Simplified Physics

Relation between Object and Image velocity for a spherical mirror along principal axis.

2021-01-20T09:29:00.005+05:30

We know the mirror formula is:

Case 1: differentiating the above equation w.r.t. time, we get

the (-ve) sign shows that if the direction of object is in positive direction, then the direction of image will be in opposite direction i.e. object and image will always have their velocities opposite to each other. In other words, if the object approaches the mirror then the image will go away from the mirror and vice versa.

In case |u| = |v|

i.e. |m| = 1

This will be observed when the object is at the center of curvature.

Case 2: When object moves between center of curvature and focus:

In this case for a concave mirror the image will lie beyond C.

So, |v| > |u|

Speed of image will be more than the speed of the object.

Case 3: Object moves between focus & pole of the mirror

In this case, for a concave mirror the image will lie behind the mirror.

The image is also virtual and

u is (-ve)

f is (-ve)

v is (+ve)

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The chapters we need to study in kinematics

2020-11-14T13:00:00.002+05:30

The chapters involved in the study of kinematics are:

Vectors and Scalars
Motion in One dimension
Motion in two dimensions ( Projectile motion)

Vectors and Scalars :

The study of Kinematics starts with the concept of Vectors and Scalars.

In this chapter we define different quantities depending on their definition. Like few quantities which can be defined just with their magnitudes like distance, speed, work etc. These quantities are called Scalar quantities. On the other hand few quantities can be defined with the help of their magnitude and direction and they are called Vector quantities like displacement, velocity, force etc.

Now, we can perform mathematical operations (addition, subtraction, multiplication and division) for both these quantities and the process for each is different. For scalar quantities we can do the operations just the way we have been doing in the algebraic operations. Whereas for vector quantities, it is not possible to do it by that method. For addition we use Parallelogram law or triangle law or polygon law of vector addition. For multiplication there are two types- Scalar ( dot ) product and Vector ( cross ) product (taught in class 11th). So, these operations which we are performing are for all the vector quantities like velocity, displacement, force etc. We just simply can't add them.

Along with these we should be familiar with different algebraic results and basic calculus understanding ( for class 11th ).

These were some of the basic concepts which we needed to learn before entering into the Kinematics.

Before moving further with Kinematics, let us first understand what do we study in kinematic? What is Kinematics all about?

Kinematics :

👉 Kinematics is all about studying the state of rest or motion of any object without taking care of what caused the object to come into motion or to rest. The reasons will be studied in detail in the dynamics chapter.

Bunny - Sir, what comes under the state of rest or motion? Please explain me in detail.

Simplified Physics - Sure....

Just stand at a place in a market and look all around you.

What do you see?

Bunny - People, bikes, bi-cycles, autos...

Simplified Physics - Are all in the same state? I mean are they all at rest? or all in motion?

Bunny - No sir few people are walking down the road and few are standing in front of the store. I can see few bikes running and few parked in the parking area.

Simplified Physics - What else do you see? are all the moving objects having the same velocity?

Bunny - No Sir .. Not at all.. few are moving slowly and few are faster. Few are slowing down and few are speeding up. Their state of motion are not at all same.

Simplified Physics - Excellent observation Bunny. This is what we are going to study in kinematics. We will be studying about the state of motion or rest of different objects. We will be determining how far they will go in a particular time? How much will a car move after the brakes are applied before the car stops.

Bunny - Great, Its very interesting. Please tell me more about it.

Simplified Physics - Sure.

Now, let's move further. When we study the state of motion of any object, we define the dimensions. Like we define whether the motion is in One Dimension, or Two Dimensions or Three dimensions. For class 9, we concentrate only on One Dimension motion. For class 11, we learn about One and Two dimensions of motion. Two dimensional motion is termed as Projectile motion. There we study about any particle thrown from one place on the ground to another place.

