STATES OF EQUILIBRIUM

STATES OF EQUILIBRIUM 

There are three states of equilibrium. 
They are the following. 

STABLE EQUILIBRIUM 

Definition 
A body is said to be in stable equilibrium if it returns to its original position when tilted a little. 
                                                                                               OR 
The centre of gravity of a body rises with a jerk is called stable equilibrium. 
Examples 
• Book on a table. 
• Chair on flat ground. 
• Table on a floor. 
• A standing car on a smooth road. 

UNSTABLE EQUILIBRIUM 

Definition
 A body is said to be in unstable equilibrium if it moves further away from its original position when tilted a little. 
                                                                                               OR 
The C.G of a body lowered with a slight move the equilibrium of that body is called unstable equilibrium. 
Examples 
• A stick standing vertically on the tip of a figure. 
• A standing pencil on the table. 
• An acrobat walking on a rope. 

NEUTRAL EQUILIBRIUM 

Definition 

A body is said to be in neutral equilibrium if it neither returns to its former position nor moves further away when tilted a little. 

                                                                                                OR 

The equilibrium of that body is called neutral equilibrium whose C.G is neither raised nor lowered on disturbing.

Examples 

• Horizontally lying cylinder and funnel. 

• Lying a ball on the floor. 

CENTRE OF GRAVITY  

Definition 

It is the point at which the entire weight of the body is said to be situated. 

                                                                                                 OR 

The point on a body at which the whole weight of the body appears to act. It may be on the body or out side the body in case of a hollow object. 

TORQUE OR MOMENT OF A FORCE

Definition 

It is the turning effect of a force about the axis of rotation. 
Formula 
Torque = force x moment arm 
                t =f x d 
Unit 
Its unit is N-m. 

TYPES OF TORQUE 

Torque or moment may rotate a body in clock wise or anti clock wise direction. 

NEGATIVE TORQUE 

The clock wise torque is called negative torque. 

POSITIVE TORQUE 

The anti clock wise torque is called positive torque. 
Notation It is denoted by the Greek letter t (tau) 
Formula 
Torque = Force x moment arm. 
                        t= F x d 
Unit The unit of torque is (N-m) 
Nature 
It is a vector quantity. 

MOMENT ARM 

Definition 
The perpendicular distance between the line of the force and the axis of rotation is called the moment arm. 
Notation 
It is denoted by d. 

FACTORS ON WHICH TORQUE DEPENDS

 Torque depends upon two factors. 
1. Magnitude of the applied force. 
2. The moment arm Torque increases with the increase of force. Torque is directly proportional to the applied force. Torque is directly proportional to the moment arm. 

PRINCIPLE OF MOMENT

Statement 

According to the principle of Moment -If a system is in equilibrium under influence of some Torques then the sum of clock wise torques is equal to the sum of anti clock wise torques i.e. 

Mathematically 

In Equilibrium position. 

Clock wise torque = Anti clock wise torque. 

EQUILIBRIUM

Definition 

When the resultant of all the forces acting on a body comes to zero, the body is said to be in the state of equilibrium. 
                                                                                             OR 
In other words the body is said to be in the state of equilibrium if left-ward forces are equal to the rightward forces and upward forces are equal to the downward forces. 
Example 
• A book lying on the table.
 • A train moving in a straight line with a constant velocity. 
• A body hanging at rest from the ceiling by a vertical string. 
• A Paratrooper moving down with uniform velocity after opening his parachute. 

TYPES OF EQUILIBRIUM  

There are two types of equilibrium. 
1. Static equilibrium 
2. Dynamic equilibrium 

STATIC EQUILIBRIUM 

Definition
If some forces are acting on a body vertically or horizontally and the body maintains its state of rest, Then it is called static equilibrium. 
Example 
• A book lying on the table. 
• A body hanging at rest from the ceiling by a vertical string. 

DYNAMIC EQUILIBRIUM 

Definition 
If some forces are acting on a body vertically or horizontally and the body maintains its state of motion, then it is called dynamic equilibrium. 
Example 
• Train moving with uniform velocity.
• Paratrooper falling down with uniform velocity. 

