Physics X Notes

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MEASUREMENT Meter

Meter is the unit of length in S.I. System.Meter is defined as "The distance between the tw o marks on a Platinum-Iridium

bar kept at 0 OC in the Internationa l Bureau of Weig ht and Measures in Paris." One meter = 100 cmOne meter = 1000 mm

Kilogram Kilogram is the unit of mass in S.I. System."K ilogram is defined as the mass of a platinum cylinder placed in the

Internation al Bureau of W eight and Measures in Paris." One kilogram = 1000gram Second

Second is the unit of time in S.I. System.A second is defined in terms o f the time period of Cs-133 atoms.i.e." one second is equal to 9,192,631,770 periods of vibration s of Cs-133

atoms." 60 seconds = one minute3600 seconds = one hour

Least Count Minimum m easurement that can be made by a measuring device is known as "

LEAST COUNT'. Least count (vernier callipers) = minimum measurement on main scale / total number of

divisions on vernier scale .

Least count (screw gauge) = minimum measurement on main scale / total number of divisions on circular scale

Smaller is the magnitude of least count of a measuring instrument, more precise themeasuring instrument is.

A measuring instrument can not measure any thing whose dimensions are less than themagnitude of least count.

Least Count of Vernier Callipers = 0.01 cmLeast Count of Micrometer Screw gauge = 0.001 cm

Zero Error It is a defect in a measuring device (Vernier Callipers & Screw Gauge).

When jaws of a Vernier Callipers or Screw Gauge are closed, zero of main scale mustcoincide with the zero of vernier scale or circular scale in case of screw gauge.

If they do not coincide then it is said that a zero error is present in the instrument. Types Of Zero Error

Zero error may be positive or negative. A positive zero error in the instrument shows a larger measurement than the

actual measurement.In order to g et exact measurement, positive zero error is subtracted from the

total reading. .



A negative zero error in the instrument shows a smaller measurement than theactual measurement.

In order to g et exact measurement, negative zero error is added to the totalreading.

Pitch "P erpendicular distance betw een two consecutive threads

of the screw gauge or spherometer is called P ITCH." Pitch = Distance traveled on main scale / total number of rotations

Error An error is defined as

"The difference betw een the measured value and actual value."

If two persons use the same instrument for measurement for finding the samemeasurement, it is not essential that they may get the same results. There may arise adifference between their measurements. This difference is referred to as an "ERROR".

Types Of Error Errors can be divided into three categories:(1) Personal Error(2) Systematic Error(3) Random Error

Personal Error An error comes into play because of faulty procedure adopted by the observer is called

"PERSONAL ERROR".Personal error comes into existence due to making an error in reading a scale. It is due to

faulty procedure adopted by the person making measurement. Systematic Error

The type of error arises due to defect in the measuring device is known as "SYSTEMATICERROR".

Generally it is called "ZERO ERROR". It may be positive or negative error. Systematic errorcan be removed by correcting measurement device.

Random Error The error produced due to sudden change in experimental conditions is called "RANDOM

ERROR".For example:Sudden change in temperature, change in humidity, fluctuation in potential difference

(voltage).It is an accidental error and is beyond the control of the person making measurement.




SCALARS & VECTORS SCALAR QUANTITIES Physical quantities w hich can completely be specified by a number (magnitude)

having an appropriate unit are know n as "SCALAR QUANTI TIES". Scalar quantities do not need direction for their description.Scalar quantities are comparable only when they have the same physical dimensions.Two or more than two scalar quantities measured in the same system of units are equalif they have the same magnitude and sign.Scalar quantities are denoted by letters in ordinary type.Scalar quantities are added, subtracted, multiplied or divided by the simple rules of algebra.

EXAMPLES

Work, energy, electric flux, volume, refractive index, time, speed, electric potential,potential difference, viscosity, density, power, mass, distance, temperature, electriccharge, electric flux etc.

VECTORSQUANTITIES

Physical quantities having both magnitude and d irectionwith appropriate unit are known as "VECTOR QUANTITI ES".

We can't specify a vector quantity without mention of direction. Vector quantities are expressed by using bold letters with arrow sign such

as:vector quantities can not be added, subtracted, multiplied or divided by the simple rulesof algebra.Vector quantities added, subtracted, multiplied or divided by the rules of trigonometryand geometry.

EXAMPLES Velocity, electric field intensity, acceleration, force, momentum, torque, displacement,electric current, weight, angular momentum etc. REPRESENTATION OF

VECTORS On paper vector quantities are represented by a straight line with arrow head pointingthe direction of vector or terminal point of vector.

A vector quantity is first transformed into a suitable scale and then a line is drawn withthe help of the Scale chosen in the given direction.




ADDITION OF VECTORS PARALLELOGRAM LAWOF VECTOR ADDITI ON

According to the parallelogram law of vector addition: "I f two vector quantities are represented by two ad jacent sides or a

parallelogramthen the diagonal of parallelogram w ill be equal to the resultant of these two

vectors." EXPLANATION

Consider two vectors . Let the vectors have the following orientation

parallelogram of these vectors is :

According to parallelogram law:

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MAGNITUDE OFRESULTANT VECTOR

Magnitude of resultant vector can be determined by using either sine law or cosine law.

