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gravity force simulation screenshot

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General Physics

# Introduction
![momentum](//images.ctfassets.net/4yflszkpcwkt/5jNp97qRTZlUHTP0Ps5y6h/700838ebfdaea75431acfaeb66509d3c/bhyve.jpeg)
[Source](https://imgur.com/bhyve)

If you have seen videos of artillery guns being fired by soldiers, you will notice that the gun kicks back along with firing the shell. __Newton’s third law__ states that every action has an equal and opposite reaction. Therefore the gun recoils with the same momentum as the shell flies forward. But why is it that the gun doesn’t fly away in the opposite direction, unlike the shell that flies for miles? That’s explained by the principle of __conservation of momentum!__ 

## WHAT IS MOMENTUM? 
- Momentum is the concept of physics that explains how much motion is contained in a moving body. 
- In simpler terms, a moving object that has a lot of momentum takes more effort to stop. 
- The mathematical definition of momentum is given by: 

__Momentum = Mass x Velocity__

Or

__P = mv__

Here, 
Mass of the moving body is ‘m’ in Kg.

The velocity of the moving body is ‘v’ in m/s.

The momentum of the object is p.

The unit of momentum is Kg m/s.

## THE CONSERVATION OF MOMENTUM PRINCIPLE
- According to the __law of conservation of momentum__, in a closed system, the total momentum of the bodies within the system remains constant. 
- What that means is that the momentum of the individual bodies in the system can change, but the sum of the momentum of all bodies within the system __remains the same__. 

## CONSERVATION OF MOMENTUM IN COLLIDING SYSTEMS

![pool](//images.ctfassets.net/4yflszkpcwkt/1s7XAArEkNY4rxpr1ywjl7/154ce34ea5ccf485df8716fd50601d37/Cue_ball_after_collision.jpg)
[Source](https://letstalkscience.ca/sites/default/files/styles/width_800px/public/2020-03/Cue_ball_after_collision.jpg?itok=sYIj3EUS)
- Consider a pool table where the fast-moving white ball strikes a second ball. 
- After the collision, the sum of the momentum of each ball will be equal to the momentum of each ball before the collision. Conservation of momentum in one dimension equation is written as:

__p = p1 + p2__

Where p1 is the momentum before collision and p2 is the momentum after the collision.

If p1 is the momentum of the white ball and p2 is the momentum of the ball on the table, then according to the law of conservation of momentum, 

__p1(before) + p2 (before) = p1 (after) + p2 (after)__   

## CONSERVATION OF MOMENTUM IN EXPLODING SYSTEMS

![canon](//images.ctfassets.net/4yflszkpcwkt/DdTtn5POYZU3Q3z3SMVMU/8fd6908c651a6d98f97189edc5be57f2/cannon.gif)
[Source](http://www.ipodphysics.com/resources/cannon.gif) 

One of the applications of the law of conservation of momentum in one dimension involves the __design of guns__. 
Even in an exploding system such as artillery cannon, __the law of conservation of momentum__ holds good. 
When the cannon fires, if the shell acquires 100 units of momentum in the forward direction, the cannon acquires 100 units of momentum in the backward direction. 
However, because the mass of the cannon is significantly higher than the mass of the ball, the cannon only recoils and doesn’t fly in the opposite direction.  

# SUMMARY
- In a closed system, the total momentum remains the same. 
- The law of conservation of momentum applies to both colliding and exploding systems. 

## FAQs

__Q. What does the law of conservation of momentum state?__

According to the law of conservation of momentum, in a closed system, the total momentum is always constant.                                    

__Q. The law of conservation of momentum is based on which law of motion?__

It is based on Newton’s third law of motion, which states that every action has an equal and opposite reaction.                          

__Q. What is the real-life example of the law of conservation of momentum?__

The recoil of a gun is a real-life example of the law of conservation of momentum. The gun and the bullet have the same momentum but in opposite directions after it is fired. 

__Q. What is the law of conservation of momentum in one dimension formula?__

p = p1 + p2
Where p1 is the momentum before collision and p2 is the momentum after the collision.

*We hope you enjoyed studying this lesson and learned something cool about the __Conservation of Momentum in One Dimension!__ Join our Discord community to get any questions you may have answered and to engage with other students just like you! Don't forget to download our App to experience our fun VR classrooms - we promise, it makes studying much more fun!😎*

## SOURCES 
1. Conservation of Momentum in One-dimension: https://flexbooks.ck12.org/cbook/ck-12-physics-flexbook-2.0/section/6.2/primary/lesson/conservation-of-momentum-in-one-dimension-phys/ Accessed 13th April 2022.
2. Conservation of Momentum: https://www.bbc.co.uk/bitesize/guides/zsvxdxs/revision/6#:~:text=Momentum%20is%20conserved%20in%20collisions,the%20total%20momentum%20is%20zero. Accessed 13th April 2022.
3. Momentum Conservation in Explosion: https://www.physicsclassroom.com/class/momentum/Lesson-2/Momentum-Conservation-in-Explosions Accessed 13th April 2022.
4. Law of Conservation of Linear Momentum: https://byjus.com/physics/law-of-conservation-of-linear-momentum/ Accessed 13th April 2022.
5. Momentum Conservation Principle: https://www.physicsclassroom.com/class/momentum/Lesson-2/Momentum-Conservation-Principle#:~:text=The%20law%20of%20momentum%20conservation%20can%20be%20stated%20as%20follows,two%20objects%20after%20the%20collision. Accessed 13th April 2022.

