Test Papers – ICSE – Class – X
Physics, Kinetic Energy and Work
Work, power and energy.
Now there should be no disturbance and no one talking.
WPE, okay. Till now we were solving physics problem with force analysis. First we
studied Kinematics and then we studied Newton’s Law of Motion on frictions. What
we were doing, we used to draw free body diagram and then we use to see forces
and then which way the resultant force is generated, there we assumed
acceleration. And then used equation of f is equal to ma motion in various situations,
okay. This was something which we have already done.
Now onwards we will see the physics problems can also be analysed by using the
idea of energy. Now, same problems of physics which you have studied till now in
NLM and kinematics, all those problems will be solved by energy analysis. But we will
learn this slowly, slowly. If we study everything philosophically, you won’t be able to
understand. We will talk to the point, write the heading – Kinetic Energy.
Kinetic Energy, energy due to the motion of the particle is known as its kinetic
energy. Energy due to motion of the particle is known as the kinetic energy. Kinetic
energy is written as half m v square, we can also write like that. What is P – Linear
momentum. So the same kinetic energy formula can also be written as P square by
2m. Multiply m on both the sides, there it will come as m square and P square. Then
it will become P square, okay. How this is done? Kinetic energy is all type of scalar
quantities, it has no directions, obviously if it is scalar quantity it should not have any
particular direction. Unit of energy is Joule represented by capital J. 1 J is equal to
Newton into meter, okay. Now, see this is all about kinetic energy, 99% will be done
with this particular idea. You should remember it, anyway you will remember it
automatically. If anything, now what examiner will do? Now, kinetic energy is there,
when he will discuss kinetic energy, he will ask questions whatever you have learned
related to velocity. Till now, we had studied in kinematic many things related to
speed and velocity. Many ideas related to speed apart from directions, whatever
ideas you have discussed in terms of magnitude, the examiner will use that and ask
questions on kinetic energy.
First example, find the kinetic energy of a particle. If mass is in kg and velocity is
meter per second then your kinetic energy will be in Joule, be careful with that. If
mass is not in kg, then we have to convert it into kg, we should be very careful about
unit. If mass is in kg and velocity is in meter per second, then the kinetic energy will
be in Joule. Find your kinetic energy. I think, we can go through half m into V square.
V square can be written as V dot V, so effectively, what I am doing? I am making the
dot product of V, velocity vector with itself. Now, 14 Joule is the kinetic energy,
everyone is fine, done.
Then next question, three particles are moving in a straight line. Three particles are
moving in straight line. Their x co-ordinates varies with time, where x co-ordinates
varies with time, then write the order of their kinetic energy, write the order of their
kinetic energy, where t is equal to t naught. T is equal to t naught.
Three particles of identical masses, this is what I said. I mentioned that the masses
are same? Masses are same. Did I say identical particles? I had not said that it is
identical? Three identical particles are moving in straight line and their position
varies with time according to this graphs, these graphs, this is 1. See, here I want to
recall a small idea. If position time graph is given, so how we were commenting on
the velocity? Slope of the tangent. So, I have to write velocity for first particle, write
velocity for second and also have to write velocity for third. So, we can see clearly,
the slope of the tangent for 1 is highest, then for second and then for third. Whose
slope is highest, its velocity will also be highest. I can say, V1 is greater than V2 is
greater than V3, so kinetic energy is greater than 1, 2, and 3. Done, any doubt, next
question.
Draw the graph between kinetic energy and velocity and kinetic energy into square
of velocity. Class, we know the kinetic energy is half m v square and if I draw the
between kinetic energy and velocity, so, we are making graph of power 1 and power
2. How will the graph be – Parabolic. So when velocity is zero so kinetic energy is
zero, so it will be upward opening parabola, you remember, we had discussed in the
graph. And if we are making graph with v square, then it will be a graph of power 1
and power 1. V square will be treated as a quantity, what type of graph it will be? It
will be a straight line, done. If velocity is negative and speed is negative, you are
telling the truth, it can be done this side also. Kinetic energy will be positive, velocity
can be negative also, okay. But, generally, here kinetic energy, suppose if we are
discussing this for speed. So in the speed graph we will ignore this side, because,
obviously speed will never be negative. For most of the cases they will ask you
kinetic energy versus speed graph.
