Class 11 physics chapter 6 | Work,Energy and Power 02 | Conservative and Non Conservative Forces|

Hello kids, how are you? Today we will talk about the second lecture of WorkPyEnergy. You must have seen the thumbnail.

conservative force and non-conservative force. So, this topic may be very new and you may not even know the actual concept of it, what is conservative and non-conservative force. So, if you know the basics, then skip the video and see further where I am solving it with 6 examples. Like, those who know this topic, I would like to ask them, f = 4y i cap + 3x j cap.

Is this force conservative or not? If you know the answer to this then you don't need to watch the video. Leave it on the video. And if you don't know then watch the video. Let's start. What is the benefit of reading conservative and non-conservative forces? And what is their meaning? My name is Malik Pandey and better you know me by the name of Physics Wala. So, two types of forces are defined in physics. Conservative and non-conservative.

This conservative force is very important to read if you want to feel the potential energy. If you want to understand the potential energy. When I will teach you to read potential energy, you will jump. You will feel for the first time that potential energy is something. Potential energy is not MGH. H.C. Verma read carefully. He wrote such a lovely book. He did not edit the book even once in 25 years. In 25 years. And potential energy concept is best in that book. So if you want to understand potential energy, then conservative force should come in your heart.

So let's understand first of all what is conservative force and then we will talk about non conservative. Conservative force, such force, the work done by such force, point number one does not depend upon path, point number two depends

Only and only, with love and slowly, only and only on initial and final position. So it's 1 in the night and the video of conservative and non-conservative forces is being made and we have complete trust, complete trust, this language of Kolkata has come, don't mind that you will like this video very much. Does not depend upon path, workday, depends only upon initial and final position.

Suppose there is a point A and this is any body and it is having a force F. If this force is conservative, then suppose I go from A to B. I go from A to B through this path. The name of the path is 1. Then I go from A to B through this path. The name of the path is 2. Then I go from A to B through this path. The name of the path is 3.

If this force is conservative then work done by this force, work done by first path, second path or third path will be same. Work done does not depend upon path. It depends only and only upon initial and final path.

Here initial position A, B in the first path, in the second path also initial A, final B and in the third path also initial A. If initial and final position are same and force is conservative then work done is same. The force whose work done does not depend on path, no matter from where we go, we do not care.

Means in such a question, let's say he asks us what is the work done on this path, it will be tough. So what we will do is we will take out the work done on this path and say that it is of this path. Brother, it is tough to take out the work done on this path. So we will take out this path and clear the answer. The question is solved. This is the advantage of the conservative forces. If the force is conservative, then it will not depend on the work done on the path. Just hold the initial final position, hold the displacement and answer. It will only depend on the initial and position. This is the main meaning of this. Okay.

Okay, okay, okay, okay, then it comes to bring some feel of it, right? Without feeling, where is the fun? So, we will bring the feel. So, feel is a simple example of conservative force, which is gravitational force. Gravitational force. We will get more examples in our syllabus, right? Like spring force, for now, you have read spring force, minus kx, right? We had read, f is equal to minus kx. I have made a video of spring force, Newton's laws of motion, 05 physics.

And the third is our electrostatic force. So, you will get electrostatic force in 12th, then we will talk about it here. Today we will talk about gravitational force. Suppose I have a mass M and it is kept on this inclined plane. I want to take mass M from point A to point C. And this distance is L. This angle is theta. I will take from A to C on this path, path number 1.

and then I will take path no. 2 from this path, that is, I will take path no. 2 from A to B and B to C. I will take path no. 2 from both the paths A to C and I will see whether the work done by gravitational force is same on both the paths or not. If the work done by both the paths is same, then gravitational force will become conservative force. And this will happen. So, the gravitational force on this path is mg and displacement is L.

so, what is the angle between force and displacement? see from here, this angle is 90 and this angle is theta so, angle is 90 + theta so, work done is = force * displacement * cos theta so, force is mg displacement is L and angle is 90 + theta see, force is mg and displacement is L so, angle is theta and angle is 90