In this chapter, we will study the law of conservation of momentum and how it governs colliding and exploding systems. 

Conservation Of Momentum In One Dimension Study Guide

Classical Physics

# Introduction

![rock](//images.ctfassets.net/4yflszkpcwkt/67SWwtOvWNHmSkUBEWmv2Y/7b2094c9ca030ed0f97dd0c16f8b2416/DWemnoAW58tbQnhsP2tPdC-650-80.jpg.webp)
[Source](https://cdn.mos.cms.futurecdn.net/DWemnoAW58tbQnhsP2tPdC-650-80.jpg.webp)

Ever heard of the saying “the higher you climb, the harder you fall”? It’s literally true because the higher you go above the surface of the Earth, the more ‘potential energy’ you accumulate. The same idea is true for a bow and arrow- the further you pull back the string, the faster the arrow flies. So what is potential energy, and how do we understand this phenomenon? Let’s find out! 

## ENERGY 
Before we go about grasping the concept of potential energy, we need to understand what ‘energy’ is and what it does. The definition of energy goes like this: 

__“Energy is the capacity to do work.”__ 

If you miss your lunch, you won’t have the energy to play in the evening. Similarly, energy enables some form of __‘work’__ to be done, such as moving an object from one place to another or changing its shape. Energy can be stored and released to do different types of work. 

## STORED ENERGY OR POTENTIAL ENERGY 

![potential](//images.ctfassets.net/4yflszkpcwkt/2S6dLY1LpHeNHF2GxBLK0C/c8b5c59c6a43ed2dbe0ab4a78bb242a8/Potential-energy.jpg)
[Source ](https://d1whtlypfis84e.cloudfront.net/guides/wp-content/uploads/2018/02/15100858/Potential-energy.jpg)

When you pull back on the string of a bow or climb up a flight of stairs, you are doing work against a potential. You need to put in the energy to bend the bow against its stiffness and put in the energy to move up the stairs against gravity. This energy is stored in the form of __potential energy__, which can be released at any moment. 

Think of the last time you went on a hike and pushed a small boulder resting atop a hill. The boulder rolls off the slope picking up speed and finally coming to rest at the bottom. Where did all that energy come from? It was already stored in the boulder as potential energy because of the height at which it sat at rest. 

## TYPES OF POTENTIAL ENERGY 
Now that we know the meaning of potential energy, we understand that it can be stored in different forms: 

__1. Gravitational Potential Energy__

Gravitational potential energy is stored in objects as a function of their __position__ above the surface of the Earth.
The Potential energy formula, in this case, is expressed as __(Pe) in Joules__. 

__Pe=mgh__

Here,
 __m__ = mass of the object

 __h__ = height of the object above the ground

 __g__ = acceleration due to gravity @ 9.8 m/s2

With both the mass and gravitational acceleration remaining constant, it can be seen that potential energy depends directly on the height of the object. 

__2. Elastic Potential Energy__ 

![arrow](//images.ctfassets.net/4yflszkpcwkt/1y9HDDkaq1WV8iTH8pqImD/0d8a1cf9798d05cee65f65d1823bc846/6ba702d7fa9cda90312a8f275ec16a4e.gif)
[Source](https://hi-static.z-dn.net/files/d7a/6ba702d7fa9cda90312a8f275ec16a4e.gif) 

- This is the potential energy stored in a stretched elastic object. 
- Examples include a stretched bow and a twisted rubber band. 
- When you pull on the string of the bow, you are causing the bow to stretch and bend while storing potential energy. 
- As soon as you let go, the energy is transferred to the arrow to shoot it forward.   

__3. Chemical Potential Energy__

- This is the type of energy stored in the reactants of a chemical process. Examples include the energy stored inside a battery’s electrolytes and energy stored in the oxidizer and fuel of a firework. 
- When the chemical reaction takes place, this energy is released in the form of heat, light, and sound. 

# SUMMARY 
- Energy is the capacity to do work.
- Potential energy is a type of energy that can be stored in objects 
- Energy stored in objects because of their elevation from the Earth is gravitational potential energy.
- Energy stored in an object because of a change in its shape is called potential energy. 

## FAQs

__Q. What are the types of potential energy?__

The different potential energy examples include: 
- Gravitational potential energy
- Elastic potential energy
- Chemical potential energy
- Electrical potential energy

__Q. What is the potential energy dimensional formula?__

The formula for gravitational potential energy is Pe (mgh)=Mass X acceleration due to gravity X height. The dimensional formula is (M1 L2 T-2)

__Q. Give examples of potential energy.__

- The gravitational potential energy is stored in rocks on top of a mountain. 
- The gravitational potential energy is stored in the water of a power station reservoir.
- The chemical potential energy is stored inside a battery.
- The elastic potential energy is stored inside a stretched rubber band. 
- The chemical potential energy stored inside firecrackers.   

