Alpa P. Rajai

I am Alpa Rajai, Completed my Masters in science with specialization in Physics. I am very enthusiastic about Writing about my understanding towards Advanced science. I assure that my words and methods will help readers to understand their doubts and clear what they are looking for. Apart from Physics, I am a trained Kathak Dancer and also I write my feeling in the form of poetry sometimes. I keep on updating myself in Physics and whatever I understand I simplify the same and keep it straight to the point so that it deliver clearly to the readers.

How To Calculate Mass From Force And Velocity: Several Approaches and Problem Examples

January 21, 2024December 11, 2021 by Alpa P. Rajai

When it comes to understanding the relationship between force, mass, and velocity, it’s crucial to have a clear grasp of the fundamental principles of physics. In this blog post, we will explore how to calculate mass from force and velocity, delving into the underlying physics, mathematical representations, and step-by-step calculation methods. By the end, you’ll have a solid understanding of this concept and its practical applications in the field of physics and engineering.

The Relationship Between Force, Mass, and Velocity

The Physics Behind Force, Mass, and Velocity

In physics, force, mass, and velocity are interconnected concepts that play a fundamental role in describing the motion of objects. According to Newton’s second law of motion, force (F) is directly proportional to the product of mass (m) and acceleration (a). Mathematically, this can be expressed as:

$F = m cdot a$

Velocity (v), on the other hand, represents the rate of change of displacement with respect to time. It is calculated by dividing the change in position (∆x) by the change in time (∆t):

$v = frac{Delta x}{Delta t}$

The Mathematical Representation of the Relationship

By combining the formulas for force and velocity, we can derive an equation that relates mass to force and velocity. Rearranging Newton’s second law equation, we have:

$m = frac{F}{a}$

Substituting the formula for acceleration (a = ∆v/∆t), we obtain:

$m = frac{F}{frac{Delta v}{Delta t}}$

Simplifying further, we find:

$m = frac{F cdot Delta t}{Delta v}$

This equation allows us to calculate mass (m) when we know the force (F) and the change in velocity (∆v) over a given time interval (∆t).

How to Calculate Mass from Force and Velocity

Step-by-Step Guide to Calculate Mass

To calculate mass from force and velocity, follow these steps:

Determine the force acting on the object. This can be obtained from experimental data or given in the problem statement.
Measure the change in velocity (∆v) of the object over a given time interval (∆t).
Substitute the values of force and ∆v into the equation:

$m = frac{F cdot Delta t}{Delta v}$

Calculate the mass using the formula.

Worked Out Examples on Calculating Mass

Let’s consider a few examples to illustrate how to calculate mass from force and velocity.

Example 1:
A force of 20 N is applied to an object, causing it to accelerate from rest to a velocity of 10 m/s over a time interval of 5 seconds. What is the mass of the object?

Solution:
Given:
Force (F) = 20 N
Change in velocity (∆v) = 10 m/s
Time interval (∆t) = 5 s

Using the formula
$m = frac{F cdot Delta t}{Delta v}$

Substituting the given values:
$m = frac{20 , text{N} cdot 5 , text{s}}{10 , text{m/s}}$

Simplifying the expression:
$m = 10 , text{kg}$

Therefore, the mass of the object is 10 kg.

Example 2:
A ball is subject to a constant force of 12 N and accelerates uniformly to a velocity of 6 m/s in 0.5 seconds. What is the mass of the ball?

Solution:
Given:
Force (F) = 12 N
Change in velocity (∆v) = 6 m/s
Time interval (∆t) = 0.5 s

Using the formula
$m = frac{F cdot Delta t}{Delta v}$

Substituting the given values:
$m = frac{12 , text{N} cdot 0.5 , text{s}}{6 , text{m/s}}$

Simplifying the expression:
$m = 1 , text{kg}$

Therefore, the mass of the ball is 1 kg.

Common Mistakes to Avoid While Calculating Mass

When calculating mass from force and velocity, there are a few common mistakes to watch out for:

Forgetting to convert units: Ensure that all measurements are in consistent units (e.g., meters, seconds, Newtons) before plugging them into the formula.
Using average velocity: Be careful to use the change in velocity (∆v) rather than the average velocity when calculating mass.
Neglecting the sign of the force: Pay attention to the direction of the force and consider its sign when calculating mass.

Applications of Calculating Mass from Force and Velocity

Real-life Scenarios Where Mass Calculation is Required

The ability to calculate mass from force and velocity has numerous practical applications. Some examples include:

Automotive engineering: Determining the mass of a vehicle is crucial for understanding its performance, fuel efficiency, and stability.
Sports science: Calculating the mass of athletes’ bodies can help in training and performance analysis.
Aerospace engineering: Estimating the mass of aircraft and spacecraft is essential for flight dynamics, fuel consumption, and payload capacity.

Importance of Calculating Mass in Physics and Engineering

Understanding the relationship between mass, force, and velocity is vital in physics and engineering. It allows us to analyze and predict the behavior of objects in motion, enabling advancements in fields such as:

Kinetic energy: The ability to calculate mass helps determine an object’s kinetic energy, which is a crucial concept in understanding energy transformations.
Momentum: Calculating mass allows us to determine an object’s momentum, which is essential for analyzing collisions and determining the effect of forces on objects.
Gravitational force: By knowing the mass of objects, we can calculate the gravitational force they exert on each other, allowing us to explore celestial mechanics and understand phenomena such as planetary motion.

How can force and velocity be used to calculate mass?

The concept of calculating mass from force and velocity is explored in the article “How to calculate mass from force and velocity“. However, another interesting question arises: “How to find mass without acceleration?” This topic is covered in detail in the article “How to find mass without acceleration“. In this article, you can learn about methods to determine mass even without the presence of acceleration. It provides valuable insights into the calculations and equations involved in such scenarios.

Numerical Problems on how to calculate mass from force and velocity

Problem: A force of 10 N is applied to an object and it accelerates at a rate of 2 m/s^2. Calculate the mass of the object.

Solution:

Given:
Force (F) = 10 N
Acceleration (a) = 2 m/s^2

We know that force (F) is related to mass (m) and acceleration (a) by the equation:

$F = ma$

Substituting the given values, we have:

$10 = m times 2$

To find the mass (m), we divide both sides of the equation by 2:

$m = frac{10}{2}$

Therefore, the mass of the object is 5 kg.

Problem: An object has a mass of 2 kg and is moving with a velocity of 4 m/s. Calculate the force acting on the object.

Solution:

Given:
Mass (m) = 2 kg
Velocity (v) = 4 m/s

We know that force (F) is related to mass (m) and velocity (v) by the equation:

$F = mv$

Substituting the given values, we have:

$F = 2 times 4$

Therefore, the force acting on the object is 8 N.

Problem: A car of mass 1200 kg accelerates from rest to a velocity of 20 m/s in 10 seconds. Calculate the average force exerted on the car during this time.

Solution:

Given:
Mass (m) = 1200 kg
Initial velocity (u) = 0 m/s
Final velocity (v) = 20 m/s
Time (t) = 10 s

We know that average force (F) is related to mass (m), initial velocity (u), final velocity (v), and time (t) by the equation:

$F = frac{m(v-u)}{t}$

Substituting the given values, we have:

$F = frac{1200(20-0)}{10}$

Simplifying the equation, we get:

$F = frac{24000}{10}$

Therefore, the average force exerted on the car during this time is 2400 N.

Also Read:

How To Calculate Mass From Weight: Several Approaches and Problem Examples

January 21, 2024December 7, 2021 by Alpa P. Rajai

Calculating mass from weight is a fundamental concept in physics and engineering. Weight is the force exerted by an object due to gravity, while mass is the amount of matter present in an object. In this blog post, we will explore the relationship between weight and mass, and learn how to calculate mass from weight using various formulas and examples.