CONDITIONS OF EQUILIBRIUM  

FIRST CONDITION OF EQUILIBRIUM 

 Statement 
The body is said to be in the state of equilibrium if the resultant of all forces acting on a body is equal to zero i.e.

In other words the algebraic sum of all the forces acting along X-axis should be zero i.e.

And the algebraic sum of all the forces acting along Y-axis should be zero i.e. 

When first condition of equilibrium is satisfied. the body is in translational equilibrium and there is no linear acceleration. 

SECOND CONDITION  OF EQUILIBRIUM 

Statement The body is said to be in the state of equilibrium if the sum of all the torques or moments acting on the body must be zero i.e. 

RESULTANT OF TWO FORCES

Definition 

The net effect of the forces is a single force which is called the resultant of the forces. 
                                                                    OR 
A single that gives combined effect of forces is called resultant force. 

 

If two forces F1 and F2 are acting on a body at a straight line but in opposite direction and body remains at rest or in equilibrium. Then we say that F1 and F2 are equal in magnitude but opposite in direction. 

If two forces F1 and F2 are acting on a body at a straight line but in opposite direction and body moves in the direction of any one of them which is greater than the other. Net force is calculated as: 

                               F2-F1 net force
                   or        F1-F2 net force
            Body will move in the direction of greater force.

RESULTANT OF TWO FORCES ACTING AT AN ANGLE

 If two forces are acting on an object making a certain angle. In this case the force can be represented in magnitude and direction by two adjacent sides of a parallelogram (I In). The resultant force FR is a vector represented by the diagonal from the point of intersection. This is called the parallelogram of forces.

As PR is diagonal of I Im PQRs so the resultant is diagonal. And the I Im is called I Im of force F1 and F2. 


By head to tail rule, we can draw force F- from the terminal point of force F2. To get the resultant FR we draw a vector from the initial point of force F2 to the terminal point of the force Fr. This is the same force as obtained from the I l 1 of force as shown in the figure. 

FACTORS ON WHICH THE FRICTION DEPENDS

Friction depends upon the following two factors. 

1. Normal Reaction 
2. Nature, of Surfaces 

NORMAL REACTION

Force of friction is directly proportional to the normal reaction R which acts in upward' direction against the weight of the body sliding on a surface i.e. 

NATURE OF SURFACES

Force of friction also depends upon the nature of two surfaces in contact with each other, it is constant for various pairs of surfaces in contact and this value is called co-efficient of friction. 

SELF ADJUSTING FORCE 

The force of friction' has the ability to increase its value with the increase of applied force till it reaches a maximum value..,Due to this strange nature of frictional forces we call them as the self adjusting force. It is denoted by Fs. 

LIMITING FRICTION  

Definition 

The maximum force of friction which just stops the body from moving is called limiting friction 

COEFFICIENT OF FRICTION 

Definition

 Coefficient of friction is the ratio between force of friction and perpendicular reaction. 

p is coefficient of friction. R is perpendicular reaction. F is force of friction. 

ROLLING FRICTION 

Definition :

Then a body rolls over a surface it experiences an opposing force that is called rolling friction. polling friction between two bodies is much less than the sliding friction because in rolling the contact S-Irface is much less than that in sliding. 

ADVANTAGES OF FRICTION  

• Frictional forces help us to move forward. 

• Nut and bolt can hold a body due to friction. 

• A nail stays in the wood because of friction. 

• We can not hold any thing without friction. 

• We can tie a knot because of friction. 

DISADVANTAGES OF FRICTION  

There are so many disadvantages of friction but some are as follows. 

In a car engine oil under pressure is supplied continuously to ball bearing surface. Failure of the oil supply will allow metal to metal contact and the resulting friction, often raises the temperature and due to this ball bearings and piston are sized up. 

MOMENTUM

Definition 

Momentum of a body is the product of its mass and velocity. 
                                                                                                   OR 
The quantity of motion of a body is called its momentum. 

Mathematically 

If "m" is the mass and "v" is the velocity of a body then Momentum P is given by: 
                                                                         P = mv 

Unit 

In M.K.S. system the unit of Momentum is kg-m/s or N-s 

Nature 

It is a vector quantity. Its direction is same as that of velocity, 

LAW OF CONSERVATION OF MOMENTUM 

Statement 

The total momentum of a system remains constant provided no external forces act on it. 
                                                                         OR 
The Momentum of an isolated system always remains constant. 