Cost 90 plus theta, kids, how much is it? Minus sine theta. So, this will become minus MGL sine theta. If you want to take a field, then understand one more field. How much is the component of Mg coming this way? Mg sine theta. This will be known along the incline, Mg sine theta. Now, see, Mg sine theta is force. Displacement L happened in both opposite directions. So, force into displacement Mg.

sin theta into L minus because force of displacement opposite direction. You can understand like this also. MG sin theta is force and displacement is L and in opposite direction so I have given minus sign. Anyways, work done through first path is clear. It will be minus MGL sin theta. Work done by gravitational force. By which force? By gravitational force. Very good. Now let's go to path number 2. Path number 2.

So, on path no. 2, first we have to move from A to B and then from B to C. In path no. 2, work done in path 2, that is, A to B and then from B to C. So, work done in A to B plus work done in B to C because we will add our work scalar quantity.

In AB, look, gravity will not work. Why? When you come in the AB path, the force of gravity is like this and displacement is like this. What will be the angle? 90. Means, when A to B is moving, the angle between force and displacement is 90. Cos 90 is 0. So, in this path, our work is done. 0. Force like this, displacement like this, angle 90. So, in this path, there is no work.

Now, we have to see the work in B to C. So, we have reached B. The force is down, mg, displacement is up. How much will this length be? Children, this is L, this is theta. So, the component of L is here, L cos theta. The component here is L sin theta. So, how much will this length be? L sin theta. So, the force is down, mg, displacement is up, L sin theta. So, the work then will be mg, L sin theta. We have put minus in front because the angle is 180.

See, there will be no work in this path because force is like this, displacement is like this, angle is 90. Whenever 90 degree angle is there in force displacement, then work done is 0. If we think about the work done in this path, then force below is mg and l's component is l sin theta. So, mg below, displacement is l sin theta over angle 180 minus l sin theta.

So, the total work done from the second path is minus MGL sin theta, and from the first path also MGL sin theta. That means work done through first path is equal to work done through second path. This happened because the initial point and final point were from the first path and from the second path. What was it? Same. That means, which is the gravitational force? It is the conservative force. Okay, there are some problems here from the past few days. There is a little disturbing voice. Bear with it. Okay, bear with it a little.

So, you understood that the work done is coming on two paths. If there was another path, then also the work done would have come. So, you can solve big questions. So, I have given you the path of Jai, you don't take the path. You take another path whose displacement is easy and take out the work done there. If the force is like this, then you can consider.

So gravitational force is conservative. Its work done depends on initial position and final position. Do you understand the proof? I have proved it very clearly. That on this side, work done is zero. Then here, mg is below. L sin theta displacement is above. Minus mg L sin theta. And here. Similarly, spring force is conservative. And electrostatic force is conservative. But I want you to get a feel of conservative force. I want to give you a feel of conservative force. What will you give me, sir?

Let's see. Okay, what does the work done of the conservative force depend on? Work done depends on initial position and final position. It only depends on this, initial and final position. Okay. Suppose, children, we take a closed path.

Closed path means we came back from where we started. We went from A to somewhere, then somewhere, then somewhere, then somewhere, then somewhere, then somewhere, then we came back to A. From A we went to B, from B we went to C, from D we went to D, and the curvature path is E here and we came back to A. If we come back from A to A, then the initial and final point will be the same. This is the initial point. If the initial and final position is same and the force that is applied is conservative,

then work done will be zero because conservative force does not depend on path but on initial and final position. Whether we go like this or go like this and come back like this or we stand here because that is also a path to stand. That means work done by conservative force conservative force in a closed path in a closed path is always zero.

If there is a conservative force and if it comes back then the work done by the conservative force will be zero. If there is a close path and if it comes back then the work done is zero because the work done by the conservative force depends on the initial and final position.

and in the close path, this is the initial position and this is the final position so, brother, work done! Zero! No, it is not believed. For example, this is mass M, if I take it up from A to B and then bring it down from B to A, now tell me work done by gravity. For example, height is H, here also H. So, when A to B goes, down is force, mg, and up is displacement, H. So, work done by gravity.