*We hope you enjoyed studying this lesson and learned something cool about __Potential Energy!__ Join our Discord community to get any questions you may have answered and to engage with other students just like you! Don't forget to download our App to experience our fun VR classrooms - we promise, it makes studying much more fun!😎*

## REFERENCES: 
1. Potential Energy: https://flexbooks.ck12.org/cbook/ck-12-physics-flexbook-2.0/section/6.5/primary/lesson/potential-energy-phys/ Accessed 11th April 2022
2. Energy: https://flexbooks.ck12.org/cbook/ck-12-middle-school-physical-science-flexbook-2.0/section/14.1/primary/lesson/energy-ms-ps/?referrer=crossref  Accessed 11th April 2022
3. Potential Energy: https://www.physicsclassroom.com/class/energy/Lesson-1/Potential-Energy  Accessed 11th April 2022
4. Potential Energy: https://byjus.com/physics/potential-energy/  Accessed 11th April 2022

In this article, we explore the concept of potential energy and its application. Potential energy can exist in different forms, such as gravitational potential energy and chemical potential energy. 

Potential Energy Study Guide

## Introduction

![cars](//images.ctfassets.net/4yflszkpcwkt/ROzcOJSCEBqWEyX0qCkB0/9d21cb8743d700d6c52e97dd7bfc8001/article-2052533-0E802AA300000578-817_308x185.jpg)
[Source](https://i.dailymail.co.uk/i/pix/2011/10/23/article-2052533-0E802AA300000578-817_308x185.jpg)

We’ve all seen collision videos of trains, cars, and bikes on the internet. The most obvious thing we see is that the faster the vehicle is going, the more damage it sustains. Two cars bumping into one another in slow-moving traffic is a fender bender at best. When a car that’s speeding at 100 miles an hour hits a solid wall, it gets completely wrecked. What’s the difference between the first and second scenarios? Lots of kinetic energy!  

## ENERGY
- Energy is defined as the __capacity to do work__. 
- It is measured in units called __joule (J)__. 
- Energy can exist in different forms in all objects, but the one which we commonly experience every day is __Kinetic Energy__. 
- When we say “the capacity to do work,” it means anything from getting a stationary object to move to bringing moving objects to rest or changing the shape of the object. 
- The energy in a system or an object can __only be transformed__ from one form to another. 

Energy can be used to perform work, or work can be done to transform energy from one form to another. 

## KINETIC ENERGY

![kinetic](//images.ctfassets.net/4yflszkpcwkt/3GN1IpYufvuhiIbNL19LOf/fb6c2fc54f44b4d7394378b69669f5c0/definition-potential-energy-defined-image.jpg)
[Source](https://assets.taraenergy.com/wp-content/uploads/2020/11/definition-potential-energy-defined-image.jpg) 

- Kinetic energy is the energy possessed by objects that are __in motion__. 
- If a car is standing still on the top of a hill, it has __zero kinetic energy__ (but lots of potential energy). 
- When you give it a push and get it rolling over the slope, it begins to transform its __potential energy into kinetic energy__. 

## THE FORMULA FOR KINETIC ENERGY

The formula for kinetic energy is given by: 

__KE = m__

__KE__ is the kinetic energy of the object 

__m__ is the mass of the moving object

__v__ is the velocity of the moving object

The unit of kinetic energy is joules (J)

## DIFFERENCE BETWEEN KINETIC ENERGY AND POTENTIAL ENERGY

![kinetic](//images.ctfassets.net/4yflszkpcwkt/4RFeucgPuYfpGZFdCcZYyT/a03d46357295c0733b60fbe615079ccd/Potential-and-Kinetic-Energy-edited.png)
[Source](https://engineerfix.com/wp-content/uploads/2021/04/Potential-and-Kinetic-Energy-edited.png?ezimgfmt=ng:webp/ngcb1) 

- Going back to the example of the car on top of a hill, we see that the vehicle has two types of energy. 
- When you tow the car uphill, you are storing potential energy in the car by elevating its position and doing work against gravity. 
- When it sits still on top of the hill, it is full of potential energy and zero kinetic energy. 
- As the car gets rolling down the hill, the potential energy starts getting converted into kinetic energy. 
- By the time the car is moving at the bottom of the hill, it is full of kinetic energy and zero potential energy. 

# SUMMARY
- Energy is the capacity to do work. Energy and work are interchangeable.
- Kinetic energy is the energy possessed by moving objects. 
- Kinetic energy can do work by changing the shape of objects (like in a car crash).
- Kinetic energy is directly proportional to the mass of the object and the square of its velocity. 

## FAQs

__Q. Is kinetic energy a vector or a scalar quantity?__

Kinetic energy is a scalar quantity as it has only magnitude and no direction.                   

__Q. Can the kinetic energy be negative?__

By the definition of kinetic energy KE = m, we can see that mass cannot be negative, and the velocity also cannot be negative as the square of a negative number is positive. 

__Q. What happens to the kinetic energy when the speed decreases?__

When speed decreases, the kinetic energy decreases as the square of the speed. 

__Q. When is the kinetic energy maximum?__

Kinetic energy is maximum when objects reach the maximum possible velocity in their path of motion.                             

__Q. How is the kinetic energy different from the potential energy?__

Kinetic energy is the energy in moving objects, while potential energy is stored when the object is stationary.  

*We hope you enjoyed studying this lesson and learned something cool about __Kinetic Energy!__ Join our Discord community to get any questions you may have answered and to engage with other students just like you! Don't forget to download our App to experience our fun VR classrooms - we promise, it makes studying much more fun!😎*

## REFERENCES 
1. Kinetic Energy: https://flexbooks.ck12.org/cbook/ck-12-physics-flexbook-2.0/section/6.6/primary/lesson/kinetic-energy-phys/ Accessed 11th April 2022
2. Energy: https://flexbooks.ck12.org/cbook/ck-12-middle-school-physical-science-flexbook-2.0/section/14.1/primary/lesson/energy-ms-ps/?referrer=crossref  Accessed 11th April 2022
3. Kinetic Energy: https://byjus.com/physics/kinetic-energy/ Accessed 11th April 2022 
4. What is Kinetic Energy? https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-kinetic-energy Accessed 11th April 2022 
5. Kinetic Energy: https://www.vedantu.com/physics/kinetic-energy Accessed 11th April 2022 

 In this article, we learn about the definition of kinetic energy and its effects on physical objects. 

