emits heat to surroundings
When we heat a metal rod using an external heat source, the rod gets heated up by the process of conduction. This heated rod transfers the heat to surroundings using radiation heat transfer. We need not touch the rod in order to feel the heat, we can just put our hand near the rod and we will know the rod is warm or not.
Molten metal used in casting emits heat in the surroundings
For casting a product, metal is melted into liquid. This requires immense heat, this heat is then emitted back to the surroundings. This happens as a result of radiation heat transfer between molten metal and surroundings.
Magma emits heat to its surrounding areas
Similar to molten metals, magma is molten rock. These molten rocks emit heat to the surroundings with the help of radiation heat transfer.
Standing beside a fire makes us feel warm
Fire emits heat to the surroundings. Without touching fire also, one can get burns on his hands. We can say that fire emits heat by the process of radiation heat transfer.
Bike’s silencer emits heat when the bike is being driven or has just been driven
The silencer used in bikes become hot after a long ride. The silencer is so hot that our legs can feel the heat just by keeping them near the silencer. If we touch the silencer we are surely going to get burnt due to heat transfer by conduction. But when we feel hot without touching it, it is due to radiation heat transfer.
We feel warm when standing beside a stove
When we lit up a stove, the heat from the stove s transferred to the surroundings with the help of radiation heat transfer.
Laptop’s body emits heat when it is used for long hours
The electronics used in laptop get hot when the laptop is used for long hours. This heat is transferred to the surroundings with the help of radiation heat transfer.
Hot metal emits heat after being machined
A metal becomes hot after it gets machined. This heat is generated due to friction. This generated heat is emitted back to surroundings with the help of radiation heat transfer.
This article discusses about examples of heat transfer. Heat transfer is a branch of thermal engineering that concerns with generation, use and exchange of heat energy from one system to another.
Heat can be transferred by many ways. Most commonly known methods are conduction, convection and radiation. This article discusses about different modes of heat transfer and then we will discuss about examples of heat transfer that we see in our daily lives.
As discussed above, heat transfer is the branch of thermal engineering which deals with generation of heat, use of heat and transfer of heat through various physical systems.
Heat does not necessarily need a medium to get transferred from one system to another. These systems are at different temperatures. The heat will flow from a system with high temperature to a system that is at lower temperature. We shall study about its types in the later sections of this article.
The heat can be transferred from one system to another by many ways. Some methods need a medium whereas some methods like radiation don’t need any medium for heat transfer to take place.
The different methods of heat transfer are given below as follows-
Conduction – Conduction is a mode of heat transfer where the heat s transferred through systems when they are in contact with each other. The molecules of these systems vibrate and transfer energy through these vibrations. The vibrations although fade away as the distance becomes larger proving that conduction is inversely proportional to the length of the systems.
Radiation – Radiation is a process of heat transfer in which the heat is transferred without the help of any medium or physical contact between the systems.
Examples of heat transfer
Heat transfer takes place almost everywhere around us in daily lives. The most commonly seen examples of heat transfer are given below-
Our skin gets warm after going out in sunlight
The heat emitted by the Sun gets radiated towards Earth. This radiated heat is absorbed by our skin and hence we feel warm when we go outside in sunlight. Long exposures may even burn the skin (tanning is an example).
The steel spoon gets warm after coming in contact with hot container
When the steel spoon is kept in touch with a hot container, the steel spoon gets warm due to heat transfer by conduction. As the steel spoon is a good conductor of heat, the heat gets easily transferred to steel making the steel spoon’s temperature higher.
Boiling water
The water is boiled due to convection and conduction both. The vessel inside which the water is kept becomes hot first. This is due to conduction heat transfer. Then the water gets heated as a result of heat transfer between the water surface and the hot vessel. The remaining water gets hot by the process of convection.
Thermometer
In thermometer, the level of Mercury rises when the heat from body is transferred to it. The rise in Mercury is used to determine the temperature of our body.
Image Credit: Pixabay
We get burned after touching hot pan
When the pan is hot and we touch it, we feel hot or burn our hands sometimes. This is due to heat transfer taking place due to conduction. The heat from hot pan is transferred to our skin as we make contact to the pan.