First, tell me the distance. How much will it be? Minus mgh. Because force is below, displacement is above. While returning, this mass m, gravity's force is below. Displacement is also below. Work done by gravity. How much will it be while returning? mgh. Yes or no? Force is also below. Displacement is also below. So, work done is positive. Here, force is below. Displacement is above. Work done is negative. Now, from a to b, b to a, total work done is added. Minus mgh plus mgh. How much did it come? Zero. Because path is closed. Let's go from a to a.

Back to A. A to B, work done. Minus MGH. B to A, MGH is also below, displacement is below. Plus MGH. And added, net work done, zero. Means in closed path, in which path? In closed path, work done of conservative force is always zero. Now we will use this in a very good way. Write this point, note it down. We are going to use this in very good questions. There will be questions coming in future.

If the force is conservative, then work done will only depend on initial and final position. That is, if it comes back after turning, then the initial and final position means displacement zero. Means work done zero. Sir, this always happens. If we come back there, then work done zero happens because we all have said that if the body comes back to its position, then displacement zero and work done zero. Wrong. It is not like that. It is only for conservative force.

It is not necessary that if the body's displacement is zero then the total work done is zero. Write it in the notes. Write it, I will make you believe later. Write it in the notes. It is not necessary, write it in the notes. It is not necessary that if the displacement is zero then the total work done is zero. It is not necessary. It is necessary when the force is conservative. Then this will happen. This will not happen in every type of force. If you go to school and you come back to home then total work done is not zero.

because we didn't talk about force, what force are we talking about? sir, you are confusing me a lot keep watching the video, all the confusion will be cleared, children with true heart and honesty, I have come here to give you all my concepts as much as I have learnt from this industry, I have come here to return that much let's see I am going to prove that even if the displacement is zero, work done is not necessary to be zero, watch carefully assume this is an object of mass m I will take it from A to B

and again I will bring it from B to A. Now let's talk. I have taken it from A to B, where will the force of friction be applied? Will it be applied like this? Yes or no? In the opposite direction. If you pull it here, the friction will be applied in the opposite direction. Suppose this displacement is S. So work done by friction force in the path A to B will be minus Fs, yes or no?

Force is here, displacement is here. Friction's work done will be minus Fs. Then this block reaches here B. Now I have brought it here by pulling it from B to A. Where will friction be applied?

Yes, Friction will oppose the motion and displacement will be here. Yes or No? When you pull it here, friction will be in opposite direction. This time, work done by friction in the path B to A will again be minus Fs because displacement and force are in opposite direction. Yes or No? Total work done by friction

in A to B to A, say 0 or non-zero, say 0 or non-zero, here minus Fs, here minus Fs, it is not equal to 0, it is equal to minus 2 Fs. Did you understand? In closed path, means if displacement body is 0, then it is not necessary that work done is 0. It will depend on which force of work done you are talking about.

Friction force work done in closed path is not zero. I have shown you. When you take friction from A to B, then work done minus Fs. When you take friction from B to A, then work done minus Fs. Total work done in closed path is not equal to zero.

all forces work done in close path means displacement is not zero note this point is it clear? why? because my dear children friction is non conservative force this was concept clear? friction is non conservative what is non conservative force? definition

A force which is not conservative is a non-conservative force. See this is the definition. A force which is not conservative, which is not conservative, that is non-conservative. Its work done does not depend on initial and final point, it depends on the way. Friction's work done depends on the way. You went this way, then you came back this way, it depends on the story. If it depends on initial and final position, then A to A, work done comes to zero, but it does not come.

What is a non-conservative force? Is it clearing? Is something going on? How do I look? You look very ugly, sir. You look very good in the picture. You are studying in the night, in the morning, writing notes. It's not fun. You came to have fun, you are in 11th grade, you will love, you will go out with friends, you will watch movies, you have come to Ant-Man, sir, show me. Okay, let's do one thing. So, what is a non-conservative force?