In kinematics, we not only learn about the uniform motion of bodies but also the motion in which the velocity is constantly increasing or constantly decreasing. We also study about the motion of any object with respect to another object. The objects may be in motion or rest.

We also come across a term called frame of reference. Frame of reference is the observer who observes and defines the state of motion or rest of an object. Let's try to understand this with a very simple example: Suppose you are standing inside a train and your friend is standing on a platform. Currently the train is at rest. So, your friend will see that you are also at rest. All other passengers around you will also observe that you are at rest. Now, if the train starts to move, your friend will see that you are also moving along with the train. But will the passengers around you will also see you moving? No... they will see that you are standing still just as before.

What do you observe here?

It is observed that with respect to different observers our state of rest or motion is different. For one I am at rest and for others I am in motion. This is called frame of reference. All these observers are different frame of references. So, Frame of reference is anything with respect to which we can define any object's motion.

After we understand frame of reference, then we understand the concept of Relative velocity. Relative velocity is the velocity of any object with respect to any other body or the observer or the frame of reference anything we can say. Using this concept we will understand different vehicle overtaking problems that we come across.

So, these were certain concepts we learn in the chapter kinematics. Now, Let me tell you something about the projectile motion. In this chapter, we study about the motion of any particle which is moving on a plane. For example, a ball thrown in air. We can determine how high the ball will go and how far from the point of projection. We often use this concept while playing cricket. we throw the ball in air and the ball reaches the wicket keeper.

Simplified Physics: So Bunny, I hope you understood the motive behind studying the kinematics.

Bunny: Thanks a lot sir.

Is it possible to measure the depth of well using kinematics equations?

2020-10-23T19:31:00.002+05:30

Yes, it is possible to measure the depth of a well using kinematic equations. Let's learn how to do it.

We are going to determine the depth of a well ( D meter ).

To perform this activity we will use sound as a medium.

Let's learn How???

👉Take a stone and drop it into the well and start the stopwatch.

Note:- Keep in mind that you don't throw the stone, you just drop in such a way that its initial velocity is zero.

👉You will hear the sound of the stone striking the water surface. Stop the stopwatch and note down the timing.
Now, we should be clear with the fact that the total time is divided into two parts-

T1 = time taken by stone to reach the water surface after it is dropped.

T2 = time taken by the sound of stone hitting the water surface. It travels from the surface to us.

We will be considering the speed of sound in air equal to 343 m/s.

So, we know that T = T1 + T2

Suppose, we assume the total time taken to be 3s i.e T = 3s.

First of all let's calculate the time taken by the stone to reach the water surface.

Now, let's us calculate the time taken by the sound waves to reach the top from the surface of the water.

So, we got the value of the depth of the well. We have skipped the calculations part, where we did the calculations with the help of a calculator.

Newton's Laws of Motion || H. C. Verma -I

2020-10-04T22:33:00.003+05:30

Hello my dear friends, we have come up with the solution to the exercise problems from the chapter Newton's laws of motion. Please go through the solution in detail. If you face any doubt in understanding any question, please reach us on telegram by clicking here.

👉Q 01 - Q 10

The law of conservation of linear momentum

2020-09-13T06:55:00.011+05:30

let's learn what is the law of conservation of momentum ?

The law states that the initial momentum of a system is equal to the final momentum of the system when there is no external force is acting on the system.
Now, the question arises- "what is a system?"
System is the area or space where our work is concentrated. Suppose a ball '1' is colliding with another ball '2'. So, the system will be ball '1' and '2' together and we will be concentrating on their collision.
Now, let us consider that balls '1' and '2' are moving with initial velocities U₁ and U₂ respectively.
If U₁ > U₂, they will collide after travelling some distance. It means that if the ball '1' will be travelling with a greater velocity it will definitely collide with the ball '2' which is traveling with lesser velocity.
The bodies have collided and after collision they start moving with some different velocities suppose V₁ and V₂.