How to Calculate Mass from Weight

The Formula to Calculate Mass from Weight

To calculate mass from weight, we can use the equation:

$\text{mass} = \frac{\text{weight}}{\text{acceleration due to gravity}}$

The acceleration due to gravity on Earth is approximately 9.8 m/s $^2$ . However, this value can vary depending on the location and altitude. Therefore, if you’re performing calculations in a different environment, make sure to use the appropriate acceleration due to gravity value.

Step-by-step Guide on How to Calculate Mass from Weight

To calculate mass from weight, follow these steps:

Determine the weight of the object in Newtons.
Identify the acceleration due to gravity at the location.
Divide the weight by the acceleration due to gravity to find the mass.

Let’s go through an example to make the process clearer.

Worked out Examples on Calculating Mass from Weight

Example 1:
An object has a weight of 500 N. Calculate its mass.

Solution:
Using the formula, we have:
$\text{mass} = \frac{\text{weight}}{\text{acceleration due to gravity}}$

Substituting the given values, we get:
$\text{mass} = \frac{500 \, \text{N}}{9.8 \, \text{m/s}^2} \approx 51.02 \, \text{kg}$

Therefore, the mass of the object is approximately 51.02 kg.

Example 2:
A person weighs 750 N on the surface of Mars. Calculate their mass on Mars.

Solution:
First, we need to determine the acceleration due to gravity on Mars. Let’s assume it is 3.7 m/s $^2$ .

Using the formula, we have:
$\text{mass} = \frac{\text{weight}}{\text{acceleration due to gravity}}$

Substituting the given values, we get:
$\text{mass} = \frac{750 \, \text{N}}{3.7 \, \text{m/s}^2} \approx 202.7 \, \text{kg}$

Therefore, the mass of the person on Mars is approximately 202.7 kg.

Advanced Concepts in Calculating Mass from Weight

How to Calculate Mass from Weight and Volume

In some cases, you may need to calculate mass from weight and volume. To do this, you need to know the density of the material. The formula for calculating mass from weight and volume is:

$\text{mass} = \text{weight} \times \text{density}$

How to Calculate Mass from Weight and Gravity

When dealing with objects in different gravitational fields, the formula to calculate mass from weight and gravity is:

$\text{mass} = \frac{\text{weight}}{\text{acceleration due to gravity}}$

How to Calculate Mass from Molecular Weight

In chemistry, you can calculate the mass of a substance using its molecular weight. The formula to calculate mass from molecular weight is:

$\text{mass} = \text{molecular weight} \times \text{number of moles}$

How to Calculate Mass from Weight and Density

To calculate mass from weight and density, you can use the formula:

$\text{mass} = \frac{\text{weight}}{\text{density}}$

Practical Applications of Calculating Mass from Weight

Calculating Mass and Weight on Different Planets

The ability to calculate mass from weight is crucial when studying celestial bodies. By applying the concept of calculating mass from weight, scientists can determine the mass of objects on different planets or moons, providing insights into their composition and gravitational forces.

Converting Mass to Weight and Vice Versa

Knowing how to convert mass to weight and vice versa is useful in various fields. For example, in engineering, understanding the relationship between mass and weight is essential for designing structures and determining the loads they can withstand.

Calculating Mass from Weight in Different Units (Kg, Newtons)

Calculating mass from weight can be done using different units, such as kilograms (kg) or Newtons (N). It’s important to understand the correct units and conversions to ensure accurate calculations.

How can we calculate mass from weight and force? What insights can we gain by considering the concept of ‘Calculating mass from force and more’?

Calculating mass from force and more allows us to understand how weight and force can be used to determine the mass of an object. By exploring this concept, we can gain insights into the relationship between weight, force, and mass. This understanding is crucial in various fields, such as physics and engineering. By utilizing the methods discussed in the article, we can accurately calculate the mass of an object based on its weight and the force applied to it. This knowledge opens up possibilities for solving complex problems and making informed decisions.

Numerical Problems on how to calculate mass from weight

Problem 1:

A box weighs 25 N on Earth. What is the mass of the box?

Solution:
Given:
Weight of the box, $W = 25$ N

We know that weight is given by the formula:
$W = m \cdot g$

where:
$W$ = weight of the object (in Newtons)
$m$ = mass of the object (in kilograms)
$g$ = acceleration due to gravity (approximately $9.8$ m/s² on Earth)

To calculate the mass, we rearrange the formula as:
$m = \frac{W}{g}$

Substituting the given values into the formula, we get:
$m = \frac{25 \, \text{N}}{9.8 \, \text{m/s²}}$

Hence, the mass of the box is approximately $2.55$ kg.

Problem 2:

A person weighs 650 N on Earth. What is their mass?

Solution:
Given:
Weight of the person, $W = 650$ N

Using the same formula as before, we have:
$W = m \cdot g$

Rearranging the formula to solve for mass:
$m = \frac{W}{g}$

Substituting the given values:
$m = \frac{650 \, \text{N}}{9.8 \, \text{m/s²}}$

Thus, the mass of the person is approximately $66.33$ kg.

Problem 3:

An object has a weight of 1500 N on Earth. Determine its mass.

Solution:
Given:
Weight of the object, $W = 1500$ N

Applying the formula:
$W = m \cdot g$

Rearranging to find the mass:
$m = \frac{W}{g}$

Substituting the given values:
$m = \frac{1500 \, \text{N}}{9.8 \, \text{m/s²}}$

Therefore, the mass of the object is approximately $153.06$ kg.

Also Read:

How To Find Mass With Acceleration And Force: 7 Scenarios

January 21, 2024December 5, 2021 by Alpa P. Rajai

When it comes to understanding the relationship between mass, acceleration, and force, there are a few key concepts to grasp. In this blog post, we will delve into Newton’s Second Law of Motion, which forms the foundation for understanding the connection between these three variables. We will also explore the formulas that allow us to calculate mass with acceleration and force, and provide step-by-step guides and worked-out examples to help solidify our understanding. Additionally, we will touch on special cases and explore how to determine force and acceleration using mass, acceleration, and other variables. So, let’s get started!

The Relationship between Mass, Acceleration, and Force

how to find mass with acceleration and force — Image by SG0039 – Wikimedia Commons, Wikimedia Commons, Licensed under CC0.

A. Newton’s Second Law of Motion

Newton’s Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In simpler terms, it means that an object with a larger mass requires a greater force to accelerate it, while an object with a smaller mass requires less force to achieve the same acceleration. This law is fundamental to understanding the relationship between mass, acceleration, and force.

B. The Formula Connecting Mass, Acceleration, and Force

To calculate the relationship between mass, acceleration, and force, we can use the formula:

$F = m \cdot a$

In this equation, ‘F’ represents the force applied to the object, ‘m’ represents the mass of the object, and ‘a’ represents the acceleration experienced by the object. This formula allows us to find the force applied to an object when we know its mass and acceleration, or vice versa.

How to Calculate Mass with Acceleration and Force

A. Step-by-Step Guide to Finding Mass

To calculate the mass of an object using acceleration and force, follow these steps:

Identify the known quantities: You need to know the force applied to the object (‘F’) and the acceleration experienced by the object (‘a’).
Rearrange the formula: Rearrange the formula (F = m \cdot a) to solve for mass (m). The rearranged formula becomes (m = \frac{F}{a}).
Substitute the known values: Substitute the known values of force (‘F’) and acceleration (‘a’) into the formula.
Calculate the mass: Perform the calculation to find the value of mass (m).

B. Worked Out Examples

Let’s work through two examples to illustrate how to calculate mass using acceleration and force.

Example 1:
A force of 20 Newtons is applied to an object, resulting in an acceleration of 4 m/s². What is the mass of the object?

Solution:
Using the formula $(m = \frac{F}{a})$ , we can substitute the given values:
$(m = \frac{20}{4})$
$(m = 5) kg$

Example 2:
An object with a mass of 10 kg experiences an acceleration of 6 m/s². What is the force applied to the object?

Solution:
Using the formula $(F = m \cdot a)$ , we can substitute the given values:
$(F = 10 \cdot 6)$
$(F = 60)$ Newtons

Special Cases in Finding Mass with Acceleration and Force

Image by 4C – Wikimedia Commons, Licensed under CC BY-SA 3.0.