Physics, News Law of Motion & Friction
Okay, tell me if you have any doubt about theory of friction, one is static and there is kinetic, that’s it
the end of theory. The value of static is zero, between fx maximum it can be anything, the value of
kinetic is fixed, uk into n. The value of fx is from zero to fx maximum and it can be uk into n. Now the
biggest problem in friction is that friction requires something very rare and that’s the application. I
never understood friction when I would study it. So it will take time to understand, no problem.
First example, the first thing is that the common error that all of you are doing is that you have not
forgotten what you have been taught by some people in the lower classes and which has had a bad
effect on your mind, and to erase that is difficult. If I say that friction will be opposite, will be
opposite, will be opposite, you will have to stop saying this. If this is going forward then friction will
follow. This is all nonsense, this is all nonsense. You cannot say where the friction will take place. If
you want to understand friction I will show you one technique, if you have a slight knowledge about
relative motion then you will understand, friction is based on relative motion. There are two
surfaces, always discuss one surface with respect to another surface. Suppose I stop one, now if this
is stopped then with respect to this and if it goes ahead then friction will follow. If it goes behind
then friction will be ahead. But the word ‘relative’ will be applied, with respect to. You understand?
If you look at one surface with respect to another surface then you will be able to predict easily the
direction of friction. And if you just check in general then it will not be possible.
Now I will show you, write down predict the direction of friction in given cases, predict the direction
of friction in given cases. These are two blocks which are at rest on rough surfaces. You are pulling
these in this way, you are pulling one block here and one block here. Now tell me where will friction
be applied?
Opposite.
Now when you say opposite, you are getting ready to make a mistake. Don’t say opposite, because if
you say opposite, the answer here will be correct, but in the next question we will be confused.
Don’t say opposite, let’s plan, how? There are two surfaces, one is the block and one is the ground.
Let’s discuss block with respect to ground. Now the ground is at a standstill already. If the surface
below is at rest then this funda of opposite will work. And when you are taught friction in the 9th
standard you are given these easy, easy cases to solve. So the teacher to avoid problems, says that
use ‘opposite’ and be happy. And that becomes a major problem for us in the XI. I feel sad. So we
will think of a new way even though it is an ordinary example.
With respect to the ground, the block that is here is trying to move ahead, right. With respect to
ground the tendency of motion of the block is to the right, tendency of motion is to the right so
where will the friction be, it will be behind. Now don’t say ‘opposite’, we will throw the word
‘opposite’ out of our dictionary for some time. Now with respect to ground, the block has the
tendency to move left, so friction will act in right.
Next example, the question is the same, you have to predict the direction of friction. There are two
surfaces, block and the truck. Let us discuss with respect to truck. If I am discussing block with
respect to truck then should I apply pseudo here, yes or no. Then with respect to the truck, pseudo is
pushing this block behind that is tendency of motion is towards left. So friction will act towards right,
okay, done.
Next question, write this down. B block is kept on top of A block, we are pulling A block, and B is
being pulled along with A. Now we have to predict friction on B and friction on A. See I will teach
you, I will teach you and then ask you, don’t worry. See A or B, see any one of them with respect to
the other. Let’s see it with respect to B. If I stop B, then the force will try to shift A from under B to
the right, yes or no. If I look at it with respect to B, then this force will try to shift the block to the
right. So B will use friction to stop this, where will it apply friction, that means where will friction on
A be? Left, yes or no. On what will the reaction be? B, where, to the right. This is the easy method
and logically also if B is travelling with A, I am pulling A, but who is pulling B, which force is pulling B
to the right. There can be friction so where will the friction on B be.
Newtons Law of Motion & Friction – Pseudo forces
Pseudo Force.
Relax, settle down.
What is the meaning of Pseudo?
False.
Which is not real. Do you know the meaning of Law?
L-a-w.
Is there any other Law that you know of? There is only type of Law, according to me. What is the
meaning of Law?
Justice (Kanoon).
Justice which has a long arm.
It is blindfolded.
That is not necessary it depends on the country, in our country it is blindfolded. But my meaning of
law is something which is applicable to all, something which is universally applicable. The general
meaning of the word law is it is something that is valid over everyone equally, which is not at all like
that here. It is different for the common man and different for politicians.