Initial momentum of the system ( balls 1 and 2 ) is : M₁U₁ + M₂U₂
final momentum of the system is : M₁V₁ + M₂V₂
So, from the law of conservation of momentum.
Initial momentum = final momentum
M₁U₁ + M₂U₂ = M₁V₁ + M₂V₂

Some examples:

Firing of bullet from a gun
a man walking on a boat
a boy getting off from a running bicycle
a man jumping from a boat towards the shore

So, all these are some of the examples where momentum is being conserved during the process. In all these processes, there is a system. Like, bullet and the gun, man and the boat and boy and bicycle. All these come under a system. Now, as I said for the conservation of momentum, there should not be any external force acting on the system. The external force may be force which is being acted from outside of the system.

→ Let's see what is the main concept here. It's the internal forces.

Now, what are those internal forces acting on the system?
you see the first example i.e. firing of a bullet from gun, here the spring in the gun itself provides the force on the bullet and the gun itself feels the backward ( or recoil force ). So, this is an internal force of a system which is developed from within the system only.

Now, let's move to another example, i.e. a man walking on a boat. What happens here ?
As the man walks here, he pushes the boat backwards from his leg. This force is the same force which a person applies on the ground and the ground pushes him back and enables him/her to walk. So, this force which acts on the boat makes the boat move in backward direction to the motion of the man. We observe here that these two forces are action and reaction pair which acts within the system.

In the next example, it is given that a boy is getting off from a running bicycle. Now, when the boy will get off he pushes himself away from the bicycle so that he lands safely on the ground and in the process he also pushes the bicycle with the same force in the direction of motion of the bicycle. Again these two form an action reaction pair which are the internal forces of the system.

The same concept as above is applied for a man jumping off a stationary boat towards the shore. As a Reaction Force, the man pushes the boat in the opposite direction. So, at all these places, we observe the conservation of momentum taking place.

Newton's laws of motion

2020-09-13T06:49:00.003+05:30

Three laws of Newton are the fundamental laws which describe the motion of bodies. These laws are thus known as the Newton's laws of Motion. These laws help us to analyse the forces acting on a body and the effect of the forces on their motion. Let us discuss these laws and learn their importance and applications.

Newton's First Law:

When a body remains at rest it will tend to remain at rest until an external force is applied to it. Also, if a body remains in motion then it will tend to remain in motion until an external force is applied on it. Now lets understand it in a funny way, if you are sleeping in the morning then you will definitely want to sleep more until an external force like papa's words wake you up. Also, if you are playing in the lawn then you will always want to play more and more until same papa's words, which will be like and external force which makes you do something which you want to continue.

Jokes apart😀. Now considering scientific examples like when you are standing in a stationary bus, then which part of your body is in contact with the bus? your feet.. right??

so the feet will move along with the bus but the upper part of you body is still wanting to remain at rest and behave lazily and what happens? we tend to bend backwards. You must have had such an experience. And again looking at it with another aspect like suppose you are standing on the bus and the bus is moving with some velocity and when the driver suddenly applies brakes, then the part of your body which is in contact with the bus i.e. your feet, will come to rest instantly along with the bus but your upper body part it is still in jolly mood and want to remain in motion and as a result you fee a force towards front right? and you lean forward.

Now, let's work on more examples. Suppose, you are travelling by a train. And you are throwing any wrapper out of the window. ( But you shouldn't ) so now, what will happen? will the wrapper directly fall down following a vertical path?

No, the ball will still be in motion as it was before and thus it will not fall just downwards but it will also move some distance forward.

If you fall from an air balloon which is moving upwards with some velocity, then you will at first move a bit upward because of the inertia of motion and then when its velocity is zero, it will start falling downwards under gravity.

There are a lot more examples of the inertia of rest and motion.

Newton's second law of motion:

It states that the force applied on an object is directly proportional to the rate of change of momentum and change in momentum takes place in the direction of force.

First of all let us learn what is momentum?

👉It is the product of a body's mass and it's velocity.