Kinetic Energy In Physics Study Guide

## INTRODUCTION

![conservation](//images.ctfassets.net/4yflszkpcwkt/30Sn1ej2YAf8nBItNBWatW/0716fb9173b39eabd0babe0038c0a1c9/Law-of-Conservation-of-Energy.png)
[Source](https://cdn1.coolgyan.org/wp-content/uploads/2020/09/Law-of-Conservation-of-Energy.png) 

Have you ever wondered where all the energy that runs the world and the natural processes in the environment comes from? Or where it goes? If your first guess is the sun, you would be right, but, partially. The sun doesn’t create any of the energy that we receive on Earth; it merely transforms it from nuclear energy to heat, light, and other forms of radiation. That is also what happens on Earth- energy only circulates; it is neither created nor destroyed. Let’s take a look at the nature of energy and the law of conservation of energy.  

## WHAT IS ENERGY? 

- In simple terms, energy is the __capacity to do work__. 
- That could mean anything from moving an object from one place to another, bringing a moving object to stop or to even change the shape of objects. 
- You will have to expend energy to kick a football on the ground. 
- The ball is at rest, and your kick transfers a certain amount of kinetic energy to the ball to get it moving. 

## ENERGY AND CLASSIFICATION OF ENERGY                             

Energy occurs in different forms such as: 

1. **Chemical energy:** Energy stored in the reactants of a chemical reaction. 

2. **Electrical energy:** Energy carried by moving electrons in power lines and circuits.

3. **Mechanical energy:** Energy stored in physical form such as in a spring under tension or a flywheel. 

4. **Thermal energy:** Energy in substances that occurs in the form of heat, such as cooking stoves. 

5. **Nuclear energy:** This is the energy that exists as atomic bonds. The sun’s heat and light comes from nuclear energy. 

## THE LAW OF CONSERVATION OF ENERGY 

![energy](//images.ctfassets.net/4yflszkpcwkt/3dcCGEZlGeH36oU8Hu5Ie2/3333d763d733b2148e41903a7e595b1c/Screen_Shot_2019-04-08_at_12.02.46_PM.png)
[Source](https://cebrightfutures.org/sites/default/files/Screen%20Shot%202019-04-08%20at%2012.02.46%20PM.png) 

- According to the law of conservation of energy, in a closed system, energy can neither be created nor destroyed; it can only transform from one state to another. 
- Think of a closed system as an isolated space or bubble that cannot exchange any form of heat, work, or matter with its surroundings. 
- Within such a system, energy cannot enter or leave. Therefore it cycles in the processes happening within. 

The __conservation of energy formula__ is given by 

__UT = Ui + W + Q__

Here,

UT is the total energy within the system

Ui is the initial energy of the system

W is the work done by/on the system

Q is the flow of heat to or from the system

## SUMMARY 
* Energy is the capacity to do work. 
* Energy can exist in many forms, such as potential energy, kinetic energy, and chemical energy. 
* Energy can be transformed from one form to another. 
* According to the law of conservation of energy, in a closed system, energy can neither be created nor destroyed; it can only transform from one state to another.

## FAQs

**Q. What are the ways in which energy can be transferred?**

Energy can be transferred in following ways: 

* The chemical energy of batteries can be converted into electrical energy. This electrical energy can be converted into mechanical energy in a motor or into thermal energy by using a resistance coil.
* Gravitational potential energy stored in a reservoir can be converted into mechanical energy in turbines to generate electrical energy at a power plant.                                                                   

_We hope you enjoyed studying this lesson and learned something cool about **Conservation of Energy**! Join our Discord community to get any questions you may have answered and to engage with other students just like you! Don't forget to download our App to experience our fun, VR classrooms - we promise, it makes studying much more fun! 😎_

## REFERENCES 

1. Conservation of Energy: [https://flexbooks.ck12.org/cbook/ck-12-physics-flexbook-2.0/section/6.7/primary/lesson/conservation-of-energy-phys/](https://flexbooks.ck12.org/cbook/ck-12-physics-flexbook-2.0/section/6.7/primary/lesson/conservation-of-energy-phys/) Accessed 11th April 2022.
2. Energy: [https://flexbooks.ck12.org/cbook/ck-12-middle-school-physical-science-flexbook-2.0/section/14.1/primary/lesson/energy-ms-ps/?referrer=crossref](https://flexbooks.ck12.org/cbook/ck-12-middle-school-physical-science-flexbook-2.0/section/14.1/primary/lesson/energy-ms-ps/?referrer=crossref) Accessed 11th April 2022.
3. Law of Conservation of Energy: [https://byjus.com/physics/law-of-conservation-of-energy/](https://byjus.com/physics/law-of-conservation-of-energy/) Accessed 11th April 2022.
4. Conservation of Energy: [https://courses.lumenlearning.com/physics/chapter/7-6-conservation-of-energy/](https://courses.lumenlearning.com/physics/chapter/7-6-conservation-of-energy/) Accessed 11th April 2022.
5. What is Conservation of Energy? [https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-conservation-of-energy](https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-conservation-of-energy) Accessed 11th April 2022.
6. Forms of Energy: [https://vikaspedia.in/energy/energy-basics/forms-of-energy](https://vikaspedia.in/energy/energy-basics/forms-of-energy)Accessed 11th April 2022.