So when we say Newton’s Law of Motion, so effectively when the word ‘law ‘ is used a special
condition is assigned to that that it should be applicable in all scenarios which does not happen in
real life. So ideally speaking Newton’s Laws are not true or completely laws which you can apply in
all situations. Better to say then Newton’s Definition of or Newton’s three different statements.
Newton was a very famous person, he had a lot of respect and value, he was a famous scientist and
because of that respect we still call it Newton’s Law. You can challenge the validity, people have
done it earlier so you don’t have to take that tension.
Newton’s Laws of Motion are not valid in a non inertial frame of reference, okay. So first let’s take a
look at what is frame of reference.
The Pseudo Force that we are going to study about, to find out about pseudo force there are a few
small steps in between that we have to look at. So first we take a look at frame of reference.
Anything which is taken as a reference, anything which is taken as a reference to discuss motion of
an object is called frame of reference. If there is any object that you are considering as reference to
discuss the motion of an object, that will be considered as frame of reference. It can be a car, it can
be a jeep, it can be you yourself, or it could be a point, anything can be taken as a reference. If you
are explaining about the motion of an object that is with respect to you or according to you, as a
frame of reference. If I am in a moving car, and if I am explaining about the motion of an object
while I am in the moving car so that will become, the car will become my frame of reference. So
anything which is used to discuss the motion of any object will be known as the frame of reference,
anything.
We have divided frame of references into two broad categories. One is Inertial Frame and the
second is Non-inertial Frame of Reference. We will see them one by one.
Inertial Frame of Reference – there is no real inertial frame that exists in the world.
Next point, under Newtonian physics we have considered ‘earth’ as inertial frame. That means in
Newtonian physics or phenomena of physics in day to day life we have considered earth as an
inertial frame. So now with respect to earth we will define which frame we can call as inertial and
which frame we can call as non-inertial, okay.
So write the definition of Inertial Frame, any frame of reference, any frame of reference which is at
rest, any frame of reference which is at rest or moving with constant velocity, moving with constant
velocity, constant velocity with respect to earth, with respect to earth will be taken as, will be taken
as inertial frame of reference, will be taken as inertial frame of reference. On the other hand,
anything which is accelerating with respect to earth.
Physics 04, Problems based on Constrained Relations
Motion on inclined plane. Motion on inclined plane. What is inclined plane? See, the
triangular prism structure, this is called inclined plane. And if we see from this side, what we
can see is, this one, the cross section view of inclined plane sides, okay. This is the base, this
is the height and this particular angle, which is most important. It is known as angle of
inclination. This is the angle we are talking about. So, this kind of structure will be
represented like that. We will discuss about motion of block. Actually, the block is kept here
and the block will slip along the inclined plane. This is the structure which we will get. This is
the structure we will get always in books, text books, tests. So, this is the story of inclined
plane. Sometimes, we fix this on horizontal surface on this inclined plane, we make this type
of structure. This represents the surface. So, this inclined plane is placed on the surface,
okay. Any situation based on any topic of Newton’s laws of motions, its basic analysis starts
from, in the first step we will draw a free body diagram. What is our planning? WTN, so, let’s
say mass of the block is m. So, on this block, mg, downward force will be applied, yes or no.
And which other force will be applied. T, T is there and, where will the normal force be
applied. I told we have to apply normal on the block. Keep your hand on the other surface
and push it. Where will it get pushed? Perpendicular, away. So there will be normal on the
block. So, there are two forces presently acting on the block, one is the weight and the other
one is the normal force. This is the normal on the block due to wedge, got my point. Wedge
is the triangular plane or inclined plane. Call it wedge or triangular plane or triangular
wedge, is one and the same thing, done. And we can see that, we can see that this block can
move along this direction. Otherwise the inclined plane will come down or it may go
upwards, depending upon the other forces available in the systems, okay. First of all we will
see what happens. First I will tell you one thing which will almost come into use of every
problem of inclined plane. Listen carefully, what I did here is, I drew a line here like this. This
angle is 90 degree, sorry, this angle is theta, this angle is 90 degree, so what this angle will
be? It will be 90 minus theta, so, this angle is theta, yes or no. if this angle is theta, can I
make two components of this weight. One is mg cos theta and other one mg sin theta. What
we will take from the vector, only components, mg cos theta and mg sin theta, done. Now,
see for yourself, if this can move in this direction then this force should be balanced or not.