( p = mv ) where p denotes the momentum, m denotes the mass of the object or body and v denotes its velocity.

Now, what actually happens is suppose a body is moving with an initial velocity 'u'. Then, some amount of force is applied and under the action of force, the body accelerates.

Now, if the body will accelerate, its velocity will increase. The velocity will keep on increasing until the force ceases to act. Now, suppose that after acceleration, the velocity of the body becomes 'v' m/s.

Now, we can write that

initial momentum of the body = mu

final momentum of the body = mv

change in momentum = final momentum - initial momentum

rate of change of momentum = change in momentum / time = (mv - mu ) / t = ma

as a = ( v-u ) / t

So, we see that force can also be defined as the rate of change of momentum ( Here it is Linear momentum. There is also another term called angular momentum which we will be discussing further ).

And thus this explanation describes us the second law of motion.

Now, let's learn what is the law of conservation of momentum ?

The law states that the initial momentum of a system is equal to the final momentum of the system when there is no external force is acting on the system.

Now, the question arises that what is a system?

System is the area or space where our work is concentrated.

Suppose a ball '1' is colliding with another ball '2'. So, the system will be ball '1' and '2' together and we will be concentrating on their collision.

Now, let us consider that balls '1' and '2' are moving with initial velocities u1 and u2 respectively.

If u1 > u2, they will collide after travelling some distance. It means that if the ball '1' will be travelling with a greater velocity it will definitely collide with the ball '2' which is traveling with lesser velocity.

The bodies have collided and after collision they start moving with some different velocities suppose v1 and v2.

So, initial momentum of the system ( balls 1 and 2 ) is

m1u1 + m2 u2

final momentum of the system is

m1v1 + m2v2

So, from the law of conservation of momentum.

Initial momentum = final momentum

m1u1 + m2u2 = m1v1 + m2v2

Newton's Third Law of Motion:

Newton's third law states that every action has equal and opposite reaction

Now, what does this mean?

This means that when you apply a force on any body or object you will experience the same amount of force.

As you can see in the figure that the block's weight is applied on the ground and as a reaction force the ground applied a Normal force on the block. You can consider any example like hitting a wall with your hand the harder you hit the wall you also feel the same amount of force from the wall.

But one thing is very important here it is that both the forces are applied on two different bodies. If you think that both the action and reaction forces are applied on the block and cancel each other its wrong!!

In the figure you can see that the action force ( the block's weight) and the reaction force ( the normal applied by the ground) are being acted upon two different objects.

Now we can consider more examples on this. Do you know how rockets move?

The fuel burning there throws out the hot air from the rocket (you might have seen fire like thing at the bottom of it ) so as the hot air rushes outward from the rocket it pushes the rocket upwards as a reaction force.

When you jump on the ground from a height, you will experience pain on your foot. This happens because your feet applied some force on the ground as an action and the ground also applies the same amount of force on your feet so harder you fall harder you feel the pain

These are all examples of Newton's third law of motion.

What is conduction, convection and radiation

2020-09-13T06:40:00.006+05:30

Conduction, Convection and Radiation

The way we travel from one place to the other, in the same way the heat also travels from one place to the other by different modes. This process of the travelling of heat from one body to other or one place to other is called Heat Transfer.

There are different modes of heat transfer:

Conduction
Convection
Radiation

Generally the process of conduction takes place in solids or solid fluid interface. Where as the process of Convection takes place in the fluids such as air and water. The Radiation process does not require any material medium for their transfer.

Conduction:

We know that conduction takes place in solids or solid fluid interface.

But how ????

👉 In solids, the molecules are very close to each other. They are very closely packed such that they can't move from one place to other unlike the fluids.

Like in this figure, we can see the packaging of the molecules.

Now, what will happen if we start heating the side A ?

The molecules at side A will start getting hot.
The molecules which are just close to the hot ones will start getting hot by absorbing the heat energy from them. " You can see there are columns of molecules." So, heat will start travelling from one molecule column to the other.
All this happened because the molecules were in touch with each other.
Slowly the molecules which are on side B will become hot

📌📌

What did just happen ?