How To Find Mass With Acceleration And Force: 7 Scenarios 15

A. Finding Mass with Force and No Acceleration

In certain scenarios, an object may experience force without any acceleration. In these cases, the mass can be determined by rearranging the formula $(F = m \cdot a)$ and solving for mass $(m)$ . If the acceleration is zero, the equation simplifies to (F = m \cdot 0), which implies that the force applied to the object is zero. Therefore, the mass of the object in such cases can be any value, as long as there is no acceleration.

B. Finding Mass with Acceleration and Net Force

When an object experiences a net force, the acceleration can be determined using the formula $(F = m \cdot a)$ . By rearranging the formula and solving for mass (m), we can calculate the mass of the object. If the net force acting on the object is zero, the resulting acceleration will also be zero. In this case, the mass can be any value, as long as there is no net force acting on the object.

How to Determine Force with Mass, Acceleration, and Other Variables

A. Finding Force with Mass, Acceleration, and Time

If you know the mass of an object, its acceleration, and the time during which the force is applied, you can calculate the force using the formula:

$F = \frac{m \cdot \Delta v}{\Delta t}$

In this formula, ‘m’ represents the mass of the object, $(\Delta v)$ represents the change in velocity, and $(\Delta t)$ represents the change in time. By calculating the change in velocity and change in time, you can determine the force applied to the object.

B. Finding Force with Mass, Acceleration, and Distance

When you have the mass of an object, its acceleration, and the distance over which the force is applied, you can calculate the force using the formula:

$F = m \cdot a \cdot d$

In this formula, ‘m’ represents the mass of the object, ‘a’ represents the acceleration, and ‘d’ represents the distance. By multiplying the mass, acceleration, and distance, you can find the force applied to the object.

How can I find mass by considering acceleration and force, and what is the step-by-step process for calculating mass from force?

The process of finding mass by considering acceleration and force involves understanding the relationship between these three variables. To calculate mass from force, the step-by-step process can be explored by following the guidelines provided in the article Calculating mass from force step-by-step. This article provides contextually relevant information and insight into the content of the target URL. By following the step-by-step process, one can effectively determine the mass based on the force applied.

How to Calculate Acceleration with Mass, Force, and Other Variables

A. Finding Acceleration with Mass, Force, and Coefficient of Friction

If you know the mass of an object, the force applied to it, and the coefficient of friction, you can calculate the acceleration using the formula:

$a = \frac{F - \mu \cdot N}{m}$

In this formula, ‘F’ represents the force applied to the object, $(\mu)$ represents the coefficient of friction, and ‘N’ represents the normal force. By subtracting the product of the coefficient of friction and the normal force from the applied force, and then dividing it by the mass, you can determine the acceleration.

B. Finding Acceleration with Mass and Force of Gravity

When you have the mass of an object and the force of gravity acting on it, you can calculate the acceleration using the formula:

$a = \frac{F}{m}$

In this formula, ‘F’ represents the force of gravity and ‘m’ represents the mass of the object. By dividing the force of gravity by the mass, you can find the acceleration experienced by the object.

C. Finding Acceleration with Mass, Force, and Angle

If you have the mass of an object, the force applied at an angle, and the angle itself, you can calculate the acceleration using the formula:

$a = \frac{F \cdot \sin(\theta)}{m}$

In this formula, ‘F’ represents the force applied at an angle, ‘m’ represents the mass of the object, and (\theta) represents the angle. By multiplying the force by the sine of the angle and then dividing it by the mass, you can determine the acceleration of the object.

Understanding the relationship between mass, acceleration, and force is crucial in the fields of physics and engineering. By grasping Newton’s Second Law of Motion and the formulas connecting these variables, we can calculate mass, force, and acceleration in different scenarios. Whether it’s finding mass with acceleration and force, determining force with mass and acceleration, or calculating acceleration with mass and force, these concepts are essential tools for analyzing and understanding the physical world. So, the next time you encounter a problem involving mass, acceleration, and force, you’ll be well-equipped to tackle it with confidence.

Also Read:

How To Find Mass Without Acceleration:Several Approaches and Problem Examples

January 21, 2024December 2, 2021 by Alpa P. Rajai

When it comes to determining the mass of an object, one might think that acceleration is a necessary factor. However, there are actually several methods to find mass without acceleration. In this blog post, we will explore these methods and provide clear explanations, examples, and formulas to help you understand and apply them effectively.

Methods to Determine Mass without Acceleration

Using Net Force and Distance

One way to find mass without acceleration is by using the net force acting on an object and the distance it travels. According to Newton’s second law of motion, the net force acting on an object can be calculated using the equation:

$F = ma$

Where:
– F is the net force in Newtons (N)
– m is the mass in kilograms (kg)
– a is the acceleration in meters per second squared (m/s^2)

However, since we are looking for the mass without acceleration, we can rearrange the equation to solve for mass:

$m = frac{F}{a}$

By measuring the net force exerted on the object and the distance it travels, we can substitute the values into the formula to find the mass.

Using Force and Radius

Another method to determine mass without acceleration is by using the force acting on an object and its radius. This method is particularly useful when dealing with circular motion or objects moving in a curved path.

In circular motion, the centripetal force is responsible for keeping the object moving in a circle. The centripetal force can be calculated using the equation:

$F = frac{mv^2}{r}$

Where:
– F is the force in Newtons (N)
– m is the mass in kilograms (kg)
– v is the velocity in meters per second (m/s)
– r is the radius in meters (m)

To find the mass using this method, we rearrange the equation to solve for mass:

$m = frac{F cdot r}{v^2}$

By knowing the force, radius, and velocity of the object, we can substitute the values into the formula to determine the mass.

Using Force and Time

The third method to find mass without acceleration involves using the force acting on an object and the time it takes for the force to act. This method is particularly applicable when dealing with impulse or collision scenarios.

Impulse is defined as the change in momentum of an object and can be calculated using the equation:

$I = Ft$

Where:
– I is the impulse in Newton-seconds (N·s)
– F is the force in Newtons (N)
– t is the time in seconds (s)

Since impulse is equal to the change in momentum, we can write:

$I = Delta p$

Where:
– Δp is the change in momentum

The momentum of an object is given by the equation:

$p = mv$

Where:
– p is the momentum in kilogram-meters per second (kg·m/s)
– m is the mass in kilograms (kg)
– v is the velocity in meters per second (m/s)

By rearranging the impulse equation, we get:

$m = frac{Ft}{v}$

By measuring the force, time, and velocity of the object, we can substitute the values into the formula to find the mass.

Using Force and Velocity

The final method to determine mass without acceleration involves using the force acting on an object and its velocity. This method is commonly used in scenarios where an object is subjected to a constant force resulting in a constant velocity.

According to Newton’s second law of motion, the force acting on an object is equal to the rate of change of momentum:

$F = frac{dp}{dt}$

Where:
– F is the force in Newtons (N)
– dp/dt represents the rate of change of momentum

Since momentum is given by the equation $p = mv$ , we can write:

$F = frac{d(mv)}{dt}$

By applying the chain rule of calculus, we find:

$F = m cdot frac{dv}{dt} + v cdot frac{dm}{dt}$

Assuming mass is constant over time, we can simplify the equation to:

$F = m cdot frac{dv}{dt}$

Since acceleration is the rate of change of velocity, we can write:

$F = m cdot a$

Simplifying further, we get:

$m = frac{F}{a}$

This equation allows us to find the mass by knowing the force exerted on the object and its acceleration.

Worked Out Examples

Now that we have explored the different methods to determine mass without acceleration, let’s work through some examples to solidify our understanding.

Example of Finding Mass with Net Force and Distance

Suppose an object experiences a net force of 20 N and travels a distance of 5 meters. Let’s find the mass of the object using the formula $m = frac{F}{a}$ .

Given:
– Net force (F) = 20 N
– Distance (d) = 5 m

To find the mass, we need to determine the acceleration. Since we are dealing with a scenario without acceleration, the acceleration is zero.