In that case, one thing is very much clear that Normal is equal to mg cos theta, okay and
which force is unbalanced, mg sin theta, so the resultant force on this side is mg sin theta.
So, that will provide some a acceleration to the block, yes or no. We will make FBD, we will
draw acceleration and we will write resultant force is equal to mass into acceleration. So,
what is the final acceleration? It is g sin theta. And we have to make a component, this is a
bright idea. It will be more useful to you in future that is why, keep this as a standard in your
mind. If a block, is going along the inclined plane is going up or down, we will comprehend it
with one force that will be mg. Remember mgcos theta and mg sin theta. Use your head and
write straight away mg cos theta and mg sin theta. If this theta is given then then this will be
mg cos theta and this will be mg sin theta. Suppose the examiner uses his head and gives
you this theta then what will happen. Cos will become sin and sin will become cos. So just
remember this FBD always….okay, mg cos theta mg sin theta. N is equal to mg cos theta is
always valid. But acceleration g sin theta (6:53) but there are only two forces, WTN and
Normal. (07:03) constant acceleration g sin theta. But if there is some force along with this
so definitely g sin theta (07:18). But the motive behind giving you this example are these two
things which you should stick it inside your mind mg cos theta and mg sin theta (7:29-7:45).
Find the acceleration of the block? Find the acceleration of the block? Done, there is one
stationary triangular wedge, on that we placed a pulley and connected two blocks with it
with a string. We are releasing the system from rest, you have to calculate the acceleration
of the block. What will be our first step? Free body diagram, let’s see if everybody is
connected correctly in first step, 60, T after that T now mg sin theta. How much is it? 60, mg
cos
Physics 03, Pulley Block Problems
Okay, we have the questions, I will tell you the answers. Have you reviewed the lectures?
Are you telling the truth? Kids, make a permanent habit of this, such small things are very
useful.
First part was, when the man is at rest means T must be equal to Mg. In fact, we will make
free body diagram. This year man and string diagram will be used frequently. Many
questions are solved by this free body diagrams. T and Mg. See, stand in the place of this
man. Suppose you have to hang to a string, what will you do? You will pull string
downwards, right. You will pull the string downwards, so the string will pull you upwards.
Suppose we see tension force on the string, then it will be downwards and if we see tension
force on man, it will be upwards. So, keep this in mind it is always true. And if the man is at
rest than must be T equal to Mg.
Second case, if man is moving upwards with constant speed, constant velocity means
acceleration is zero. So, what will be the answer of part b? T is equal to Mg. Has everybody
done this question?
Third, moving down with constant speed means, down with constant speed T is equal to Mg.
Moving upwards with constant acceleration means T minus Mg is equal to Ma, yes or no. So,
effectively T is M into g plus a. Man is moving down with constant acceleration, so, it will
become Mg minus T equal Ma. So T will be M into g minus a, okay. How many of you have
done it correctly, everyone, okay?
Last example, Pulley block. This is a popular variety, it will come of use many times, see it
carefully. Find the acceleration of the blocks. Let’s see the first part of the question. Find the
acceleration of the block. Okay, calculate. Okay, then what should our first step be, kids?
Free body diagram. Okay, let’s make our first step clear. 100 Newton, Tension, Tension 50
Newton. Is it clear, kids? Next, step will be to assign acceleration, so, 10kg will come down
and 5kg will go up. Done, any doubts, okay. Let’s write the resultant force on 10kg and that
should be mass into acceleration, any doubt. For 5kg this equation will be. Now we have two
equations in two variables. Add them, how much, 50 is equal to 15a. a will be 50 by 15, 10 by
3, done. Everything is clear, each and everyone. Now, we will proceed further, each and
every students except new students, other students answer should be correct, done. Now,
we will take part b of this question. Find the force applied by string, force applied by string
on the pulley, string on the pulley. Students, see here, I will do it. We will make free body
diagram of this pulley. We will make free body diagram of everything. Now, the pulley is
massless. Stop writing, listen carefully, other examples you have to do. I will just do this one.