RESOLUTION OF VECTOR DEFINITION

The process of splitting a vector into various parts or components is called "RESOLUTIONOF VECTOR" These parts of a vector may act in different directions and are called "components of vector". We can resolve a vector into a number of components .Generally there are threecomponents of vector viz.Component along X-axis called x-component Component along Y-axis called Y-component Component along Z-axis called Z-component

Here we will discuss only two components x-component & Y-component which areperpendicular to each other. These components are called rectangular components of vector. METHOD OF RESOLVIN G

A VECTOR I NTORECTANGULARCOMPONENTS

Consider a vector acting at a point making an angle θ with positive X-axis. Vectoris

represented by a line OA. From point A draw a perpendicular AB on X-axis. Suppose OBand BArepresents two vectors. Vector OA is parallel to X-axis and vector BA is parallel to Y-axis.Magnitudes of these vectors are V x and V y respectively. By the method of head to tail we

notice that the sum of these vectors is equal to vector .Thus V x and V y are the

rectangular components of vector .



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Vx = H orizo ntal com po nen t o f .

Vy = Vertical component of .

MAGNITUDE OFHORIZONTALCOMPONENT

Consider right angled triangle ΔΟΑΒ

MAGNITUDE OFVERTICAL COMPONENT

Consider right angled triangle ΔΟΑΒ

MULTIPLICATION & DIVISION OF VECTOR BY A NUMBER (SCALAR) MULTIPLICATION

OF A VECTORBY A SCALAR

When a vector is multiplied by a positive number (for example 2, 3 ,5, 60 unit etc.) or ascalar only its magnitude is changed but its direction remains the same as that of the



original vector.If however a vector is multiplied by a negative number (for example -2, -3 ,-5, -60 unitetc.) or a scalar not only its magnitude is changed but its direction also reversed.

The product of a vector by a scalar quantity (m) follows the following rules:

(m) = (m) which is called commutative law of multiplication.

m(n ) = (mn) which is called associative law of multiplication .

(m + n) = m + n which is called distributive law of multiplication .DIVISION

OF A VECTORBY A SCALAR

The division of a vector by a scalar number (n) involves the multiplication of thevector by the reciprocal of the number (n) which generates a new vector.

Let n represents a number or scalar and m is its reciprocal then the new vector isgiven by :

where m = 1/nand its magnitude is given by:

The direction of is same as that of if (n) is a positive number.

The direction of is opposite as that of if (n) is a negative number. Addition of vectors by Head to Tail method (Graphical Method)

Head to Tail method or graphical method is one of the easiest methods used to find theresultant vector of two of more than two vectors.

DETAILS OFMETHOD

Consider two vectors and acting in the directions as shown below:




In order to get their resultant vector by head to tail method we must follow the followingsteps:

STEP # 1

Choose a suitable scale for the vectors so that they can be plotted on the paper. STEP # 2

Draw representative line of vector

Draw representative line of vector such that the tail of coincides with the

head of vector .

STEP # 3

Join 'O' and 'B'.represents resultant vector of given vectors and i.e.




STEP # 4

Measure the length of line segment and multiply it with the scale chosen initially to

get the magnitude of resultant vector. STEP # 5

The direction of the resultant vector is directed from the tail of vector to the head of

vector .

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"Kinematics is the branch of Physics in which w ediscuss bodies at rest or motion

w ithout the reference of external agent that causesmotion or rest."

OR"The branch of physics which deals w ith the

description of motion of objects withoutreference to the force or agent causing motion in it,

is called Kinem atics." REST

"I f a body does not change its position with respect to its

surroundings thenthe body is said to be in a state of rest."

MOTION "I f a body continuously changes its position with respect to its

surroundingthan it is said to be in a state of mo tion."

TYPES OF MOTION Motion of objects can be divided into three categories. (i) TRANSLATIONAL M OTION(ii) ROTATIONAL MOTION(iii) VIBRATIONAL MOTION

TRANSLATIONAL MOTION "M otion of a body in w hich every particle of the body is beingdisplaced by the same amount is called Translational Motion" .

EXAMPLE:(i) Motion of a person on a road.(ii) Motion of a car or truck on a road.

ROTATIONAL MOTION "Type of motion in w hich a body rotates around a

fixed point or axis is called Rotational Motion ." EXAMPLE:(i) Motion of wheel(ii) Motion of the blades of a fan

VIBRATIONAL MOTION "Type of motion in w hich a body or particle moves to and froabout a fixed point or mean position is called Vibratory Motion ."

EXAMPLE: (i) Motion of simple pendulum(ii) Motion of the wires of guitar(iii) Motion of swing

DISPLACEMENT

" Distance between two points in a particular direction is calledDisplacement."

OR





FIRST EQUATION OF M OTIONVf = V i + a t

Consider a body initial moving with velocity "Vi". After certain interval of time "t",its velocity becomes "V f ". Now

Change in velocity = V f - V i OR

Δ V =V f – V i

Due to change in velocity, acceleration "a" is produced in the body. Acceleration isgiven by

a = Δ V/ t Putting the value of " Δ V"

a = (V f – Vi) / tat = V f – V i at + V i =V f

OR

SECOND EQUATI ON OFMOTION

ORS = Vit + 1/ 2at 2

Consider a car moving on a straight road with an initial velocity equal to ‘V i’. Afteran interval of time‘t’ its velocity becomes ‘V f ’. Now first we will determine theaverage velocity of body.