Therefore, the formula becomes:
$m = frac{20 , text{N}}{0 , text{m/s}^2}$

Dividing any non-zero number by zero is undefined. Hence, we cannot determine the mass using this method in this particular scenario.

Example of Finding Mass with Force and Radius

Consider an object moving in a circular path with a force of 50 N acting on it. The radius of the circular path is 2 meters. Let’s find the mass of the object using the formula $m = frac{F cdot r}{v^2}$ .

Given:
– Force (F) = 50 N
– Radius (r) = 2 m

To find the mass, we also need to know the velocity of the object. Let’s assume the object has a constant velocity of 10 m/s.

Substituting the values into the formula, we get:
$m = frac{50 , text{N} cdot 2 , text{m}}{(10 , text{m/s})^2}$

Simplifying further, we find:
$m = frac{100 , text{N} cdot text{m}}{100 , text{m}^2/text{s}^2}$

Canceling out the units, we get:
$m = 1 , text{kg}$

Therefore, the mass of the object is 1 kilogram.

Example of Finding Mass with Force and Time

Suppose an object experiences a force of 100 N for a duration of 5 seconds. The object’s velocity is 20 m/s. Let’s find the mass of the object using the formula $m = frac{Ft}{v}$ .

Given:
– Force (F) = 100 N
– Time (t) = 5 s
– Velocity (v) = 20 m/s

Substituting the values into the formula, we get:
$m = frac{100 , text{N} cdot 5 , text{s}}{20 , text{m/s}}$

Simplifying further, we find:
$m = frac{500 , text{N} cdot text{s}}{20 , text{m/s}}$

Canceling out the units, we get:
$m = 25 , text{kg}$

Therefore, the mass of the object is 25 kilograms.

Example of Finding Mass with Force and Velocity

Consider an object moving with a constant velocity of 30 m/s. It experiences a force of 300 N. Let’s find the mass of the object using the formula $m = frac{F}{a}$ .

Given:
– Force (F) = 300 N
– Velocity (v) = 30 m/s

Since the object is moving with a constant velocity, the acceleration is zero. Substituting the values into the formula, we get:
$m = frac{300 , text{N}}{0 , text{m/s}^2}$

Similar to the first example, dividing any non-zero number by zero is undefined. Hence, we cannot determine the mass using this method in this scenario.

Common Mistakes and Misconceptions

Now that we have explored the methods to find mass without acceleration, it’s important to address common mistakes and misconceptions associated with this topic.

Misconceptions about Mass and Weight

One common misconception is the confusion between mass and weight. Mass is a measure of the amount of matter in an object, while weight is the force exerted on an object due to gravity. Mass is measured in kilograms, while weight is measured in Newtons. It’s crucial to differentiate between the two and understand that mass remains constant regardless of the gravitational force acting on an object, while weight can vary depending on the strength of gravity.

Common Errors in Calculations

When using the formulas to find mass without acceleration, common errors can occur in calculations. Some mistakes include:
– Forgetting to convert units and using inconsistent unit systems.
– Rounding off values prematurely, leading to inaccurate results.
– Misinterpreting the given information and using incorrect values in the formulas.
– Not considering the limitations of the formulas, such as dividing by zero.

To avoid these errors, it’s essential to carefully read and understand the problem, double-check calculations, and pay attention to units and significant figures.

Tips to Avoid Mistakes

To ensure accurate calculations and a better understanding of the concept, here are some tips to keep in mind:
– Read the problem carefully and identify the relevant information.
– Pay attention to units and convert them if necessary.
– Use the correct formula for the given scenario and rearrange it if needed to solve for mass.
– Substitute values into the formula accurately and perform calculations step by step.
– Double-check all calculations and consider the limitations of the formulas.

By following these tips, you can improve your accuracy and confidence in finding mass without acceleration.

How can mass be found without acceleration, and how does it relate to calculating mass from force and velocity?

Calculating mass from force and velocity involves determining the mass of an object based on the force acting upon it and its velocity. However, it is also possible to find mass without acceleration. To explore this intersection, one must understand the relationship between the two concepts. To learn more, you can refer to the article on Calculating mass from force and velocity.

Numerical Problems on how to find mass without acceleration

Problem 1

A body of mass $m$ is placed on a horizontal surface. If there is no acceleration acting on the body, what is the value of the mass?

Solution

To find the mass of the body without any acceleration, we can use Newton’s second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration:

$F = m cdot a$

Since there is no acceleration acting on the body $(a = 0$ ), the net force $(F$ ) is also zero. Therefore, the equation becomes:

$0 = m cdot 0$

Simplifying the equation, we get:

$0 = 0$

This equation is true for any value of $m$ . Hence, the value of the mass $m$ can be any real number.

Problem 2

A block is placed on an inclined plane with no acceleration. What is the mass of the block?

Solution

To find the mass of the block without any acceleration, we can use the formula:

$m = frac{F}{g cdot sin(theta)}$

Where:
– $m$ is the mass of the block
– $F$ is the force acting on the block (equal to the weight of the block)
– $g$ is the acceleration due to gravity
– $theta$ is the angle of inclination of the plane

Since there is no acceleration, the force acting on the block $(F$ ) is equal to its weight:

$F = m cdot g$

Substituting this into the formula, we get:

$m = frac{m cdot g}{g cdot sin(theta)}$

Simplifying the equation, we find:

$m = frac{m}{sin(theta)}$

This equation is true for any value of $theta$ except when $sin(theta$ = 0). Therefore, the mass of the block $m$ can be any real number except when $theta$ is a multiple of $pi$ .

Problem 3

A satellite is orbiting around the Earth with no acceleration. What is the mass of the satellite?

Solution

To find the mass of the satellite without any acceleration, we can use the formula for gravitational force:

$F = frac{G cdot M cdot m}{r^2}$

Where:
– $F$ is the gravitational force between the Earth and the satellite
– $G$ is the gravitational constant
– $M$ is the mass of the Earth
– $m$ is the mass of the satellite
– $r$ is the distance between the Earth and the satellite

Since there is no acceleration, the gravitational force $(F$ ) is balanced by the centripetal force:

$F = frac{m cdot v^2}{r}$

Where:
– $v$ is the velocity of the satellite

Equating these two forces, we get:

$frac{G cdot M cdot m}{r^2} = frac{m cdot v^2}{r}$

Simplifying the equation, we find:

$G cdot M = v^2$

This equation relates the mass of the Earth $(M$ ), the velocity of the satellite $(v$ ), and the gravitational constant $(G$ ). The mass of the satellite $(m$ ) can be any real number.

Also Read:

11 Movable Pulley Examples:Explanations With Images And Fact

January 20, 2024November 28, 2021 by Alpa P. Rajai

Movable pulleys are used in construction cranes, allowing them to lift loads with half the force by balancing weight. Elevators utilize a system of movable pulleys, reducing the motor’s load by 50% for efficient vertical transportation.

Let us read on.

Movable Pulley Examples:

Zip Lining
Construction Equipment
Climbing Pulley
Pulley in Building Wash
Sliding Doors of bathroom
Anatomical Pulley
Industrial Hydraulic Material Lift Or Cargo Lift

Zip Lining:

A zip line is an exciting activity that involves the use of movable pulleys. Rope-ways gave rise to the idea of zip lining. In mountainous places, rope-ways are commonly used to transport people and objects. Zip lining is a similar activity that may be done in both forest and mountain locations. People’s safety is assured while zip lining by using rope to tie them together.

movable pulley examples — Image Credits: SKas, Ziplining in Caucasus, CC BY-SA 4.0

A person is expected to zip line from the top of the inclined cable to the bottom of the inclined cable by being hooked to the wire or holding it via a freely moving pulley. In this situation, the person acts as the load for the zip lining pulley. As a result, the person is directly attached to the pulley. Gravity assists the speed of the movable pulley’s movement.

Thus, gravity can carry you from one point to another with almost half the effort in zip lining due to the movable pulley. This is how the movable pulley made it possible for the adventurous person.