Water gets warm after leaving under hot sun
When we leave water under hot sun, the heat radiated by the Sun makes the water warm. This happens so because the water absorbs the radiated heat which in turn makes it warm. This is the same reason why we feel hot after stepping outside the house under scorching heat.
Food gets warm after heating it in microwave
Microwave is used for warming the food. The microwave sends out waves which makes the food warm. This entire heat transfer process takes place in the form of radiation.
Food gets cold when left in room
When we leave the food untouched in our room, then the food tries to make thermal equilibrium with the surroundings which happens by lowering the temperature of food. As the food gets colder, thermal equilibrium is established. This is also an example of heat transfer as heat is transferred from the food to surroundings.
Tea cup gets hot after tea is poured in the cup
After tea is poured in the cup, conduction takes place between the outermost layer of tea and the surface of the cup. This way the heat is transferred from tea to the cup as a result of which the cup becomes hot.
Phone gets hot when its battery gets hot
When the battery gets hot due to longer operation of phone, the phone also gets hot. This is because the battery is in contact with the mobile phone. The heat is transferred from battery to the phone with the help of conduction.
Phone charger gets hot when the wires inside get hot
The wires inside a charger adaptor get hot due to excessive charging. These wires are in contact with the adaptor from inside, this way heat transfer due to conduction takes place and adaptor in turn also becomes hot.
TV gets hot after its coil gets hot after excessive usage
After excessive usage, the coils inside TV get hot. The coil being in contact with the inside of TV, makes the tv also hot. This is why it is recommended to watch television under control.
Forest fire
When the heat from sun is very strong, the dry leaves may catch fire due to excessive heat. This is an example of radiation heat transfer. It is important to note that radiation can cause fire too!
Ice melts after being dipped in a warm drink
After dipping the ice in a warm drink, convection takes place between ice and the drink which makes the temperature of ice higher. This result in melting of ice.
Steamer
Steamer is a device that emits out steam. This steam is used for getting rid of cold or skin treatment etc. The heat from the steam is transferred to our skin with the help of convection. The steam carries the heat with it and transfers it to the skin when in contact with it.
Examples of heat transfer by radiation
Radiation heat transfer does not physical contact of both the systems nor it needs a medium to get the heat transferred from one system to another. Let us see some of the examples of radiation heat transfer given below-
Hot metal rod transferring heat to surroundings – When a metal rod is heated, it emits out heat to its surroundings, this heat transfer takes place with the help of radiation. If we put our hand near the metal rod, we will feel hot even without touching it.
Microwave – Food is warmed inside a microwave by the action of heat transfer by radiation. The microwaves inside the microwave make the food warm with the help of radiation.
Solar UV radiation – Solar UV radiation is the radiation emitted by the sun. This radiation can be used for generating electricity using solar panels. Even our skin gets warm due to the action of UV radiation. This is solely due to heat transfer by radiation.
Emission of Gamma rays – Gamma rays are a type of em wave. These waves move by the principle of radiation after being emitted.
Light being emitted by incandescent lamp -Light from incandescent lamp is an example of radiation as we feel warm while standing beside the lamp even without touching it.
Heat coming out from bonfire – Bonfire is a small controlled fire used to make ourselves feel warm during cold weather. The heat transfer takes place with the help of radiation. We do not touch the fire of bonfire but still feel the heat being emitted by it.
Heat emitted by a radiator – A radiator in vehicle becomes hot when the vehicle has travelled too much. The heat emitted from the radiator can be felt by us. This is due to radiation heat transfer. We do not physically touch the radiator but still feel the heat.
This article discusses about examples of electromagnetic waves. As in the name suggests, the electromagnetic waves are related to both electricity and magnetism.
In this article we will be studying about different types of waves. After that we shall carry our discussion further to electromagnetic waves and its examples. Let us start with our discussion on electromagnetic waves first.
Electromagnetic waves, the name itself suggests that these waves are related to both electricity and magnetic field.
These waves are formed by the vibrations taking place between electric and magnetic field. These type of waves constitute of oscillating electric field and magnetic field. We shall study more about waves in later sections of this article.
There are many types of waves. These are waves are sorted into two main groups of waves. The two main types of waves are given below-
Transverse waves– Transverse waves are those waves which oscillate along a path perpendicular to the direction of wave propagation. EM waves, ripples in water etc are some examples of transverse waves.