Average velocity = (In itial velocity + final velocity)/ 2 OR

Vav = ( V i + V f ) / 2 but V f = V i + at Putting the value of V f

Vav = ( V i + V i + at ) / 2Vav = (2V i + at ) / 2Vav = 2 V i / 2 + a t/ 2

Vav = V i + at / 2Vav = V i + 1/ 2at ....................................... (i)

we know that S = V av x t

Putting the value of ‘V av ’ S = [V i + 1/ 2at] t




THIRD EQUATION OF MOTIONOR

2aS = V f 2 – V i

2

Initial velocity, final velocity, acceleration, and distance are related in thirdequation of motion. Consider a body moving initially with velocity ‘V i’. After certain interval of time itsvelocity becomes ‘V f ’. Due to change in velocity, acceleration ‘a’ is produced in thebody. Let the body travels a distance of ‘s’ meters. According to first equation of motion:

Vf = V i + a tOR

Vf – V i = a tOR

(V f – V i) / a = t ....................(i) Average velocity of body is given by :

Vav = (Initial velocity + Final velocity)/ 2Vav = ( V i + V f ) / 2 .................. (ii)

we know that : S = V av x t .................. (ii)

Putting the value of V av and t from equation (i) and (ii) in equation (iii) S = { (V f + V i) / 2 } { ( V f – V i) / a }

2aS = (V f + V i)(V f – V i)

According to [ (a+b)(a-b)=a2

-b2]

ACCELERATION DUE TO GRAVITY OR FREE FALLING OBJECTS

"Galileo was the first scientist to appreciate that, neglecting the effect of air resistance, all bodiesin free-fall close to the Earth's surface accelerate vertically downwards with the sameacceleration: namely 9.8 m/s2"

Example

If a ball is thrown vertically upward, it rises to a particular height and then falls back to theground. However this is due to the attraction of the earth which pulls the object towards theground"





CHARACTERISTIC OF FREE FALLING BODIES

1, When a body is thrown vertically upward, its velocity continously decreases and become zeroat a particular height During this motion the value of acceleration is negative and V f is equal tozero (a = -9.8m/s 2 , V f = 0).

2, When a body falls back to the ground , its velocity continously increases and becomemaximum at a particular height During this motion the value of acceleration is positive and V i isequal to zero (a = 9.8m/s 2 , V i = 0).

3, Acceleration due to gravity is denoted by a and its value is 9.8m/s 2 .

4, Equation of motion for the free-falling bodies be written as,

Vf = Vi + gt

h = Vit + 1/2 gt 2

2gh = Vf 2 - Vi 2



FORCE & MOTION

FORCE "Force is an agent w hich changes or tends to change the state

of rest or of uniform motio n of a body."In the light of Newton's 2nd law of motion Force may be defined as :

"Force acting on a body is equal to the product of themass and acceleration produced in the b ody."

i.e. F = ma

Force can accelerate or decelerate a body.

Force is a vector quantity. UNI TS OF FORCE

(i) NEWTON (N) in S.I system(ii) DYNE in C.G.S system(iii) POUND (Lb) in BRITISH ENGINEERING SYSTEM (F.P.S)

NEWTON Newton is the unit of force and can be defined as:

"The amoun t of force that produces an acceleration of 1 m/ s 2 in a body of mass 1-kg is equal to 1 N EWTON."

1 N = 1 kg x 1m/ s 2

[ N = kg m/ s 2 ] NEWTON 'S FIRST LAW OF

MOTION STATEMENT: Newton 's first law of motion states that:

"Every body remains at rest or continues to move with uniformvelocity in straight line unless an unbalanced force acts upon it" .EXPLANATION

First law of motion consists of two parts: PART NO 1:

The first part states that a body at rest remains at rest unless an unbalanced force actsupon it.

This part is in accordance with our common experience for example, a book lying on atable remains at rest unless it is lifted or pushed by an external force. PART NO 2 :

Second part states that a body in motion remains in motion with uniform velocityunless an unbalance force acts upon it. This part is not self-evident because a ballpushed once does not continue its motion forever. A little consideration however,shows that there is an opposing force like ground friction and air friction acting in thiscase. These frictional forces are responsible to stop the ball. If we eliminate these

opposing forces, a body in motion will continue its motion forever.





INERTIA "Tendency of a body by virtue of which the body at rest or

moving w ith uniform velocity retains its state is called INERTI A."OR

"P roperty of a body by which a body resists a force, applied toit to change its state of rest or of uniform velocity is called I NERTIA ."

INERTIA of a body is directly related to its mass. Heavy bodies have greater inertiawhile lighter bodies have little inertia.

LAW OF IN ERTIA AND THEFIRST LAW OF MOTION

Every body in the universe opposes the force which tends to change its state of rest or

of uniform motion. This property INERTIA is a direct consequence of FIRST LAW OFMOTION. As heavy bodies due to greater INERTIA requires forces of large magnitude andbodies of small masses require small forces.

By the above explanation of INERTIA we conclude that the state of rest or motion doesnot change by its self unless an external force acts upon it, which is according to theFIRST LAW OF MOTION.

Thus the FIRST LAW OF MOTION is also called LAW OF INERTIA.

NEWTON'S 2ND LAW OF MOTION STATEMENT:

When an unbalanced force acts upon a body, it is accelerated in the direction of force.The magnitude of acceleration is directly proportional to the appliedforce and is inversely proportional to the mass of body.