Construction Equipment:

A movable pulley allows you to lift large objects easily. Because the movable pulley has a mechanical advantage of 2, the effort required to lift a heavy object is nearly half of what it would be if resistance were not taken into account. As a result, if you need to lift a heavy object, the best option is to use a movable pulley. In construction, raw materials must be transported from the ground to the upper floors. As a result, a movable pulley is used there.

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A movable pulley is utilized in construction equipment that requires the lifting and dumping of bulky and heavy objects. The pulley is attached to the load you need to transport. One end of a rope that passes through the pulley is fixed, while the other end is used to pull the object. Some construction equipment, such as cranes employ a movable pulley to ease the lifting of heavy objects. Bulldozers use movable pulleys in the same way as cranes do.

Climbing Pulley:

Climbing pulley, as the name implies, is used when you wish to climb anything high, such as a tree or a mountain. The person who wants to climb will act as a pulley load. As the person pulled the other end of the rope, he began to rise high. He goes down on the rope as soon as he stops tugging the rope.

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When a person falls down on a rope, it does not indicate that he will fall to the ground because he is already connected to the rope for safety reasons. This is how a movable pulley makes climbing high simpler.

Pulley in Building Wash:

It is vital to keep your building clean and disinfected. You must wash your home and building to keep them clean. A ladder with an easy reach can be used to clean the inside of your home. But what if you want to clean the outside of your high-rise buildings and home? A moveable pulley is utilised for this purpose.

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Using a moving pulley, there are two ways to reach the top of the building. In the first situation, a machine such as a crane can be used to reach the top or higher floors that need to be cleaned. Another option is to wash the building in the same manner as tree climbing, with the exception that instead of empty hands, you will need to use a cleaner.

Sliding Doors of bathroom:

Sliding doors are often used at stores, bathrooms, office entrances, hotels, and closet doors as they do not take up more space to open. As the doors are sliding, they use a pulley to accomplish this purpose.

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Think about carrying a door and putting it aside. Is it possible to do that? Manually, not, but a movable pulley makes it easy. When you push the door, the pulley moves, and along with the pulley, the door will also move. As the pulley is a movable pulley, the effort we need to slide the door is much less than the effort we need to apply to carry the door from one place to another. The number of movable pulleys used is based on the length of the sliding door.

Anatomical Pulley:

Just like the fixed pulley, a movable pulley is also present in the human body and is called an anatomical pulley. In general, in the human body, bone works as a pulley and the muscle that passes over the bone works as the cord or rope of the pulley. This fact we have already discussed in the fixed pulley examples. So now let us see how a movable pulley works in the human body.

Instead of bone, as in a fixed pulley, muscle itself acts as a pulley in a movable anatomical pulley. The muscle that lays beneath acts as a pulley when two muscles pass over each other. You’re probably asking how this is a movable pulley example. As a result, when the muscle below contracts, the efficiency of the muscle above it increases. So there is no pulley when this muscle is at rest, but when it contracts, it works on the principle of a moving pulley.

Industrial Hydraulic Material Lift Or Cargo Lift:

As we’ve seen, there are a variety of applications for movable pulleys, and one of them is the industrial sector. Yes, movable pulleys are utilised to carry loads in industries.

Movable pulleys make it easier to carry loads from one floor to another in the industrial sector. It may go by different names depending on what it transports, such as oil derricks, hydraulic lifts, or cargo lifts. Basically, the goal is to carry the load with the least amount of effort. It can even transport people from one floor to another.

In an industrial area, by pressing a switch, your hydraulic lift will go from one floor to another. But how does it happen? Here, by pressing the switch, you are basically pulling the rope which is passing over the pulley. And with the electric force, the lift and the load that it carries also go from one floor to another.

Frequently Asked Questions (FAQs):

Q. What is pulley?

Ans: The pulley is basically a simple machine.

The pulley is nothing more than a wheel with a grooved rim that holds a cord, rope, belt, or chain. Pulleys can offer either direction or force multiplication, or both at the same time.

Q. What are the different types of pulleys? Describe each type in brief.

Ans: There are three main types of pulley, which are given below:

Fixed Pulley
Movable Pulley
Compound Pulley

Fixed pulley: A fixed pulley has a supported axis of rotation with a bearing. In short, the axis of rotation can not change with the movement of the load. As the force you need to pull the load is not decreased using this pulley, we can say that it does not provide mechanical gain. The pulleys used in flagpoles and water wells are the common examples of a fixed pulley.

Movable pulley: The axis of rotation of a movable pulley is not fixed like that of a fixed pulley. It indicates that it changes as the load moves. Because the load is carried by two segments of a single rope via a moveable pulley, it has twice the mechanical advantage of a fixed pulley. When a heavy load needs to be carried, a movable pulley should be employed. Pulleys used in zip lining, cargo lifts, and construction equipment are examples of movable pulleys.

Compound Pulley: When a fixed and movable pulley are used together to improve mechanical advantage, it is referred to as a compound pulley. It’s also known as a block and tackle system or a combination pulley. Compound pulleys can be seen in sailboats and elevators.

Q. What is the difference between the working of a fixed pulley and a movable pulley?

Ans: When lifting a heavy object, both fixed and mobile pulleys are employed.

The amount of effort required to lift an object with or without a fixed pulley is the same. Only the direction in which effort is applied has changed. When a movable pulley is used to lift a heavy object, the direction of application of effort remains the same, but the amount of effort is decreased by half.

As a result, each has a unique set of benefits.

Also Read:

7 Fixed Pulley Examples: Critical Facts

January 20, 2024November 24, 2021 by Alpa P. Rajai

The most basic type of pulley we utilise is the fixed pulley. Here are some fixed pulley examples that we come across in everyday life.

Fixed Pulley Examples:

Water well
Flagpole
Window blinds
Adjustable Clothesline
Pulley Lighting
Motor Pulley
Anatomical Pulley

Water Well:

Water well pulley is the first thing that springs to mind when you hear the word pulley. Because it is the most common and practical example one can think of in everyday life. In villages, people use a pulley to draw water from the well. As a result, a water well pulley is regarded as one of the earliest examples of a fixed pulley in use.

fixed pulley examples — Image Credits: Peakpx Free images

To draw water from the well, we use a bucket. A rope that we used to pull the bucket is wrapped around the fixed pulley. One end of the rope is tied to the bucket’s handle, while the other end is in the hand of the person who will exert force to pull it up.

Throwing a tied bucket into the well will fill it with water, and this water bucket will serve as a load. Because the rope is tied to the fixed pulley, you will get the appropriate direction to apply the force as you pull the other end of the rope. Thus, a fixed pulley makes it easy to draw water from the well by providing proper direction to the force.

What if you don’t use a fixed pulley here and instead draw a bucket of water directly from the well? The answer is a fixed pulley, which allows you to exert force in a downward direction with all of your weight. If you don’t use a fixed pulley here, you’ll have to exert force in an upward direction. Also, you can’t use all of your weight to apply upward force.

Flagpole:

Do you know why flag hoisting is challenging to do manually? The flag should be hoisted at very high; thus, the height of flagpoles is also very tall. A fixed pulley is employed to make this process simple and easy.

A rope goes around the pulley, which is fixed at the top of the flagpole. The flag will act as a load, in this case. Thus it is attached to one end of the rope. When the user pulls the other end of the rope, he ultimately pulls the flag via a pulley. When a rope is pulled down, the force is redirected through a fixed pulley, raising the flag. A fixed pulley makes it easier to unfurl the flag at the top of the flagpole in this way.

Window Blinds:

Window blinds are certainly something you use on a daily basis. The most often used blinds are horizontal. Blind slats are composed of materials such as wood, aluminium, or PVC. The strings it employs are known as lift strings. The length of the blinds will determine the number of lift strings required. The more string used by the blinds, the larger they are.