 In this chapter, we take a look at energy transfer and the law of conservation of energy. You will see how energy is neither created nor destroyed in a closed system. 


Conservation Of Energy Study Guide 

You’re out playing with your kid brother and mom on the playground. They’re each on a swing, and it’s your turn to push. You’ll notice that it’s easier to push your kid brother’s swing while it takes a lot more effort and time to get your mom’s swing going. It also takes more effort to bring your mom’s swing to a stop. Common sense tells you that it is because your mom weighs more than your kid brother. But what’s the physics behind it? Impulse and momentum!

![swing](//images.ctfassets.net/4yflszkpcwkt/k1I5DgP54JPe1NgUsiwJE/1d1244b0768104c27963457c61ca68bf/let-go-swing.jpg)

## What is Momentum? 

![train](//images.ctfassets.net/4yflszkpcwkt/1xjAG9M2my7IJZF1NI14cj/99ebd2095821a6e34efb078d5f0c7cbc/810_fastTrnCrp.jpg)

- We often hear the word momentum used colloquially to describe something gaining movement such that it is difficult to stop.
- We often hear commentators talk about how sports players and political candidates have “gained a lot of momentum”. 
- You would experience the same on the playground; it takes more effort to bring a heavier person to stop on a swing. The reason is __momentum__. 
- In physics, momentum is defined as the product of __mass and velocity__. 
- It is a __vector quantity__ and is represented by the lowercase __‘p’__.

__P = mv__

Here, 
__m__ is the mass of the moving object, 

and __v__ is the velocity of the moving object. 

The unit for momentum is __kg m/s__. 

In a nutshell, the concept of momentum tells you how much motion there is in a moving object. 

### Momentum in Space

The collection of all momentum vectors that a physical system is capable of having is known as momentum space. A particle's momentum vector corresponds to its motion and has the units__ [mass][length][time]-1.__

Position and momentum's mathematical duality is an illustration of Pontryagin duality. In specifically, the Fourier transform of a function given in position space, f(r), yields the function in momentum space (p). On the other hand, a momentum space function's inverse Fourier transform is a position space function.

The locations of the component particles or their momenta may be used to describe a physical system, and both formulations convey the same information about the system under discussion. These quantities and concepts transcend all of classical and quantum physics. In the context of waves, another quantity is helpful to specify.

###  What is Specific Impulse?

Specific impulse, or how much more push you get as you utilize that fuel, is the change in momentum per unit mass for rocket fuels.

Thrust, which is basically the quantity of fuel that is thrown out of the rear of the rocket and the speed at which that propellant is flung out, is what determines the rocket's speed in relation to its weight.

## IMPULSE 
![swing](//images.ctfassets.net/4yflszkpcwkt/4BTGvzKEKeFiiIu48sZsu5/24704039463f8ceede84f517a9d29ab0/pushing-child-on-swing-1.png)

- Back in the playground, you will have to apply some amount of force (a push) for a certain amount of time to get the swing moving. 
- This is what is called an __impulsive force__. 
- The definition of impulse in physics is force multiplied by the duration for which the force acts. 
- Mathematically it is expressed as: 

__J = F Δt__

Here, __J__ is the impulse.

__F__ is the applied force, and

__Δt__ is the duration of time for which the force acts.

- The concept of impulse tells you the effect the applied force has on changing the momentum of an object. 
- An impulse can speed up or slow down a moving object. 

### Relation Between IMPULSE AND MOMENTUM                          
Consider the impulse and momentum equations: 

- Momentum is given mathematically as P = mv. The unit of mass is kilograms (Kg), and the unit of velocity is meters per second m/s. Therefore the unit of momentum is Kg m/s.
- Impulse is defined mathematically as J = F Δt. The unit of force is Newton (N) and the unit of time is seconds (s). Therefore impulse is expressed as Ns. 

- However, N can also be expressed as Kg m/. The impulse units then become Kg m/s. 
- This equivalence between momentum and impulse is known as the __impulse-momentum theorem__. 

### Summary
- Momentum is defined as the product of mass and velocity. It describes the motion contained in an object. 
- Impulse is defined by force multiplied by time. It gives a measure of the change in momentum. 
- A large impulse gives a large change in momentum. 

## FAQs

__Q. What is the application of impulse and momentum?__

- Airbags in cars use the principle of the impulse to apply a small but opposite force over a relatively long period of time to dissipate the momentum slowly. This reduces injury. 
- If you are catching a falling egg, you move your hand in the direction of the egg to slow it down. Abruptly stopping the egg would break it. 

__Q. How are momentum and impulse related?__                                    
The change in momentum is directly proportional to the impulse given to the object. 

*We hope you enjoyed studying this lesson and learned something cool about __Momentum and Impulse!__ Join our Discord community to get any questions you may have answered and to engage with other students just like you! We promise, it makes studying much more fun!😎*

In this chapter, we will take a look at how motion can be quantified in terms of momentum and impulse. While the two have the same units, they are different concepts. 