With the help of above equation 2nd law of motion can be expressed as: THE NET FORCE ACTING ON A BODY IS EQUAL TO THE PRODUCT

OF THE MASS OF BODY AND THE ACCELERATION PRODUCED IN IT.NEWTON'S 3RD LAW OF MOTION

STATEMENT: "To every action there is a reaction equal in magnitude but opposite in direction"

OR "When a body exerts a force on another body, the second body also exertsa force on the first body of same magnitude but in the opposite direction"

F ACTION = -F REACTION

Force exerted by one body is called ACTION and the force exerted by the second body iscalled REACTION.

EXAMPLES:(1) Motion of rocket: fuel burns rapidly, exerts force in downward direction and rocket

moves upwardas a reaction.

(2) Book lying on a table: weight of the book on the surface is action and the forceexerted by the surface (R) is the reaction.

R = -W



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(3) Walking on a street (4) Motion of helicopter

DIFFERENCE BETWEEN MASS AND WEIGHT

Mass Weight (1) The quantity of matter in a

body is called its mass. (1) Weight is the force by which the earth

attracts a body towards its center.

(2) Mass is a scalar quantity. (2) Weight is a vector quantity and is always

directed towards the center of the earth. (3) Mass of a body is alwaysconstant every where in theuniverse.

(3) Weight of a body vary place to place andbecome zero on the center of earth and faraway from the surface of earth.

(4) Mass of a moving body ism=F/a. (4) Weight of a body is W = mg.

(5) Mass can be determine by anordinary balance.

(5) Weight of a body is measured by springbalance.

(6) Unit of mass in S.I system isKILOGRAM ( kg). (6) Unit of weight in S.I system is NEWTON (N).

FRICTION When a body slides over the surface of another body, an opposing force is set up

between them to resist the motion. The force which opposes the motion is called frictionOR Force of Friction.

Force of friction tends to decelerate a body and always acts in the opposite direction of motion.

CATEGORIES OF FRI CTION (1) Contact friction(2) Fluid friction

LIMITING FRICTION When an external force is applied against the force of friction, the force of friction also

increases by the same amount. Therefore, It adjusts itself in such a way that it is equaland opposite to the external force. It has a maximum value just before the motion starts.So friction is a self-adjusting force. The maximum force of friction that stops the body from

moving is called LIMITING FRICTION.It is denoted by Fs.LIMITING FRICTION is directly proportional to the surface reaction. Limiting friction Fs is:

Where R = normal reactionbut R = W



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and R = mg

Where = constant known as coefficient of friction. COEFFICIENT OF FRICTION

Coefficient of friction is the ratio of LIMITING FRICTION to the NORMAL REACTION.

Coefficient of friction is constant for a given pair of surfaces but different for different

pairs Unit of :Since it is a ratio of two similar quantities, therefore it has no unit as shown.

ROLLING FRICTION When a body rolls over a surface, the force of friction is called ROLLING FRICTION. When

a sphere rolls over a surface it experiences an opposing force called ROLLING FRICTION.Rolling friction is much less than the sliding friction because in case of rolling contact area

of two surfaces is very small as compared to sliding.

Momentum - Law of conservation of Momentum

MOMENTUM Quantity of motion of a body is referred to as "MOMENTUM".

Definition Momentum of a moving body defined as :

"The product of mass and velocity of a body is called MOMENTUM." Mathematically

Momentum = mass x velocity

It is a vector quantity. Momentum is always directed in the direction of velocity.The unit of momentum is in S.I system kg .m/s or NS.Momentum depends upon mass and velocity of body.

LAW OF CONSERVATION OFMOMENTUM.

The law of conservation of momentum states that:

"When some bodies constituting an isolated system act uponone another, the total momentum of the system remains constant."

OR "The total momentum of an isolated system of interacting bodies remains constant."

OR

"Total momentum of an isolated system before collision is always equal to total



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momentum after collision."

MATHEMATICALREPRESENTATION

Consider two bodies of mass m 1 and m 2 moving initially with velocities u 1 and u 2 .

Total momentum before collision = m 1 u 1 + m 2 u 2

Let after collision their velocities become v 1 and v 2 .

Total momentum after collision = m 1v 1 + m 2 v2

According to the law of conservation of momentum m 1 u 1 + m 2 u 2 = m 1 v 1 + m 2 v 2

ADVANTAGES AND DISADVANTAGES OF FRICTION - METHODS OF REDUCIN GFRICTION

ADVANTAGES OF FRICTION

Friction plays a vital role in our daily life. Without friction we are handicap. 1. It is becomes difficult to walk on a slippery road due to low friction. When we moveon ice, it becomes difficult to walk due to low friction of ice.




2. We can not fix nail in the wood or wall if there is no friction. It is friction whichholds the nail.3. A horse can not pull a cart unless friction furnishes him a secure Foothold.DISADVANTAGES OF FRI CTION Despite the fact that the friction is very important in our daily life, it also has somedisadvantages like:1. The main disadvantage of friction is that it produces heat in various parts of machines. In this way some useful energy is wasted as heat energy.2. Due to friction we have to exert more power in machines.3. It opposes the motion.4. Due to friction, noise is also produced in machines.