PROOF 

Consider a system consisting of two balls A and B of masses m₁ and m2 moving in a straight line, with velocities U1 and U₂. On colliding with each other they move with velocities V1 and V₂ respectively as shown in the figure. 
The total Momentum of the system before collision= m₁U1 + m₂U₂ 
The total Momentum of the system after collision = m_1V1 + m_2V2 
According to the law of conservation of Momentum Initial momentum = Final momentum 
                                                              m₁U1 + m₂U₂ = m1V1+ m₂V₂ 

Hence the Momentum of a system remains constant. 

FRICTION  

Definition 

When two bodies are in contact with each other and the force is applied to the upper body to make it move over the lower body, an opposing force is developed in the plane of contact which resists the motion. This force is called friction. 

                                                                          OR 

When one bod / slides over the surface of another body, an opposing force is set up to resist the motion. The force which opposes the motion is called friction. 

CAUSES OF FRICTION 

There is no ideal smooth surface present in universe. Each surface has elevations and depressions which causes to friction. 

When two surfaces are brought into physical contact. the elevations of one impacts into the depressions of first or vice versa which causes an inter locking with two surfaces. This interlocking opposes the relative motion of one surface on the other. 

Newton's Law of Motion

 First law of motion:

 According to Newton's first law of motion :
 "A body tends to continue it's state of rest or of uniform motion unless a force is applied on it ".
 First law of motion is also known as law of inertia 

Inertia:

 "The inability of matter to change it's state of rest or of uniform motion ,is known as inertia".
 inertia of a body depends upon it's mass . Greater the mass of a body larger is it's inertia.

 Second law of motion:

 According to Newton's second law of motion :
               "When an unbalanced force acts on a- body it produces acceleration in the body in it's own direction such that the magnitude of acceleration is directly proportional to the magnitude of force ".

Where "F " represents the unbalanced force and "a" is the acceleration produced in the body of mass "m ". The direction of "a" is same as the direction of "F ".

 Unit of force:

 The unit of force can be defined with the help of Newton's second law of motion . Since,

F = m a

 Therefore the M.K.S unit of force will be kg - m/s^2 which is commonly known as Newton .
 "Force is said to be one Newton (1 N) if it produces an acceleration of 1 m/s^2 in a body of mass 1 kg".
 C.G.S unit of force is "dyne", Whereas the British unit of force is "Pound".
                                       1 Newton = 10^5 dyne.

 Third law of motion:

 According to Newton's third law of motion :
                 "To every action there is always an equal and opposite reaction".
 Action and reaction are two forces which are exchanged between two bodies ,when they interact with each other .

Definition of Physics Ch # 3

Motion under gravity: 

 If A body is thrown vertically upward with a certain velocity then due to gravity it's velocity decreases at the rate of 9.8 m/s 2,
      It means that the velocity of the body will decrease by 9.8 m/s in every second. As a result of which it's velocity becomes zero after it has-attained a certain height. At this point the body can not remain suspended in the air, therefore it starts falling down under the action of gravity with the same acceleration of 9.8 m/s 2-. This time its velocity .Increases by 9.8 m/s in every second. It hits the ground with same velocity with which it was thrown.
    During the entire motion under gravity, acceleration of the body is in the downward direction (towards the center of the earth) therefore it is taken as "-g" for upward motion, whereas for the downward motion it is taken as "+g ". The body takes a certain time "t " to reach the highest point. In the absence of air resistance it takes exactly the same time to return to the ground. Hence the total time for which the body remained in the air is "2 t "

Important note: 

For complete up and down motion g is to be taken as negative . The reason for doing so in such cases is that the direction of initial velocity vi of the body is taken as reference. It is taken as positive and any vector quantity including g , whose direction is opposite to the direction of vi will be negative. Especially in case of projectile motion g is taken as negative throughout the motion. Because at the point of projection the initial velocity in the vertical direction is upward whereas the direction of g throughout the projectile motion is downward. Hence g is taken negative at all the points, whether the body moves upward or downward. All the equations of projectile motion are derived on this assumption. 