A force whose work done depends upon path. Work done depends on path. Suppose we have A to B. Suppose this is a table. Let me give you a good example. Here I have a table. Suppose there is a mass on this table.

and I take it from A to B. So, first I took it from the first path and then I took it from this path, from the second path. Tell me, work done by friction, will it be same or different in both the paths? Think before you speak.

It will be different. Here the displacement is so small, friction took 30 days. So work done by friction will be less. Here work done by friction will be more. One will be its work done, then its work done, then its work done. This one and this one are same. Here this one and this one are extra or not? When you go like this, the displacement will be here and friction in opposite direction. When you go like this, the displacement will be here and friction in opposite direction. So minus fs, minus fs, is this extra or not? Rest this one will be equal to this.

means work done through first path is not equal to work done through second path. Work done depends on path. It does not depend on initial or final point. It depends on path. If you go through long path then friction will be more. The whole path is getting friction, work done is more. Second point, in closed path, work done will not be equal to zero.

As I have shown you, A goes from A to B and from B to A comes back. But work done total was not coming to zero. So, the simple definition is that the force which is not conservative is the force which is non-conservative. Simple. The force which is not conservative is non-conservative.

So, remember the conservative force, whose work done depends on initial and final point, whose work done does not depend on the path, and whose work done is zero in the closed path. Why zero in the closed path? Because it depends on initial and final point. What will happen in the closed path? Same. The example of non-conservative force, the most won example is frictional force. So, remember that if the displacement is zero, then the work done is not necessary. Where is this thing necessary? When the force is applied,

How? It is conservative. Non-conservative is not like that. Non-conservative work done depends on the path. Okay? If you go here and come back, then work done will not be zero. Work done will be done on this side also. Okay, I think you have understood some concepts. Okay sir, we have understood a little bit that how was our gravitational force? Conservative. And how was our frictional force? Non-conservative. We have understood the difference also, right? If you say, I will write it down. Okay, come here and write it on the side once. Conservative force. Conservative.

Vative force and non conservative force. Ok, let's write it again to remember. So in conservative force, work done through first path is equal to work done through second path. And here work done through first path is not equal to work done through second path. Here work done does not depend on path. That's why work done on both the paths is same. And here

path pe depend karta hai, raste pe depend karta hai. Doosra point ki agar closed path hui, agar closed path hui toh jaha te chale wapas wahi aaye, work done zero. Aur yaha pe work done will be not equal to zero in closed path. Yaha work done sirf kis pe depend karta hai, conservative force ka work done sirf kis pe depend karta hai, initial position and final.

And here the work then depends on what? The path. That's all. Is it clear? The thing which is potential energy is defined as only for the forces. Have you ever heard of the potential energy of friction? No. Have you heard of the potential energy of gravitation? Yes. Have you heard of the potential energy of spring? Yes. Have you heard of the potential energy of electrostatic? Yes. Yes. That means all the conservative forces give birth to potential energy.

Or maybe it takes birth from it. But for non-conservative force, any potential, friction potential energy never descend. Gravitational potential energy, yes. Spring potential energy, yes. Electrostatic potential energy, yes. Clear? Now look at some good questions.

How to find out sir, that given force is conservative or not? Like I will give you a simple example, if question comes in JEE, in mains, there is a question of 3 number, no 4 number, I am so sorry, in mains there is a question of 4 number, if F is equals to XI cap plus YJ cap is conservative or non-conservative?

or 4 options are given, conservative or non-conservative and it will say depends upon value of x, depends upon value of y, 4 options will be made. First option is conservative, second option is not, third option depends upon x, depends upon x and fourth option is given to you, depends upon both x and y, depends upon x and y. Now tell us how to do this, tell the concept to the people who know it, how to do this?