Longitudinal waves– Waves in which the medium vibrates parellely to the direction of wave propagation. The direction in which the medium is displaced has the same direction as that of direction of wave propagation.
Electromagnetic waves types
Even electromagnetic spectrum is divided in to seven other sub types. The classifiaction of these waves is done on the basis of their frequencies.
The different types of electromagnetic waves are given in the section below-
Gamma rays– The frequency range of gamma rays is >3×10^17 Hz and wavelength range is <1nm.
X rays– The frequency range of X rays is 3×10^16-3×10^17 and the wavelength ranges from 1 to 10 nm.
Ultraviolet rays– The frequency range of ultraviolet rays is 7.5×10^14-3×10^16 and the wavelength ranges from 10 to 400 nm.
Infrared– The frequency range of infrared waves is 3×10^12 to 4.3×10^14 and the wavelength ranges from 700 to 10^5 nm.
Microwave– The frequency range of microwaves is 3×10^9 to 3×10^12 and the wavelength ranges from 10^5 to 10^8 nm.
Radio waves– The frequency range of radio waves is <3×10^9 and the wavelength range is >10^8 nm.
Electromagnetic waves example
Electromagnetic waves are used in everyday applications. Some of the examples where electromagnetic waves are used are given in the section given below-
Radar waves
Radar waves are used to detect enemy vessel near our vicinity. These waves are emitted by RADAR and are reflected back after striking to the enemy vessel. This vessel can be aircraft or submarine or any other human equipped vessel.
Solar energy
UV rays are used to generate electricity using solar panels. These rays after striking the panel generate an EMF inside the panel. A capacitor can then store the generated electricity. Night vision- Infrared waves are used to see objects during night time. Night vision camera and goggles are used for security purposes to catch thieves/ terrorists roaming in the dark.
Heat sensors
Heat sensors also use infrared waves. The heat spectrum is variable for different objects. Different objects emit different amounts of heat, this spectrum can be observed by using infrared waves.
Microwaves
Microwaves are used for heating food inside the microwave ovens. Even radar uses microwaves. Food is heated instantly after microwaves strike the food.
Radio waves
Radio waves are used for audio transmission by FM stations. They use these radio waves to broadcast their content.
Television
Television sets also use radio waves for the transmission of their content. We can see different shows on television with the help of these waves.
Imaging bone structures
X rays are used for imaging bone structures. These rays penetrate inside the human body and strikes the bones giving a luminiscent images of the same.
Kill bacterias
Gamma rays are used for killing bacterias in marshmallows and to sterilise medical equipments.
Used to observe visible world
Visible light spectrum is used by humans to see the world around us. Without this spectrum, we won’t be able to see objects around us.
Electromagnetic waves in the order of increasing wavelength
We have discussed in the above sections that EM waves are divided into seven types according to their frequency/wavelengths.
The different types of EM waves in increasing order is given in the section below-
Gamma ray, X ray, UV rays, Visible light, infrared rays, microwaves and radio waves.
How are electromagnetic waves formed?
Electromagnetic waves are the waves which are related to both electric field and magnetic field. These waves are produced with the help of both the types of fields.
When magnetic field and electric field come in contact with each other, electromagnetic waves are formed. Both magnetic and electric fields make ninety degrees with each other as well as to the direction of propagation of wave.
How are electromagnetic waves propagated?
There are different media of propagation of electromagnetic waves. These are given in the section below-
Ground waves– When the electromagnetic waves are transferred along the surface then it is called as ground wave propagation.
Space waves– When the electromagnetic waves travel through vacuum of space, then that type of propagation is called as space wave propagation. Light from sun and other stars travel using this mode of propagation.
Sky waves– Sky waves uses the principle of reflection. When electromagnetic waves are transmitted from the ground and are reflected back after striking ionosphere, then this type of propagation is known as sky wave propagation.
Properties of electromagnetic waves
The different properties of electromagnetic waves are given below-
These waves move with the speed of light.
These waves are transverse in nature, meaning the electric fields and magnetic fields are perpendicular to each other and the direction of wave propagation.
These waves can undergo interference and diffraction.