5. Due to friction, engines of automobiles consume more fuel which is a money loss.METHODS OF REDUCIN G FRICTIONThere are a number of methods to reduce friction in which some are discussed here.USE OF LUBRICANTS:The parts of machines which are moving over one another must be properly lubricatedby using oils and lubricants of suitable viscosity. USE OF GREASE:Proper greasing between the sliding parts of machine reduces the friction. USE OF BALL BEARI NG:In machines where possible, sliding friction can be replaced by rolling friction by usingball bearings. DESIGN MODIFICATION:Friction can be reduced by changing the design of fast moving objects. The front of

vehicles and airplanes made oblong to minimize friction.




STATICS .

Statics Statics is the branch of mechanics which deals with the study of bodies at rest under a

number of forces, the equilibrium, conditions of equilibrium, types of equilibrium andtorque etc.

Equilibrium A body is said to be in equilibrium if it is at rest or moving with uniform velocity.In other words if the linear and angular acceleration of a body are zero, the body is said

to be in equilibrium.

Or we can say that when two or more forces act on a body such that their resultant orcombining effect on the body is Zero and the body retains its state of rest or of uniformmotion then the body is said to be in equilibrium.

Example A book lying on the table, suspended bodies, all stationary bodies, jump by using

parachute. Types of equilibrium

With respect to the state of a body, equilibrium may be divided into two categories:1. Static equilibrium .2. Dynamic equilibrium .

Static equilibrium

If the combined effect of all the forces acting on a body is zero and the body is in thestate of rest then its equilibrium is termed as static equilibrium.For example: All stationary bodies Dynamic equilibrium

When a body is in state of uniform motion and the resultant of all the forces acting upon itis zero then it is said to be in dynamic equilibrium.

For example: Jump by using parachute. Conditions of equilibrium

There are two conditions of equilibrium are as follows First condition of

equilibrium The first condition of equilibrium stated as follow : To maintain the transitional equilibrium in a body the vector sum of all the forces acting

on the body is equal to zero In other words we can say that to maintain equilibrium the sum of all theforces acting along X-axis is zero and the sum of all the forces actingalong Y-axis is zero.

Second condition of equilibrium The second condition of equilibrium stated as follow : A body will be in rotational equilibrium when the algebraic sum of clock wise torque and

anti clock wise torque is zero.In other words:



A body will be in rotational equilibrium if vector sum of all the torque acting on the body iszero.

STATES OF EQUILIBRIUM .

States of equilibrium There are three states of equilibrium:

Stable equilibrium

Unstable equilibrium

Neutral equilibrium Stable equilibrium When the center of gravity of a body lies below point of suspension or support, the body

is said to be in STABLE EQUILIBRIUM. For example a book lying on a table is in stableequilibrium.

Explanation A book lying on a horizontal surface is an example of stable equilibrium. If the book is

lifted from one edge and then allowed to fall, it will come back to its original position.Other examples of stable equilibrium are bodies lying on the floor such as chair, table etc.Reason of stability

When the book is lifted its center of gravity is raised. The line of action of weight passesthrough the base of the book. A torque due to weight of the book brings it back to the

original position.

Unstable equilibrium

When the center of gravity of a body lies above the point of suspension or support, thebody is said to be in unstable equilibrium Example

Pencil standing on its point or a stick in vertically standing position. Explanation:If thin rod standing vertically is slightly disturbed from its position it will not come back to

its original position. This type of equilibrium is called unstable equilibrium, other example of unstable equilibrium are vertically standing cylinder and funnel etc.

Reason of instability When the rod is slightly disturbed its center of gravity is lowered. The line of action of its

weight lies outside the base of rod. The torque due to weight of the rod toppled it down. Compiled By: Sir Naeem Khan http://webinfochannel.com/2010/11/x-physics-notes



Neutral equilibrium When the center of gravity of a body lies at the point of suspension or support, the body

is said to be in neutral equilibrium. Example: rolling ball. Explanation

If a ball is pushed slightly to roll, it will neither come back to its original nor it will rollforward rather it will remain at rest. This type of equilibrium is called NEUTRALEQUILIBRIUM.

Reason of neutralequilibrium

If the ball is rolled, its center of gravity is neither raised nor lowered. This means that itscenter of gravity is at the same height as before.

TORQUE - CENTER OF GRAVITY

Torque The torque or moment of force can be define as

“The tendency of a force to produce rotation in a bodyabout an axis is called torque or m oment of force. "

The turning effect of a force depends upon two factors:

The magnitude of force (F)

Moment arm (r) The torque about any axis is given by the product of force and moment arm




Torque = force x moment armOR

Positive torque:If a body rotates about its axis in anti clockwise direction, then the torque is taken

positive.Negative torque:If the body rotates in the clockwise direction, then the torque is taken as negative.

Center of gravity

The center of a body is that point in the body through which the resultant forces due tothe earth’s attraction posses and through which the whole weight of the body always acts.

ORCenter of gravity of a body is a point where total weight of the body is concentrated.Every body posses a center of gravity and this is irrespective of the body. It is not

necessary that the center of gravity should be within the body, but it may also be situatedin space out side the body.Example: center of gravity of a ring is at the center, which is in the space.

Center of gravity of different objects:

Rectangle Center of gravity of a rectangular is at the point of intersection of its diagonals

Circle Center of gravity of a circle is at its center.

Square Center of gravity of square is at the point of intersection of its diagonals.