Is this force conservative or non-conservative? Will it depend on x or on x and y? Didn't understand? Write down. Method. If any force is conservative, then first convert that force in this form. fxy i cap, fy j cap, fz k cap. Write it like this first. Now check. Condition 1.

differentiation of f with respect to y is equals to differentiation of f with respect to x. Second condition differentiation of f with respect to z is equals to differentiation of f with respect to x. Third condition. What am I doing? Pay attention this time. I will compare y and z. Pay attention. Differentiation of f

with respect to Z is equal to differentiation of FZ with respect to Y. You might have understood what I have done. The differentiation of X with respect to Y, the differentiation of the force of Y with respect to X. The differentiation of X with respect to Z is equal to the differentiation of Z with respect to Y. The differentiation of the force of Y with respect to Z is equal to the differentiation of the force of Z with respect to Y. If these three conditions, not one,

If all three conditions are satisfied then only given force will be conservative. Now why is it written del and not d? Partial differentiation. Here we have to differentiate force of x with respect to y. Here we have to differentiate force of y with respect to x. If both are equal then check this. Then only force will be conservative.

If all these three conditions are satisfied, then given force will be conservative. Note this first. Note this, then only I can ask you questions. Note this. The differentiation of x with respect to y is equal to the force of y with respect to x. This is very important. Now you don't understand the importance of this. These are good questions, but they are also very difficult. Clear? Did you write it? Let's check. Let's check whether this condition is applied in this question or not.

Here, this is f , this is f . Yes or no? This is f , this is f . And I think f is 0 because there is no term of k. Let's check the first condition. d f with respect to y, d f with respect to x. What is the value of f ? So, we have to differentiate x with respect to y. So, how will y see x? Constant. Constant differentiation? 0.

What is the value of f ? y. We have to differentiate y with respect to x. So, how will x look like y? Constant. So, 0. Yes, both are equal. Okay. Condition number 2. Differentiation of y with respect to z. Differentiation of f with respect to y. So, what is the force of y? y. And we have to differentiate y with respect to z. So, how will z look like y? Constant. Constant definition? 0. Brother, what is y for z? Constant.

For z, z will be a variable, z will be a square variable. What is yx for z? It is a constant. Differentiation of force in the z direction, the differentiation of 0 in any respect is 0. Third condition, differentiation of f with respect to z is equal to differentiation of f with respect to x. What is the force of the x direction? x. The differentiation of x is z. How will z see x? The difference of constant is 0.

z direction is 0, definition of 0 is 0 all the three conditions are satisfied, this is equal to this, this is equal to this, this is equal to this hence the given force is conservative the given force is conservative no attention, the given force is clear, let's see the next example it is not always necessary that 0 is 0, pay attention to the examples see the next example if the given force is, again you have to tell conservative or conservative

If the given force is 3YI cap plus 3XJ cap, then find the conservative and non-conservative, depends upon X, depends upon X and Y. Condition 1, differentiation of force in X direction upon del Y, differentiation of force in Y direction with respect to X. Now see, this is Fx. Why brother, sir, here Y is written, see this, I cap.

i-cap means in which direction is this force? x j-cap means in which direction is this force? y don't get confused by this that this is y and this is y i-cap tells the direction of this force in which direction is this vector? x means this is fx and fz is 0 are you getting confused? i-cap means in which direction is this force? x so how much is fx? 3y the differentiation of 3y with respect to y, how much will it be? 3

How much is f ? 3x, the difference of 3x with respect to x will be 3, oh, it is coming equally. Second condition, dfx/del z, this is called del, del fz/del x, I was saying d for a long time, so don't judge, it is called del, partial differentiation, I was saying it quickly. So, del fx, how much is it? 3y with respect to z, so how is y with respect to z? It is constant, so it is 0. del fz/del x, tell me, is it correct or not?

how much is f ? 3y, in which respect we differentiate 3y? z, for z, it is 3y, constant is 0 now, del fz, what is the value of fz? 0 with respect to f, so the definition of 0 is 0, so this condition is satisfied third condition, del fy with respect to del z, del fz with respect to del y, let's check y direction force is 3x, its definition in respect to z, how will z see 3x? constant, its definition is 0, how much is z? 0

Bro, Z has no definition. Three conditions satisfied the given forces, a conservative force. What did you understand? Did you enjoy it? Did you understand? Good? Very good?