Momentum And Impulse Study Guide

# INTRODUCTION

How often did you think you were going to sink the ball this time for sure, only to have it fly off in unexpected directions? It takes a while for any beginner to get the hang of billiards and get the direction right. To master the game, you must understand impulse force, momentum, and collisions. When you strike the cue ball in the pool, you can observe how the ball's kinetic energy splits up into the other balls to set them in motion. What are the physics principles behind billiards? Let’s find out!

![Collision](//images.ctfassets.net/4yflszkpcwkt/1E9wTNCpaIh65kcY6bJKCD/f6be72bab84194559e069c54c625ecad/S9_Mom1.jpg)
[Source](http://www.csun.edu/~psk17793/S9CP/S9%20Momentum3.htm) 

## WHAT IS A COLLISION?

In physics, a collision refers to objects in motion that come in contact with each other such that they exert a mutual impulsive force. Collisions involve the transfer of kinetic energy from one body to another. Based on that, collisions can be classified as: 

Collision in physics refers to objects in motion coming in contact such that they exert an impulsive force on one another. There is a transfer of kinetic energy between the colliding objects in collisions. In a closed system (a system that doesn’t exchange heat, work, or matter to the surroundings), the momentum is conserved.

Some collisions in a closed system occur such that the kinetic energy is also conserved. Such collisions are called elastic collisions. If any denting, deformation, or elevation against the gravity of the objects involved in a collision, then the kinetic energy is not conserved. Such collisions are called inelastic collisions. 

## ELASTIC COLLISION

![Elastic Collision](//images.ctfassets.net/4yflszkpcwkt/4Tpgt6D2LTL8UFVaxLhlkv/39afa118f1efdf543a4bcd80bc0138dc/Cue_ball_after_collision.jpg)
[Source](https://letstalkscience.ca/educational-resources/stem-in-context/billiards-and-collisions)

In an elastic collision, the net kinetic energy of the objects before and after the collision remains the same. In other words, kinetic energy is transferred between the two bodies without being lost. 

Considering the billiard balls example, the kinetic energy of the cue ball before the collision is almost equal to the sum of kinetic energy gained by all other balls after the collision. Because the balls are of the same mass and made out of a hard material that doesn’t deform under the forces of the pool, the collision of billiard balls can be considered nearly elastic.

## INELASTIC COLLISION

![Inelastic collision](//images.ctfassets.net/4yflszkpcwkt/1mkPBRVUQXWFO7DGk8mPa6/c5455b1e9b8dc5b39acf77ac69d95065/Inelastic_Collision.png)
[Source](http://bttc.shiksha/moodle/mod/glossary/print.php?id=65&mode=&hook=ALL&sortkey=&sortorder=&offset=70)

Inelastic collisions experience a loss of kinetic energy as the energy is transformed into heat, sound, or physical deformation of materials. Most collisions in the real world are inelastic. Observe the deformation of the golf ball in the picture as it collides with a club. During the collision, the golf ball compresses and expands and, in the process, loses kinetic energy in the form of sound and heat.  

## MOMENTUM AND IMPULSE

Momentum gives you a measure of how much motion exists in a moving object. A slow-moving bowling ball has lesser momentum than a fast-moving bowling ball.  Mathematically momentum is expressed as:

                               p = mv
p is momentum in kg m/s

m is the mass of the object in kg

v is the velocity of the object in m/s 

An impulse is a force that acts for a certain period, bringing about a change in momentum. Examples of an impulse include kicking a ball, striking with a bat, and breaking boards in martial arts.
Mathematically it is expressed as force multiplied by time: 

                               J = Ft
J is the impulse in Ns
F is the force in Newton 
t is the time duration in seconds

## CONSERVATION OF MOMENTUM 

![Conservation of momentum](//images.ctfassets.net/4yflszkpcwkt/3vL55FKpowUF4mvhqNSML5/4cd147e2ca7b8dcb8925aa57005fc4db/hnet.com-image.svg)
[Source](https://www.chegg.com/learn/physics/introduction-to-physics/recoil)

According to the law of conservation of momentum, in an isolated system, the total momentum of the colliding objects remains the same before and after the collision. That means the momentum gained by one object after the collision is equal to the momentum lost by the other. This is the reason why guns recoil when fired. According to Newton’s 3rd law, shooting the bullet in one direction creates an equal and opposite reaction as the recoil. The momentum of the gun's recoil is equal to the bullet's momentum. Mathematically it is expressed as:

                               MgVg = - MbVb

Mg = mass of the gun

Vg = velocity of the gun

Mb = mass of the bullet

Vb = velocity of the bullet

# CONCLUSION: 

- A collision occurs when two bodies come in direct contact and exert force on each other.
- In an elastic collision, there is no net loss of kinetic energy
- In inelastic collisions, there is a loss of kinetic energy
- According to the law of conservation of momentum, in an isolated system, the total momentum of the colliding objects remains the same before and after the collision. 

## FAQs:

__1. What is a synonym for collision?__

Going by the collision definition, it can also be called an impact or an impulse. 

__2. What are the 3 types of the collision?__

- Elastic
- Inelastic 
- Completely inelastic

__3. What happens in a collision?__

There is the transfer of kinetic energy during a collision, but the system's total momentum remains the same. 