Regular bar The center of gravity of a regular bar is at its geometrical center.

Triangle The center of gravity of a triangle is at the point of intersection of its medians.

Cylinder The center of gravity of a cylinder is at the axis of cylinder.





CIRCULAR MOTION AND GRAVITATION

GRAVITATION Every object in our universe attracts the other object with

certain fore towards its center. This force of attraction is knownas GRAVITATIONAL FORCE and the phenomenon iscalled GRAVITATION . This is gravitational force which isresponsible for the uniformity or regularity in our dailyastronomical life. The whole system of the universe is in orderonly due to this force. Due to gravitation, the system of ouruniverse is working uniformly and smoothly. The planetsaround the earth or around the sun moves in an orderly motiondue to gravitation.

NEWTON’S LAWOF GRAVITATION In order to explain the gravitational force between two bodies,

Newton formulated a fundamental law known after his namei.e. " NEWTON'S LAW OF GRAVITATION "Newton’s law of gravitation states that every object in theuniverse attracts the other object with a force and : (1) The gravitational force of attraction between two bodies is

directly proportional to the product of their masses. F α m 1 x m 2 ------- (1 )

(2) The gravitational force of attraction between two bodies isinversely proportional to the square of the distance betweentheir centers.

F α 1/d 2 --------- (2)

MATHEMATICALREPRESENTATION

Combining (1) and (2) F α m 1m 2 /d 2

F = G m 1m 2 / d2

Where G = universal gravitational constant Value of G: G = 6.67 x 10 -11 Nm 2 / kg 2

MASS OF THEEARTH

Consider a body of mass ‘m’ placed on the surface of the



earth. Let the mass of the earth is ‘M e’ and radius of earth is ‘R e’ .

Gravitational force of attraction between earth and body is F = G m M e / R e

2

We know that the force of attraction of the earth on a body isequal to weight the weight of body. i.e

F = W therefore

W = G m M e / R e2

But W = mg mg = G m M e / R e

2

org = G M e / R e2

or Me = g x R e

2 / G From astronomical data:g= 9.8 m/s 2 Re = 6.4 x 10 6 mG = 6.67 x 10 -11 N-m 2 /kg 2 Putting these values in the above equation.

Me = 9.8 (6.4 x 10 6 ) 2 /6.67 x 10 -11 or




WORK PHYSICAL

DEFINITION OFWORK

"W ork is said to be done if a force causes a displacementin a body in the direction of force".

OR"The w ork done by a constant force is defined as the product of

the component of the force and the displacement in the direction of displacement."

MATHEMATICALDEFINITION

"W ork is the scalar product of force and displacement".OR

"W ork is the dot product of force and displacement".

Work is a scalar quantity. UNIT OF WORKS

• In S.I system: Joule (j)• In C.G.S. system: Erg• In F.P.S. system: ft X lb

CATEGORIES

OF WORK (i) POSITIVE WORK: If force and displacement are in the same direction, work will be positive or if θ = 0 or θ <90°




(ii) ZERO W ORK: If force and displacement are perpendicular to each other, work will be zero. i.e.

since θ = 90°Work = 0

asW ork = Fd Cos θ

Wo rk = Fd Cos 90°Work = (F)(d)(0)

Work = 0

NEGATIVE W ORK: If force and displacement are in the opposite direction, work will be negative.

since θ = 180°W ork = - ve

asW ork = Fd Cos θ

Wo rk = Fd Cos 180°Wo rk = (F)(d)( -1)

Wo rk = -Fd ENERGY

ENERGY "The ability of a body to perform work is called Energy". A body cannot perform work if it does not posses energy. A body cannot perform workmore than the amount of energy. It is a scalar quantity.

UNITS OFENERGY




(i) Joule(ii) Calorie [NOTE: 1 Calorie = 4.2 joule.](iii) KWatt-Hour

TYP ES OFENERGY

There area numerous types of energy such as:Heat EnergyLight EnergySound EnergyNuclear EnergyChemical Energy

Electrical EnergySolar EnergyWind EnergyKinetic EnergyPotential Energy etc. etc.

POWER "The rate of work done of a body is called Pow er".

AVERAGEPOWER

Average power of a body doing work is numerically equal to the total work done dividedby the time taken to perform the work. MATHMATICALLY

Power = W ork done/ t imePower = Work/ tbut [work = Fd]

thereforePower = Fd/ t

UNITS OFPOWER

(i) watt [1 watt = 1joule/sec ](ii) Kilo watt [1Kw = 1000 watt](iii) Mega watt (Mw) [1Mw = 10 6 watt](iv) Horse power [1Hp = 746w] POTENTIAL ENERGY INTRODUCTION

Energy stored by a body by any means is called "Potential Energy". DEFINITION "The energy stored by a body due to its position in gravitational field is known as

‘Gravitational Potential Energy’".







PROVE THE LAW OF CONSERVATION W ITH THE HELP OF A SUITABLE EXAMPLE. We know that the motion of the bob of a simple pendulum is simple harmonic motion.Here we have to prove that the energy is conversed during the motion of pendulum.Proof: Consider a simple pendulum as shown in the diagram.