Let's check the question here. 3xicap + 4yjcap. Let's change it. 3yicap + 4yjcap. Let's check the conservative or non-conservative. The first condition is del fx/del y = del fy/del x.

The force of x direction is this. 3y is differentiated by y. 3 comes. The force of y direction is this. In which respect did you differentiate this? For x. You could have done anything.

the force of y direction is this because j is written and differentiate this in respect to x so the difference of 4x is 3/4 which is not equal to non conservative thinking you don't need to think now see how much more I can turn this question around how much more I can turn this question around what will I turn around? I said a force

F = I cap + 3Y j cap acts on a body and follows the path as shown. Calculate the net work done. So this is a path, this is a point O, 0, 0. We went from here to here.

at point A, its coordinate is then we went ahead at point B, its coordinate is then we came at point C, its coordinate is and then we came back at O so we went from O to A, A to B, B to C, C to O so we were asked, "work done in the path?"

O to A to B to C to O is equals to how much by this force. And the options are given to you over here. 3A minus 3A, 0D, 1 by 3A.

What are the four? Think and tell, pause and think. Pause, think and answer. What will happen? Tell me. First check if this is a conservative or not. Because how is this path? Closed.

So, first check whether it is a conservative force or not because there is an option 0 also. Let's check. Here, this will be fx and this will be fy. The value of fx is 1. The value of fy is 3y. Condition number 1. Del fx by del y is equal to del fy upon del x. So, the value of fx is 1. The differentiation of 1 will come in any respect. 0 will come. 1 is constant.

How much is del Fy? 3y. Definition of 3y in respect to x is 0. First condition is satisfied. Let's check the second condition. What was the second? Del Fy divided by del z is equal to del Fz divided by del z divided by y. So, the value of Fy is 3y. But you will differentiate 3y in respect to z.

So, for z, 3y is constant, definition is 0. And fz value is not seen here, definition of 0 is 0 only. So, this is also correct. Third condition, del fx with respect to del z is equal to del fz with respect to del x. fx value is 1, definition of constant is 0. fz value is 0, definition of 0 is 0.

Three conditions satisfied. Brother, the given force was conservative. You were made a big move. The given force was conservative. This is a closed path. The work done will be zero. Note, the work done of the conservative force in a closed path is zero. Because the work done of the conservative force depends on the initial and final position. Where the initial and final position were the same, so the work done will be zero.

So, there was a big question, it was going to take time, integrate, differentiation, what all could we do? There is variable force. Generally, the kid will see this and think that there is variable force, we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to add f , we have to

Whatever it is, I have told you everything and I have told you that potential energy is conservatively defined. Remember this. We will use this in the future. One more question. If F is equal to X square I cap plus Y J cap acts on a body and it is taken from A to B as shown which is correct? So, I am making a question.

Here is point A, here is point B and I am taking this force from A to B like this from first path and from A to B like this from second path. So, four options are there, the work done by this force. Which of the following is correct? The work done by this force is.

First path is equal to second path. Option B. First path is not equal to second one. Option C. First path is greater than second path. Option D. Second path is greater than first. So, it is possible that two are correct. Because if this is correct, then one of these two will be correct. If it is not equal, then one will be greater. And it is possible that only one is correct.

So, we have to check whether it is a conservative force or not, will it depend on the path or not. So, this is f , this is f , now we have to find out the first condition, del f = del f = del x. So, f is x^2, in respect of y, it is constant, in respect of y, x^2 is constant, differentiation is 0.

Fy value is y and in respect of x, what is y? Constant value is 0. Second, del Fy divided by del z is equal to del Fz divided by del y. So, what is the value of del Fy? y. In respect of z, what is y? Constant value is 0. What is the value of Fz? 0. The definition of 0 is 0. If you see the third one, then 0 will come and all three conditions are equal. Meaning, given force was again conservative.

and the work done of conservative force does not depend on the path, that is, the work done of the first path and the second path is more. So, guys, this was the whole story of the conservative and non-conservative force. The next video will be either on potential energy or work energy theorem. Let's see which topic is in more sequence. Keep reading. All the very best.