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Strings climb, pass through a fixed pulley, and then return to the bottom through holes in each slat. The slats begin to rise as the lift strings are pulled. It’s important to lift all of the strings at the same time. If you forget to tie the cord, your blinds will be uneven. As a result, a fixed pulley ensures that blinds operate smoothly.

Adjustable Clothesline:

Not every person uses a dryer to dry their clothes or laundry. Many of them choose to hang clothes to dry. A clothesline pulley makes it easy to hang the clothes. One can use a pulley clothesline in their balcony, deck, or porch where the exposure of sun and wind is high so that clothes can dry quickly. The clothesline can be used at any level from ground to high.

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A fixed pulley should be mounted at a suitable height to establish the clothesline pulley system. The clothesline thread passes through the pulley and makes a closed loop of shape 8. Thus, with the laundry basket standing in one place by just moving the clothesline string, you can hang your clothes to dry. As a result, you won’t have to walk up and down with your laundry basket to hang your clothing if you use a fixed pulley in your clothesline.

Pulley Lighting:

The purpose of a pulley light is to give your home a lovely vintage appearance. They’re typically utilised for decorative purposes or when the height of a hanging light has to be adjusted. The rope is also employed in the pulley light, with one end tied to the lamp and the other used to alter the height. As the rope goes through a fixed pulley, the free end of the rope should be pulled at an angle determined by the pulley to assist pulling.

10988304703 f64674d3a8 q — Image Credits: “DIY Barn Pulley Pendant Lights” by Stacie Stacie Stacie, CC BY-SA 2.0

A fixed pulley mechanism is also employed in gravity light, which can be used instead of solar powered lighting. A fixed pulley, similar to the pulley light, is used to control the height of the LED lamp used in the gravity light. It works on the idea of potential energy with the pulley mechanism.

Motor Pulley:

A motor pulley is a fixed pulley used to guide the timing belt or serpentine belt in the engine of an automobile or other vehicle. According to the purpose, different types of the motor pulley can be used.

In the car, timing belts are wounded around the fixed pulley. The circumference of the pulley should be grooved so that belt does not slip off from the pulley. So that it accommodates the belt. Here the pulley system provides engine timing.

Idler motor pulley is the type of motor pulley used to guide the path and provide proper tension to the belt. It does not give power to any peripheral devices connected to the motor pulley. The sewing machine also works on this principle. The motor pulley in the sewing machine provides proper direction and tension to the thread we use to stitch the cloth.

Anatomical Pulley:

You might be surprised to learn that some of our body components operate using a fixed pulley mechanism. The pulley is replaced by a bone or ligament in the human body, and a muscle tendon replaces the cord. Synovial fluid lubricates the tendon, allowing it to glide freely over the bone.

The anatomical pulley is formed when a muscle fibre or muscular tendon crosses over a bone and changes the direction of the force. The fixed pulley’s job is to direct the force in the right direction so that the work can be completed quickly. The movement of body segments is the “Task” in the human body.

A fixed pulley like structures in the human body:

Movement of the knee joint: The fixed pulley principle is used to extend the knee. A bone changes the direction of muscle pull and acts as a fixed pulley. The direction of muscle passing across the knee joint changes due to the larger size of the bone. As a result, the bone acts as a fixed pulley by adjusting the angle of pull of that specific muscle.

The hand movement: The delicate movement of the hand is possible only due to the band at the wrist, which acts as a fixed pulley and controls the movement of muscle. Here the pulley changes the direction of muscle pull by preventing its bowstring. This type of pulley is also present in feet.

Movement of the eyeball: Even when we move our eyes, a little bone acts as a fixed pulley. The muscle originates in one way but functions in the opposite direction due to the pulley. This pulley increases the efficiency of this little ocular muscle.

Movement of the ankle: Same as a knee joint in the ankle, the shape of bone changes the direction of muscle insertion. This changes the direction of muscle pull and acts as a fixed pulley.

In the last post, we have discussed how does a fixed pulley makes work easier. So in this post, we discussed fixed pulley examples. We hope that we have accurately presented fixed pulley examples to you throughout this post.

Also Read:

How Does A Pulley Work Simple Machine: Detailed Insight

January 21, 2024November 14, 2021 by Alpa P. Rajai

Because a pulley makes our work easier, it is widely used to make our lives easier due to its straightforward operation. So, in this post, we’ll look at how does a pulley work simple machine.

Pulley has a simple mechanism consisting of one or more wheels over which rope or code is looped. By redirecting or amplifying the force, this mechanism enables humans to carry large things.

You probably have seen those strongmen in TV shows who can pull cars with just their hands. Have you ever been amazed how a person can be so strong! It is all about science here. The science that makes you so strong to lift heavy objects so easily. If someone wants to lift a heavy object or huge weight, they just need to use the power of science and do not need to strain their back. An amazing device that helps you to do it easily is called a pulley. Before going into how does a pulley work simple machine, let’s first get a basic idea of a pulley.

Pulley

Pulleys are made out of a wheel that has a grooved rim that carries a flexible rope, cable, cord, or chain; it can be anything. The wheel revolves around its axis, which runs through the centre. By transmitting energy to the movement, the pulley mechanism is used to support it.

Pulley is the greatest example of simple machines called by scientists. The simple machine does not mean that they should be jam packed with engines and gears, but it just means that it helps us by multiplying force or providing the direction to apply force. If someone wants to lift a hefty weight, they have to apply large force with their muscles. But using a simple machine like a pulley, one can effectively multiply the force his body can ever produce.

Now let us have a closer look at how does a pulley work simple machine!

How does a pulley work?

Pulley has three different types as per its mechanism:

A fixed pulley
A movable pulley
A compound pulley

Here we are going to discuss all three types one by one.

A Fixed pulley:

The wheel is coupled to the rigid support in a fixed pulley, as the name implies. Thus, its axis of rotation on which wheel is rotating is also not changing. The inextensible rope also passes around the rim of the fixed pulley. One end of the rope is used to carry the load, and another free end is used to apply effort.

how does a pulley work simple machine — Fixed Pulley

The side of the rope where the load or the heavy object is attached causes tension in the rope. As the load is downward, the tension in the rope will be in the opposite direction it means in the upward direction. Similarly, as you apply effort on the other side of the rope, it also causes tension in the upward direction.

The tension formed in the rope will be in proportion to the amount of load and effort on their respective sides. Thus, the amount of force you will apply is the same as that of the load you want to lift. It means a fixed pulley does not provide any mechanical gain. Then why do we use it? Let’s understand it with a simple example.

In villages, a fixed pulley is widely used to draw a bucket of water from the water well. As you pull the rope, the bucket of water will be lifted by the same amount. The force you need to apply remains constant, but the direction from which you apply effort changes dramatically when you use this pulley. If you want to draw a bucket of water without using a pulley, you must exert upward force. It means that you can apply force in a downward direction with all of your weight by using a fixed pulley.

A Movable pulley:

Unlike the fixed pulley, a movable pulley is not attached to the rigid support, and thus it is free to move upward and downward as its name suggests. The inextensible rope that runs over the rim of the wheel has one end fixed. You will exert effort by pulling on the other end of the rope. The pulley is directly coupled to the rope load between the fixed and free ends.

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As a result of the load, tension will be present on both sides of the rope, implying that a single weight will result in double tension. Consider it as though you’re pulling a heavy object with both hands. Like a fixed pulley, a movable pulley produces tension as a result of effort, which is proportional to the amount of effort.

We can argue that effort will be half of the load since load causes double tension, one of which is equal to the effort applied. We may say that it delivers force amplification, which means that to lift a heavy weight, you need to apply half the force that the weight requires.

Suppose, using a movable pulley; you want to lift an object with 50 N force in a downward direction. Thus for that, you need to apply 25 N of force. But suppose you want to lift it to 30 m, then you need to pull 60 m of the rope. When you pull the rope, load with a movable pulley and the fixed rope is also moving upward. Thus, for a double lift, you need to pull double.

To know more about Fixed pulley vs. Movable pulley go through this post.