This is a pulley, FBD will be made of this. Now, pulley is mass less, so there is no role of Mg.
what is our clarity WTN. There is no W, if pulley had a weight, we would have represented
that also. Now, tension, I will take these strings. Now, if we see carefully, that this string is
pulling the pulley from both the sides, here also T and there also T. It is a rule that, if a string
passes over the pulley, that string will always pull the pulley with the help of two tension
force. It is not possible that there is only one tension available and the other tension is not
available. So, we have to make this TNT, the string which is moving over the pulley, that
string will always apply two tension forces and both of them will be of any angle, it can be
parallel or 90 degree, it can be anything. It depends on the situation, got my point. The string
which passes over the pulley will apply tension force in two directions, got my point. Two
directions means there will be two different tension forces on the pulley due to strings.
Now, as it is on same direction then both the force vector will be added and if it was in 90
degree, then we would have added it in vector way, root of a square plus b. So, in that
scenario, it is two T down. Now, listen carefully, the examiner will ask it two three questions,
listen carefully. Now, this string is there, if we see ideally, this string is holding the pulley.
This can be a string, rod or anything else. If I make a complete free body diagram of the
pulley, so will I get one more force here, yes or no, T dash. So this is the complete free body
diagram. Who applied this T dash, this one string and who applied this T and T, these both
strings. And see, we can see that the pulley is at rest, if anything is at rest, what will be its
total force, zero. So, I can say that T dash is equal to 2T and from where I can get the value
of T, from here. But what was important for me, to know that the pulley which passes over
the pulley, that pulley always has tension force in two directions or tension force is applied
in two ways. Done, everyone, any doubts, anyone. Next question. Copy it down. Pulley is at
rest, so the total force is zero then the upper force is equal to the force below. Which one,
these two, they are only one string. Mass less in extensible string, the tension in full string
will be the same. See here, this is 10 and 50, because of this both, effectively, this T will be.
Wait, I will show a magic, listen carefully. We will calculate here. 50 plus 5 into a, 50 plus 5
into 10 by 3. So, effectively, what will happen 200. Tension is 200 by 3. Now, understand this
take the 10kg block, 100 down and 200 by 3 is up, so, what will be the resultant force of
this? 100 minus 200 by 3, how much it is, 100 by 3, net force divided by its mass, what will
you get acceleration, okay. Now, take 5kg block, 200 by 3, 50, resultant force will come up,
how much, 200 by 3 minus 50. How much? 50 by 3 divided by its mass, what is the
acceleration 10 by 3. So, what is the condition, the condition is that, both the acceleration
should be same. Now see this, in this 100 is applied and on this 50 is applied. By seeing 100
and 500, the tension of string selects one unique value, that unique value on both of these
blocks will generates that much resultant force, that makes the acceleration of both the
blocks same. So, tension will be same because there is only one string there will be no
individual impact of 10kg and 50kg, it makes a net effect, what happens with the net effect,
we will select a middle tension, that is 200 by 3, which is 66 point 7. We selected a unique
value of the tension which was greater than 100 and smaller than 50, by which the
acceleration of both will effectively be same. So, there is no role of tension if mass is
separate. Tension selects its unique value. And secondly we had made a rule, that the
tension of one in- extensible mass less string will always be the same. Even if you connect
any block or you don’t connect, it will not make any difference. Okay, next question,
understood kids, I didn’t go fast, sure, everyone.
Okay, find the acceleration of the block and tension force in A, B string. Find the acceleration
of the block and tension of force in A, B string. You have not placed blocks, but still the
tension will be the same because that is the property of the massless inextensible string. 6
kg block and 60 Newton force, they are two different things. Okay, then listen very carefully.
We will solve two problems then we will compare both of them. Then we will come to know,
what is the difference between them? Listen very carefully, I had told you this thing in the
class yesterday. In any string, information means you are pulling this end of string
downwards with 60 Newton. That means tension of this string is, 60 Newton. So, in this full
string how much tension force exists, 60 Newton. This is what we had discussed yesterday.
Now, we will make FBD of 4kg, 40 and tension, how much, 60 Newton. How many of you
knew that tension will be 60 Newton? Has the force not increased? Kids, grow up, keep
some basics things with you. See, in the last lecture also, I had made like this circle and star
and told you this is a special thing, right. Okay, listen, if you see resultant force on 4kg, 60
minus 40 is equal to 4a, so, 20 is equal to 4a. So, a is equal to 5 meter per second square. a is
equal to 5 meter per second square and tension is 60Newton. But, I asked you one more
question, tension of A, B strings. If I want know the tension of A, B, then I will have to make
free body diagram of pulley. So, from here also 60 Newton and there also 60 Newton.