👉 The heat got transferred from side A to side B. But we can see here that the molecules did not move. Just the heat energy was transferred to the nearby molecules.

This is the process of conduction of heat.

Let me give you another example. Suppose five students are standing in a line as shown in figure below

Suppose the first student has the ball as you can see. If the ball has to be put in the bucket, then will the first student go and put it there?

👉 Noooo !!.. the ball will be passed to 2nd 👉to 3rd 👉to 4th👉to 5th 👉 bucket.

See.. this was similar to conduction process. Wasn't it ?

Convection:

What did we just see in Conduction?

👉 The molecules were standing at their position and they were just passing on the heat to the next molecule.

But this does not happen in case of convection.

Before getting into it, let's imagine a rugby or football match. A player who has the ball runs towards the goal post. Just the same thing happens in the molecules of fluids ( air & water ). The molecule which gets the heat start rising upward and the cold molecules which tend to remain at lower positions take its place.

Let us analyse it now.

As you can observe that the molecules which were just above the burner get the heat and start rising upwards and cold molecules from side take its place. The molecules keep on rising from middle and come down from the sides until all the molecules are heated up. This process is called Convection.

Here, the heat transfer takes place by actual movement of the molecules which was not the case in conduction.

Radiation:

Conduction and convection needed molecules for the heat transfer. In conduction molecules were passing the heat on to the next adjacent molecule and on the other hand in convection the molecules carried and moved around with the heat.

Now, the radiation : It does not need any material medium for its transfer. We know that out of the earth's atmosphere every thing is vacuum. In that vacuum only, planets and satellites are there. Now, planets and satellites are solids. Few are even compact gases. But they cannot transfer the heat energy because they are not in contact with each other. For conduction also we need to molecules to be in contact. Now, the radiation comes in to picture. Radiation is a method of transfer of heat in the form of waves. It is the same way through which heat comes from sun to earth. Even when we are sitting in front of fire, we get the heat though knowing that the hot gases will rise vertically up. Then how does heat reach us that way? It is transferred through radiations.

Problems in Graphs in Motion in One dimention

2020-07-12T11:05:00.013+05:30

Hello friends,

A graph plays a very important role in physics and mathematics. And talking about the chapter Motion in One dimension in physics for both Classes 9th and 11th, we can analyse wide range of problems through graphs and neglect the lengthy numerical methods.

So, we have been working hard to provide you the notes and practice problems for graphs in Motion in One dimension which will not only help the Class 9th students but also provide a good basic knowledge to the Class 11th students.

We will be solving the questions from different books so that we can provide you variety of problems.

Rest & Motion: Kinematics H C Verma -I

The Physics book of H C Verma is a standard book you can say for the classes 11th and 12th students. We have worked hard to provide the solution of all the graph related problems from this chapter. We have kept in mind the requirements of a student and the guidance one may need while solving a problem.

Let's look at the Exercise problems from the chapter Rest & Motion: Kinematics.

Before going through the solutions, please note that we have tried to provide the solutions in the best way possible. We have not explained them using shortcuts.

👉Click here to go to the solutions.

Rest and Motion : Kinematics || Solutions of Exercise problems || H C Verma

2020-05-29T09:42:00.012+05:30

We don't believe in shortcuts. So, we have explained the concepts in detail.

Important*
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👉Before going through the solutions, let me clear one thing. You may find few solutions very lengthy. But it is because we want you to understand the solution in detail and without any doubts. We not only give you the solution to the problems but also make you confident in solving other problems with same concepts. So, please go through the solution in detail in order to have deep understanding in the subject.
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The solution to the questions from

👉Q 01 to Q10

👉Q 11 to Q 20

👉Q 21 to Q 30

👉Q 31 to Q 40

👉Q 41 to Q 52