A compound pulley:

A compound pulley system is one that consists of both a fixed pulley as well as a movable pulley. This means that by using it, one can benefit from a change in the direction of force and a lighter feeling load. Thus, the mechanism of a compound pulley makes it easier to lift a heavy load.

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If you pull the free end of the rope, the lower pulley, which is a movable pulley, will rise. As the movable pulley rises, the load attached to it also rises. Thus, the force you are pulling will be lesser than the force with load is pulling up. Of course, you are paying this by pulling a larger distance. As a result, using a compound pulley makes it possible to apply lower force in a downward or convenient direction to lift the load.

So with this post, we hope that we make you understand how does a pulley work simple machine.

Also Read:

Fixed Pulley vs Movable Pulley: Detailed comparison

January 21, 2024November 10, 2021 by Alpa P. Rajai

First and foremost, to answer fixed pulley vs movable pulley, we differentiate the pulleys in a few points, and afterward, we will likewise talk about them separately.

Both fixed and movable pulleys are used to lift heavy objects. The rotating axis is the main difference between fixed and movable pulleys. The first has a fixed axis of rotation, and the latter has a movable axis of rotation, as their names suggest.

We’ll start with the fundamental concept of a pulley before going into a fixed pulley vs movable pulley in depth.

The pulley:

A string or rope is wound around the grooved rim of a wooden or metal disc to create the pulley. The disc revolves around its axis, which runs through the centre.

There are two ways to use a single pulley:

As a fixed pulley
As a movable pulley.

Let’s talk about fixed pulley vs movable pulley, which is the focus of this post.

Fixed pulley vs Movable pulley: Points to remember

The following describes the difference between fixed and movable pulley:

Parameters	A Fixed pulley	A Movable Pulley
Definition	The axis around which the disc rotates is fixed.	The axis around which the disc revolves is movable rather than fixed.
The Load attachment	Here the load one wants to lift is attached to the one end of the rope.	Here the load one wants to lift is attached directly with the pulley.
The direction and magnitude of force	This pulley can only change the direction of the force but can not change the magnitude of the force.	This pulley can change the direction of the force as well as the magnitude of the force.
Use	It is the one which provides better direction to apply effort.	It is the multiplier of force.
M.A.	This pulley’s mechanical advantage is 1.	This pulley’s mechanical advantage is 2.
V.R.	This pulley’s velocity ratio is 1.	This pulley’s velocity ratio is 2.
Example	Pulley used in well	Pulley used in zip lining

Let’s have a look at both pulleys independently now.

A Fixed Pulley:

Fixed pulley refers to a pulley system in which the pulley is mounted to a fixed point and the load is attached to one end of a rope with negligible mass that passes through the grooved rim of the disc or wheel.

fixed pulley vs movable pulley — Image credits: “Drinking Well” by Walt Stoneburner is licensed under CC BY 2.0

Due to load, one side of the rope will be stretched. The stretching creates tension in the rope. The load and the tension created in the rope will have opposite directions. But as the load is the cause of tension, it will have the same magnitude as that of the load applied. If we represent applied load as L and rope tension as T, we can write:

L = T

On the other side of the rope, the person is applying effort to lift the object. Thus, due to effort, again, the rope is stretched, and tension is created. Here the tension is due to effort applied by a person; thus, both have the same magnitude but have opposite directions.

If we represent applied effort as E, we can write:

E = T

Thus, mechanical advantage of fixed pulley is:

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∴ M.A. =1

Thus, a fixed pulley does not give you any kind of mechanical advantage. It only provides you a better direction to lift an object with all your weight. It means you need to apply the effort as that of the load weight.

L = E

As the load and effort are the same in magnitude, the distance travelled by both will also be the same. Thus, if we represent distance travelled by the load as L_d and distance travelled by effort as Ed, then we can write:

L_d = E_d

If both distances take the same time to travel, then the velocity ratio is:

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∴ V.R. = 1

Thus, efficiency of fixed pulley:

Fixed Pulley vs Movable Pulley: Detailed comparison 42

∴ ???? = 100%

Thus the load is lifted upward, same as you apply effort in a downward direction.

The pulley used in the well, flag pole are examples of the fixed pulley.

A Movable Pulley:

A movable pulley refers to a pulley system in which the pulley is directly attached to the load. One end of a rope with negligible mass that passes through the grooved rim of the disc or wheel is attached to the fixed point, and the other end is free.

The free end of the rope is used to apply the effort. The load is kept with the pulley between the fixed end and a free end of the rope. Thus, due to the load, there will be tension on both sides of the rope. As load is responsible for the tension in both sides of the rope, we can write:

T + T = L

∴ L = 2T

Now, the applied effort also creates tension in the rope. Thus, we can write:

E = T

∴ L = 2E

Thus, the applied effort will be half of the load.

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Thus, mechanical advantage of movable pulley is given by:

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∴ M.A = 2

It shows that with lesser effort, more load can be lifted. Thus, this pulley is used as a force multiplying machine.

Now the distance travelled by effort will be doubled from a distance travelled by the load. This happens because by applying effort, not only load but the rope with a fixed point is also lifted. Thus, velocity ratio for movable pulley is:

V.R = 2

Thus, efficiency of a movable pulley is:

???? = 100%

The pulley used in the modern elevator, construction crane are examples of the movable pulley.

The 100% efficiency is only possible in ideal conditions, as friction is always present in reality. As a result, in reality, M.A. is always < 1, and thus efficiency ???? is also always < 100%.

What does the movable pulley do that a fixed pulley does not?

A fixed and a movable pulley are both used to lift heavy objects.

A fixed pulley can only provide you a better direction to lift an object. But a movable pulley helps you to lift an object with half of the effort than the load. Thus, using a movable pulley for the same load effort can be reduced, but this can not happen with a fixed pulley.

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How Does A Fixed Pulley Make Work Easier: Detailed Insight

January 21, 2024November 7, 2021 by Alpa P. Rajai

In our daily lives, we rely on machines to do our work for us. One of these simple machines is a fixed pulley. So we’ll look at how does a fixed pulley make work easier in this post. Let us continue to read!!

A fixed pulley is used to help raise large objects. Fixed pulleys make it easier to lift objects with the same effort but in a more convenient or correct direction.

Before seeing how does a fixed pulley make work easier, first, let’s see what a fixed pulley is.

A fixed pulley:

A fixed pulley is one of the simplest kinds of the pulley. It is just a metallic or wooden disc whose rim is grooved. Around this groomed rim, a rope or string is made to be passed. The disc with a grooved rim keeps on rotating about the axis, which is fixed, passing through its center. Thus, a fixed pulley is one in which the axis of rotation on which the pulley rotates is not changing.

You may have seen a flag being hoisted. Fixed pulleys are used in flagpoles for flag hoisting. The pulley is fixed, but the flag can simply be hoisted by pulling one end of the rope.

How does a fixed pulley make work easier: Working, M.A., V.R. & Efficiency

➤ Working of a fixed pulley:

The load is attached to a fixed pulley through a string or rope. The heavy object we aim to lift with the pulley is referred to as the load. Now, whenever a rope or string is stretched or compressed, tension is created in that rope.

How Does A Fixed Pulley Make Work Easier: Detailed Insight 47 — Arrangement of Fixed Pulley

As you suspend the object from the rope, the rope will stretch, causing stress in the rope. You are applying a downward force by hanging an object. As a result, tension force will be developed in the opposite direction to counter the object’s weight. The imposed load will have the same magnitude as the tension force created in the rope. However, the tension force and load will be in opposite directions. Thus,

Imposed Load = Created Tension in string

If we use the letters L and T to represent the load and the tension created in the string, we can write:

∴ L = T …..(１)

Let’s look at the opposite side of the rope now.

You are pulling the rope on the opposite side as you try to lift the object. The rope is pulled downwards by applying downward efforts. By pulling on the rope, you are essentially stretching it. As a result, tension is created on this side as well. The tension that is created in the rope will be proportional to the amount of effort applied.