*We hope you enjoyed studying this lesson and learned something cool about __Collision__! Join our Discord community to get any questions you may have answered and to engage with other students just like you! We promise, it makes studying much more fun!* 😎

## SOURCES: 
1. 6.4 Elastic and Inelastic Collisions. https://flexbooks.ck12.org/cbook/ck-12-physics-flexbook-2.0/section/6.4/related/lecture/elastic-and-inelastic-collisions/. Accessed 27 Jan 2022.
2. 6.1 Momentum and Impulse. https://flexbooks.ck12.org/cbook/ck-12-physics-flexbook-2.0/section/6.1/primary/lesson/momentum-and-impulse-phys/. Accessed 27 Jan 2022. 
3. Elastic Collision. https://byjus.com/physics/elastic-collision/. Accessed 27 Jan 2022. 
4. What are elastic and inelastic collisions?. https://www.khanacademy.org/science/physics/linear-momentum/elastic-and-inelastic-collisions/a/what-are-elastic-and-inelastic-collisions. Accessed 27 Jan 2022. 


Collisions are a common occurrence every day. However, the effects can be different in elastic and inelastic collisions.


Collision Study Guide

# Introduction
![pool](//images.ctfassets.net/4yflszkpcwkt/2dfpIyi41ZKOzcyTYgqMIj/bf52c470bbcc76cc669b4b9f25be51c3/kinetic-energy-characteristics-image-of-pool-ball-motion.jpg)

[Source](https://assets.amigoenergy.com/wp-content/uploads/2021/01/kinetic-energy-characteristics-image-of-pool-ball-motion.jpg)

The collision between two objects in the real world seldom occurs in only one direction. Consider the game of billiards; it is critical that the shooter can visualize the direction in which the colored balls take off when struck by the cue ball. While the players might get the shot right by instinct and practice, there is precise physics that governs how the billiard balls behave. To know how this works, it is essential to understand the conservation of momentum in two dimensions. 

## THE PRINCIPLE OF CONSERVATION OF MOMENTUM

Understanding the principle of conservation of momentum is essential before we can grasp how collisions work. In all closed systems, the total momentum of all colliding objects __remains the same__ before and after the collision. 

- By definition, __a closed system__ is a system that is isolated from its surroundings such that it cannot exchange energy, mass, or work in any form. 
- In the real world, such a system doesn’t exist. 
- However, a pool table is a close approximation if we can ignore the small amounts of energy lost by the balls because of the friction of the table and air resistance.

According to the law of conservation of momentum, the total momentum of the balls before the collision is equal to the total momentum of the balls after the collision. 

Mathematically the general equation in one dimension can be expressed as: 

__Σm1v1 = Σm2v2__

Where, 
__Σm1v1__ is the sum total of momentum of all the balls before the collision

__Σm2v2__ is the sum total of momentum of all the balls after the collision 

This equation gives the __momentum relation__ when the balls collide head-on and move back in the same direction they came from. 

## CONSERVATION OF MOMENTUM PRINCIPLE IN TWO DIMENSIONS                                  
![pool](//images.ctfassets.net/4yflszkpcwkt/70QqwtENCFXSPXWF6ZmeFf/ff7337d7c93a0b9d7c97e08303f07962/conservation-of-momentum-in-two-dimensions1-l.jpg)
[Source](https://image1.slideserve.com/3190415/conservation-of-momentum-in-two-dimensions1-l.jpg)

On a pool table, the collisions and movement of the balls rarely occur in one dimension. Most often, the balls graze one another and strike at different angles. Even when balls strike at different angles, the __total momentum is still conserved__. 

Here we can apply the __conservation of momentum law in two dimensions__ to account for the x and y components of motion. In this case, the momentum in each direction is conserved independently. 

Mathematically it can be expressed as: 
__Σpxi = Σpxf__ (total momentum in the x-direction before and after collision)

__Σpyi = Σpyf__  (total momentum in the y-direction before and after collision)

# SUMMARY
- The law of conservation of momentum holds good for all closed systems. 
- In a two-dimensional system, the momentum is conserved individually for each dimension because momentum is a vector quantity. 

## FAQs

__Q. What is the law of conservation of momentum in two dimensions?__                                                  
In a closed system, when objects moving in two dimensions (x and y) collide, the momentum is conserved in each dimension individually. 

__Q. Is momentum conserved in each dimension?__

According to the conservation of momentum law in two dimensions, the momentum will be conserved independently in each direction. 

__Q. What does conservation of momentum depend on?__

The conservation of momentum is a consequence of Newton’s third law which states that every action has an equal and opposite reaction. It is also essential that the system being analyzed is closed or comes close to being isolated. The conservation of momentum cannot hold well if there is an external impulse on the objects or a significant loss of energy in the form of inelastic collisions.                                    

__Q. Why can momentum be conserved when energy is not?__

As long as the system is isolated, both the momentum and energy are conserved. 

*We hope you enjoyed studying this lesson and learned something cool about the __Conservation of Momentum in Two Dimensions!__ Join our Discord community to get any questions you may have answered and to engage with other students just like you! We promise, it makes studying much more fun!😎*

## REFERENCES: 
1. Conservation of Momentum in Two-dimension: https://flexbooks.ck12.org/cbook/ck-12-physics-flexbook-2.0/section/6.3/primary/lesson/conservation-of-momentum-in-two-dimensions-phys/ Accessed 13th April 2022.
2. What are Two-dimensional Collisions? https://www.khanacademy.org/science/physics/linear-momentum/momentum-tutorial/a/what-are-two-dimensional-collisions#:~:text=For%20a%20collision%20where%20objects,before%20and%20after%20the%20collision. Accessed 13th April 2022.
3. Collisions of Point Masses in Two-dimension: https://courses.lumenlearning.com/physics/chapter/8-6-collisions-of-point-masses-in-two-dimensions/ Accessed 13th April 2022.