Energy

Conservation AtPoint ‘A’

At point ‘A’ velocity of the bob of simple pendulum is zero. Therefore, K.E. at point ‘A’ =0. Since the bob is at a height (h), Therefore, P.E. of the bob will be maximum i.e.P.E. = mgh.Energy to tal = K.E. + P.E Energy total = 0 + mghEnergy total = mgh This show s that at point A total energy is potential energy.

EnergyConservation At

Point ‘M’ If we release the bob of pendulum from point ‘A’, velocity of bob gradually increases, butthe height of bob will decreases from point to the point. At point ‘M’ velocity will becomemaximum and the height will be nearly equal to zero.Thus ,K.E. = maximum = 1/2mV 2 but P.E. = 0.Energy to tal = K.E. + P.E Energy total = 1/2mV 2 + 0Energy total = 1/2mV 2 This show s that the P .E. at point is completely converted into K.E. at point ‘M ’.

EnergyConservation




At Point ‘B’ At point M the bob of Pendulum will not stop but due to inertia, the bob will movestoward the point ‘B’. As the bob moves from ‘M’ to ‘B’, its velocity gradually decreases butthe height increases. At point ‘B’ velocity of the bob will become zero.Thus K.E. at point ‘B’ = 0 but P.E. = max.P.E. = mgh.Energy total = K.E. + P.E.Energy total = 0 + mghEnergy total = mghThis show s that at point B total energy is again potential energy.

CONCLUSION

Above analysis indicates that the total energy during the motion does not change. I.e. themotion of the bob of simple pendulum is according to the law of conservation of energy.



MACHINE A machine is a device by means of which work can be performed easily or in a convenient manner.A machine can be used:

To lift heavy loads by applying little force.

To enlarge magnitude of force

To increase rate of work done

To change the direction of forceExample of simple machines are : Lever, pulley, inclined p lane, wedge, screw etc.

EFFORT OR P OWER The power directly applied to a machine to lift a load is called Effort or Power. It is denoted by ‘P’ .

LOAD OR WEIGHT The weight lifted by a machine is called Load. It is denoted by ‘W’ .

MECHANICAL ADVANTAGE The ratio of weight (load) lifted by a machine to the force (effort) applied on a machine is calledmechanical advantage of the machine.Greater the value of mechanical advantage of a machine, easier is the work done.Mathematically,

M.A. = Weight over-comed by Machine/ Force Applied on the Machine

UNIT: It has no unit.

INPUT Amount of work done on a machine by a given effort (force) is called input of a machine.

OUTPUT Amount of work done by a machine on the load (weight) is called output of the machine.

EFFICIENCY The ratio of output of a machine to the input of machine is called its efficiency.




UNIT: It has no unit.

IDEAL MACHINE An ideal machine is a hypothetical machine whose output is equal to its input.For an ideal machine

Efficiency of an ideal machine is 100% because there is no loss of energy in an ideal machine due tofriction or any other means that can waste useful energy. M.A of an ideal machine is d / h . LEVERLever is a simple machine which is used to lift heavy bodies or heavy load in a very easy way.Lever consists of a rigid bar capable to rotate about a fixed axis called fulcrum. Effort is applied atone end of the bar and weight can be lifted from the other end.

TYP ES OF LEVER

There are three kinds of lever depending upon the positions of load , effort and fulcrum.

FIR ST KI ND OF LEVER In the first kind of lever, the fulcrum F lies between effort ( P ) and load ( W ).

Example: common balance, seesaw, scissors, handle of hand pump.







Fixed Pulley

If the block of the pulley is fixed then it is called a fixed pulley.

Mechanical Advantage of Fixed Pulley

In a fixed pulley, the force P is the applied force and weight W is lifted. If we neclect the force of friction then:

Load = Effort

Moveable Pulley

In this pulley, one end of the rope that is passing around the pulley is tied to a firm support and effort Pis applied from its other end. The load and weight to be lifted is hung from the hook of block. In thissystem, the pulley can move. Such a pulley is called moveable pulley.

Mechanical Advantage of Moveable Pulley

In an ideal system of a moveable pulley, the tension in each segment of the rope is equal to the appliedeffort. As two segments support the weight, the ffort acting on the weight W is 2P. Therefore, accordingto the principle of lever:

W * Radius of the Wheel = 2P * Radius of the Wheel

=> 2P = W

The Mechanical Advantage is given by:

M.A = W/P

M.A = 2P/P

=> M.A = 2

Hence, the mechanical advantage of a moveable pulley is 2.



Com il ttp://webinfochannel.com/2010/11/x-physics-notes p ed By: Sir Naeem Khan h

MATTER

KIN ETIC MOLECULAR THEORY OFMATTER

According to kinetic theory of matter:

• Matter is made of very small particles called MOLECULES . • These molecules are in a state of motion. • They possess Kinetic Energy. • Molecular motion may be translational, rotational or vibrational. • These molecules attract each other. • As the temperature of a substance is increased, its molecular speed is

also increased and vice versa. • If a substance is compressed , The K.E of its molecules increases and its

temperature rises

States of Matter

Matter has been classified into three states. These states are discussed below:

1.Solid

According to the kinetic theory of matter, solid has the least kinetic energy. Theproperties of solids are given below:

• The particles are very close to each other.

• Their shape and volume is fixed.




• They have greater kinetic energy than solids but less than that of gases.

• The volume of liquid is fixed.

• They move more freely than solids.

• The attraction between molecules is lower than solids.

• The distance between the molecules is greater than that of solids.