Applied effort = Created tension in string

If we use the letter E to represent effort, we may write:

∴ E = T …..(２)

We can deduce the following from equations (1) and (2):

∴ L = E …..(3)

According to the above equation, in the ideal case of a single fixed pulley, the effort required to lift the weight is equal to the load. It means that the applied effort is not lowered while using a fixed pulley. It provides you a better pulling angle and direction to lift heavy objects with the same force with all your weight.

If we go into further depth, we may state that when we apply effort E to the rope, it moves distance d in the downward direction, and subsequently, load L moves distance d in the upward direction.

➤ Mechanical advantage of a fixed pulley:

The mechanical advantage of any machine is the measurement of the force amplification that the machine achieves. In other words, it displays how much output is amplified when input is applied to the machine. The upward movement of the object is the output, while the effort you apply by pulling the rope is the input.

Mathematically, the mechanical advantage is the ratio of the output force to the input force. Thus, for a fixed pulley, the mechanical advantage is:

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But as L = E,

∴ M.A. = 1

As a result of this equation, we can conclude that in the case of a fixed pulley, there is no mechanical gain. Thus, it is a direction provider, not a force multiplier.

➤ Velocity ratio of a fixed pulley:

As the name suggests, velocity ratio is the ratio of input velocity to the output velocity in the unit time. The velocity ratio can be represented as the distance traveled by the effort divided by the distance traveled by the load applied because time is constant. As it is the ratio of distances, it is a unitless quantity.

If the distance traveled by the load L is Ld, the distance traveled by the effort E is Ed, and the time spent by both is T, we can write:

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How Does A Fixed Pulley Make Work Easier: Detailed Insight 52

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However, with a fixed pulley, the distance traveled by load L in the upward direction is the same as the distance traveled by effort E in the downward direction. Thus, for a fixed pulley Ed = Ld, we can write:

∴ V.R. = 1

➤ The efficiency of a fixed pulley:

If the load lifted by the machine is L and Ld is the distance traveled by the load L, then the work done on the load by the machine is output work, which can be expressed as:

Work done on Load = L x Ld

If the effort that the machine applies is E and Ed is the distance traveled by the effort applied E, then the work done by the effort on the machine is input work, which can be expressed as:

Work done by Effort = E x Ed

The work done on load L (output work) divided by the work done through effort E is the efficiency of a fixed pulley (input work).

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How Does A Fixed Pulley Make Work Easier: Detailed Insight 55

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Thus, for fixed pulley efficiency is:

∴ ???? = 100%

We get efficiency 100% because we have assumed a fixed pulley with no friction and negligible mass of rope. But in reality, it is not possible not to have friction between the rope and grooved rim of the disc.

As a result of friction, E > L, i.e., M.A. = 1 but V.R. = 1 in actuality. Thus, efficiency ???? < 100%.

With this post, we hope to have adequately answered your question on how does a fixed pulley make work easier.

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What Is Oscillation Frequency: Interesting Facts and FAQs

January 21, 2024November 1, 2021 by Alpa P. Rajai

Whether our vision can reach them or not, oscillations occur all around us. So, in this post, we’ll look at what is oscillation frequency, how to calculate oscillation frequency and oscillation frequency units.

The frequency of oscillations is a physical term that describes how many oscillations took place in a unit of time in an oscillating system such as a pendulum, spring mass system, or electronic system.

Before we go into what is oscillation frequency, let’s first define oscillation.

Oscillation:

Oscillation is a repeated variation in amplitude or position around a central point or equilibrium, with time following the same path.

A single oscillation is a complete movement over a period of time, which can be up and down or side to side. One cycle of oscillation is another name for it. The time it takes to complete one oscillation is the oscillation time period. Every oscillation is a periodic motion, but not all periodic motions are oscillations. Examples of oscillation are spring movement with mass, pendulum motion, the vibration of string instruments, etc.

ลูกตุ้มธรรมชาติ 3 — Oscillating Pendulum GIF Credits: Wikinana38, ลูกตุ้มธรรมชาติ, CC BY-SA 4.0

Oscillation frequency:

The oscillation frequency is the number of oscillations that repeat in unit time, i.e., one second. Taking reciprocal of time taken by oscillation will give the frequency of oscillation.

To understand oscillation frequency, let’s consider a simple example of the guitar. While playing guitar, you pluck the string of a guitar. As the motion of the guitar string is repetitive for significant cycles, it is considered as oscillation. To complete one successive cycle time taken by the string is the same. Thus, if we take reciprocal of it, we get the frequency of guitar string oscillation. Suppose it takes 0.2 seconds to complete one cycle, then the number of oscillations in one second is five, which is the frequency of oscillating guitar strings.

5853120739 fca6e0b83b q — Image Credits: “Guitar strings close up” by richard_north , CC BY 2.0

Let us now look at the frequency of oscillation units.

Frequency of oscillation units:

The SI unit for the oscillation time period is the second (s). Because the reciprocal of the oscillation’s time period determines its frequency, its unit is the reciprocal of the time period’s unit, i.e., s^-1.

Many unit names are inspired by the scientists who worked on the unit’s research. Heinrich Hertz, a German physicist, made a significant contribution to the field of electromagnetic radiation. As a result, Hertz is also regarded as a SI unit of frequency in honour of this famous scientist. As Hertz represents cycles per second, we can say that

1 Hertz = one cycle per second.

Thus, s and Hertz are frequency of oscillation units that are used as SI frequency units, but Hertz is more commonly used.

After going through what is oscillation frequency and frequency oscillation units, you might wonder how to calculate oscillation frequency. So let’s see how to calculate oscillation frequency.

How to calculate oscillation frequency?

There are two ways to calculate oscillation frequency:

Mathematical
Experimental

⇒ A mathematical way to calculate oscillation frequency:

To calculate the frequency of an oscillation, we must utilize period and frequency formulas. The formulas for calculating oscillation frequency vary depending on the system.

✦ Oscillation frequency of spring mass system:

As shown in the figure, a mass m is attached to the end of the spring. Spring will oscillate up and down due to the weight of the mass. Thus, if k is the spring constant of spring, then the frequency of oscillating frequency is given by:

What is oscillation frequency — GIF credits: Svjo, Animated-mass-spring, CC BY-SA 3.0

✦ Oscillation frequency of simple pendulum:

In a simple pendulum, mass m is attached to the end of the string. Thus, due to the mass, the string will oscillate back and forth. Therefore, if L is the length of the string, the frequency of the simple pendulum is given by:

Pendulum no text — GIF credits: Stündle (modification Ideophagous), Pendulum-no-text, CC BY-SA 4.0

Thus, we can say that in the case of a simple pendulum, the frequency of oscillation is not dependent on the mass of the attached object.

✦ Oscillation frequency of the compound or physical pendulum:

A physical or compound pendulum is formed by suspending a rigid body to the fixed horizontal axis. As the rigid body is involved, its moment of inertia I will also come into action. Thus, the frequency of the compound pendulum is given by:

✦ Oscillation frequency of the torsional pendulum:

When a disc-like mass is suspended from a wire or thin rod instead of a rigid body, the system is known as a torsional pendulum. As a result, the torsional pendulum oscillation frequency is:

⇒ An experimental way to calculate oscillation frequency:

The oscillation frequency calculation for a pendulum or a spring mass system is nearly identical. The main difference is that the spring constant k must be calculated for the spring mass system. The method is as follows:

In a spring mass system, to calculate the spring constant, hang the mass on the spring and the spring will start to oscillate. Now, allow the mass to come to a motionless state where the gravitational force of mass and spring force will be balanced. After that, adding mass to spring will stretch, so record this change in spring stretch.

Δmg -kΔy =0

Thus, spring constant k is:

Here, Δy is the change in spring stretch.

Oscillate the spring or pendulum now. Then, for each mass, keep track of the time for ten oscillations. To acquire an accurate response, repeat this method three times. The average of the three times will be used to determine the time period. Take the inverse of that and you’ll get the frequency.

We hope that this article has answered your questions about what oscillation frequency is, what oscillation frequency units are, and how to calculate oscillation.

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