 In this chapter, we go deeper into the conservation of momentum in two dimensions. Since momentum is a vector quantity, it can be represented by axial-vector components. 


Conservation Of Momentum In Two Dimensions Study Guide

TL;DR Potential Energy

TL;DR Momentum and Impulse

TL;DR Momentum and Impluse

TL;DR Kinetic Energy

TL;DR Conservation Of Momentum In Two Dimensions

TL;DR Conservation Of Momentum In One Dimension

TL;DR Conservation Of Energy

Let's quickly learn about collisions we see all around us - a hammer and a nail head, a golf club and a ball, two railroad cars when being coupled together and many other such instances!

TL;DR Collision

## INTRODUCTION

Collision theory in chemistry allows scientists to predict a rate constant of a chemical reaction which can be used to determine reaction rates. This theory was developed by Max Trautz and William Lewis to derive meaningful insights into these chemical reactions.  

### WHAT IS COLLISION THEORY

Collision theory states that the rate of a chemical reaction is directly proportional to the number of collisions occurring between the reactant molecules. In simple terms, the collision theory in chemistry explains what initiates chemical reactions. Theoretically, the more that the reactant molecules collide with one another, the faster the rate of reaction becomes. In reality, however, only a small fraction of the collisions are what we term effective collisions, which are the only type of collision that results in the creation of a product.

To initiate effective collisions, reactant molecules are required to have activation energy, which is the minimum amount of energy required to undergo a reaction. The count of molecules possessing sufficient energy is all dependent on the reactant's temperature. If these reactants do not possess their required activation energy, they bounce back from each other without even reacting. 

### Temperature Dependency of Collision Theory 

According to collision theory, the reaction happens between the active molecules. The percentage of activated molecules and the percentage of activated collisions both climb as temperature rises. As a result, the rate of reaction rises.

The activation energy is returned in the form of vibrational energy when the reaction is finishing and the products are forming. This energy is immediately discharged as heat. Therefore, it is crucial that the molecules collide at energies larger than or equivalent to the reaction's activation energy.

Applying the Arrhenius equation to two different temperatures yields the same result (T1andT2)
Log k2/k1=Ea/2.303R(T2–T1/T1T2) 

Where k1 = specific rate at T1

k2 = specific rate at T2
Ea = activation energy
R = gas constant

### Molecular Collision
- The simple rule is that there will be more collisions the more molecules there are. As a result, depending on how many particles collide, different proportions of collisions occur.
- Before molecules may react chemically, they must first collide.
- Kinetic energy needs be present in collisions to initiate a reaction. A strong enough contact strength is required to break the binding.
- Temperature has an impact on collisions; the higher the temperature, the more collisions. The severity of crashes increases with temperature.
- In contrast to molecules with sufficient energy, neutral molecules cannot break any bonds or take part in the collision process since they have a lower energy level.
- The reaction process involves the bond being bent, stretched, and twisted. As a result, the procedure needs energetic molecules.

### POSTULATES OF COLLISION THEORY

Collision theory is based on three postulates:
The rate of reaction is proportional to the rate of reactant collision molecules. 
The reacting element should collide to allow contact between the atoms, which are meant to be bonded together. 
There must be sufficient energy to allow mutual penetration of the reactants so that the electrons can again arrange and form new bonds. 

## CONCLUSION

- Collision theory occurs at certain chemical reactions and rates. 
- The fundamental principle is that in order to react, molecules must undergo effective collisions. 
- In order to undergo an effective collision, the molecules’ collision energy must be greater than or equal to activation energy during the reaction.
- Reactants with low concentration result in few collisions, and those with high concentrations produce more collisions. 

### FAQs

__1. What is collision theory?__

Collision theory defines that the chemical reaction rate is proportional to the number of collisions occurring between the reactant molecules. This occurs at certain chemical reactions and rates. 

__2. What are the 4 points of collision theory?__

- Reactants must collide in the proper orientation.
- Collision energy must be greater than or equal to activation energy during the reaction. 
- The reactant particles must collide with one another.
- The collision frequency should be larger than the number of factors for the reaction. 

__3. What are the three postulates of collision theory?__

- The rate of reaction is proportional to the rate of reactant collision molecules. 
- The reacting molecules must collide to allow contact between the atoms, which are meant to bond together. 
- There should be sufficient energy to allow joint penetration of the reactants so that the electrons can rearrange and form new bonds.

__4. What equation is used for collision theory?__

K ∝ e-Ea/RT

K = A e-Ea/RT

where, A is the frequency factor, Ea is the activation energy, R is gas constant and T is the absolute temperature

This is the Arrhenius equation, and the collision theory equation is accommodated in this only. 

![molecular-collisions](//images.ctfassets.net/4yflszkpcwkt/5p5vzbgw5cwJchDyzvs47n/bfa4617684bd7d1ab35ee5ab311037bd/molecular-collisions.jpeg)

*We hope you enjoyed studying this lesson and learned something cool about __Collision Theory__! Join our Discord community to get any questions you may have answered and to engage with other students just like you! Don't forget to download our app to experience our fun VR classrooms - we promise it makes studying much more fun!* 😎


Collision Theory plays a vital role in this fast-developing world and results in chemical reactions.

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