• On heating, they convert into vapours.

• On cooling, they convert into solid.

3. Gas

According to the kinetic molecular theory, gases possess the following properties.

• Gases possess more kinetic energy.

• Their shape and volume are not fixed.

• The distance between their molecules is large.

• Their temperature is proportional to their kinetic energy.

• Their temperature rises with increase in pressure.

• On cooling, they convert into liquid and gases.

BROWNIAN MOTION A famous scientist ROBERT BROWN observed that molecules of a substance aremoved in ZIG ZAG path. Their motion is random. They collide with each otherand move in a new direction after collision in ZIG ZAG fashion. This type of motion present in the molecules of matter is called "Brow nian motion ".



Brownian motion ELASTICITY

The property of solid by virtue of which a solid body recovers its original shapeafter the removal of an applied force is called "ELASTICITY".

ELASTIC LIMI T

If applied force on a solid is gradually increased, a state is reached after whichthe material will not return to it original shape even after the removal of appliedforce. This limit is called "ELASTIC LIMI T". After elastic limit, material is permanently deformed. Different substances havedifferent elastic limit.

STRESS Wh en a body is deformed, the internal force came into play per unit area

to restore it to its origin al state is called " STRESS"OR

"Stress is an opposing force expressed per unit area which resists anychange in shape."

Stress is equal to the force per unit area. Mathematically:

or

Stress produces when a body is made to change in length, volume or Shape bythe application of an external force.

Hook's Law

Introduction

An English Physicist and Chemist Robert Hook discovered this law in 1678.

Statement

"Strain produced is proportional to the stress exerted within the elastic limit."





Elastic Limit

The point at which a material becomes plastic is called elastic limit on yield point.

Yield Point

the yield point is the point at which the material begins to flow. It is also the point betweenelastic region and plastic region.

Elastic Region

When the material obey's Hook's Law, it is said to be in Elastic Region.

Plastic Region

When stress is applied beyond the elastic limit, the graph is no longer a straight line. In this casestress produces a permanent change in the material. The material is said to be in its Plastic

Region.

Breaking Point

The material breaks at a certain point called the Breaking Point of the material.

Young's Modulus

Definition

"The ratio of the stress on a on a body to the longitudinal strain produced is called Young's Modulus."

Mathematical Expression

According to the definition of YOung's Modulus:

Young's Modulus = Sress / Longitudinal Strain




Unit

In S.I system, Young's Modulus is measured in N/m2.

Pressure

Definition

"The perpendicular force per unit area acting on a surface is called pressure."


Pressure = Force /Area

P = F/A

Unit

• S.I or M.K.S System - N/m 2 or Pascal.

Pressure in Liquids

In water or other liquids, the weight exerted on a body or the bottom of the liquid is its pressure.

Pascal's Principle Statement

When a pressure is applied to a liquid contained in a vessel, it is transmitted undiminishedequally in all directions and acts perpendicularly to the walls of the container.



Applications - Hydraulic Press

Pascal's Principle has the application in Hydraulic press. In a hydraulic press a narrow cylinder Ais connected with a wider cylinder B and they are fitted with airtight piston. It is filled with someincompressible liquid. Pressure can be applied by moving the piston cylinder A in the downwarddirection. Piston B is used to lift the object. The hydraulic press is provided with a rigid roof overit. When piston B moves upward, it compresses any material placed between the rigid roof andthis piston. The hydraulic press is used for compressing soft materials like cotton into a cottonbale and powdered materials into compact solids.

Pressure in Gases

The kinetic theory enables us to account for the pressure a gas exerts on the walls of itscontainer. When a moving molecule strikes the walls of its container, a force is exerted on thewalls during hte impact.

Atmospheric Pressure

The atmosphere, because of its weight exerts a pressure on the surface of the earth and on everyobject on the earth including human beings. The pressure is known as Atmospheric Pressure.





Applications of Atmospheric Pressure

The fact that the atmosphere exerts pressure has been put into use in several devices such assiphons, pumps and syringes.

Barometer

Definition

"A device for measuring the atmospheric pressure is called Barometer."

Mercury Barometer

In the laboratory, the atmospheric pressure is measured by means of a mercury barometer. Amercury barometer consists of a thick walled glass tube of 1m length, which is opened at one endand closed from the other side. The tube is filled with mercury. The open end is firmly coveredwith a thumb and then carefully inverted in a vessel containing mercury. When the open end iscompletely immersed in the mercury, the thumb is removed. Some of the mercury from thecolumns drops in the vessel leaving a space. This space is called vacuum. If the mercury columnsis measured, it is found to be 760 mm. This length always remains constant even if differentdiameter tubes are taken. The length of the mercury column is referred to as the atmosphericpressure.

Archimede's Principle

Statement

"When an object is immersed in a liquid, an upward thrust acts upon it, which is equal to theweight of the liquid displaced by the object."




Mathematically, Archimede's Principle may be represented by:

Apparent Weight = Actual Weight - Weight of the liquid displaced by the object

Buoyancy

It is the tendency of an object to float. It is equal to the up-thrust or weight of the water displacedby the object.

Conditions for Floating Bodies

• A body will float in a liquid or a gas if it displaces liquid or gas whose weight is greaterthan the weight of the body.

A body will sink if it displaces liquid or gas whose weight is less than the weight of the body.

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Physics X Notes