Definition of Physics CH # 3

Velocity: 

"Rate of displacement of a body is called velocity". 
                                                OR  
"Speed of a body in a particular direction is called velocity"- 

:Velocity is a vector quantity,it's direction is same as the direction of displacement . It's unit in M.K.S system is m/s 

Definition of Physics CH # 3

Uniform velocity :

 "If a body covers equal distances in equal intervals of time in a particular direction then it's velocity is said to be uniform. 
                                                                       OR 
"if speed of a body is constant in a particular direction then it's velocity will be uniform".
 If a body moves with uniform velocity then it's instantaneous and average velocities will be equal . 
v= uniform , when v av = v inst.   

Definition of Physics CH# 3

Average velocity: 

"Total displacement divided by total time taken. is called average velocity". 

Instantaneous velocity: 

"It is the velocity of a body at a particular instant".
 Mathematically the instantaneous velocity of a body is given by : 

Definition of Physics CH # 3

Velocity: 

"Rate of displacement of a body is called velocity".
                                                  OR
"Speed of a body in a particular direction is called velocity"- 

:Velocity is a vector quantity , it's direction is same as the direction of displacement . It's unit in M.K.S system is m/s 

Where Ar is the displacement of the body in time At 

Physics Definitions (Ch-2)

Motion

When a body continuously changes it's position with respect to it's surroundings it is said to be in motion .

Rest:

 If a body does not change it's position with respect to it's surroundings it is said to be at rest . State of rest or of motion is relative . It means that a body at rest with respect to a certain frame of reference may be in motion with respect to some other frame of reference.

Displacement: 

Displacement of a body may be defined as : 

       "The change in position of a body in a particular direction".

It may also be defined as : 

       "The shortest straight line distance between initial and final positions of a body ". 

Displacement is a vector quantity. 

It's magnitude is equal to the distance between the two positions of the body , it is directed towards the final position . 

Speed:

 "Distance covered per unit time is called speed of the body". Speed is a scalar quantity. It's unit in M.K.S system is meter per second (m/s) .

Average speed :

 "Total distance covered divided by total time taken is called average speed ".

Instantaneous speed: 

                                        "It is the a body at a particular instant".
 Instantaneous speed of a body can be calculated by finding the distance covered by it in a very short interval of time and then dividing it by the time interval . Mathematically instantaneous speed is given by: 

It means that the interval of time is very taken is very short and is close to zero

Measurements and the systems of units

System of units: 

     A set of fundamental and derived units is called a system of units. 

Names of system of units: 

• M.K.S System 
• C.G.S System 
• British Engineering System 
• System International (S.I ) 

(i) M.K.S System (Meter, Kilogram, Second System): 

In this system fundamental units of length, mass and time are meter, kilogram and second respectively. 
Units of other physical quantities can be expressed in terms of meter , kilogram and second. 

(ii) C.G.S System (Centimeter, Gram, Second System): 

In this system the fundamental units of length, mass and time are centimeter, gram and second respectively. 

(iii) British Engineering System:

In this system length, force and time are taken as fundamental quantities. Hence the fundamental units are taken as foot for length, pound for force and second for time. 

• This system is also known as F.P.S system. 
• Mass is taken as a derived quantity, it's unit is Slug.

(iv) System International (S.I ) units:

This system of units was introduced in 1960 and is now in use all over the world. This system of units is based on the following seven independent fundamental units.

Definition of Physics

Physics is a branch of science that deals with the study of properties of matter and energy and the interaction between them. Physics is basically an experimental science, it depends upon objective observations and accurate measurements of various natural phenomenon. 

Main Branches of Science: 
Science is divided into two main branches:

• Physical sciences 
• Biological sciences 

Main Branches of Physical Sciences: 
Physical sciences are divided into several branches such as: 

• Physics 
• Chemistry 
• Astronomy 
• Geology etc. 

Main Branches of Biological Sciences : 
Biological sciences are divided into following branches: 

• Botany 
• Zoology 
• Physiology etc.

Main Branches of Physics: 
Physics is divided into several branches such as: 

• Mechanics 
• Electricity 
• Thermodynamics 
• Atomic physics 
• Nuclear physics 
• Astro physics 
• Solid state physics 
• Plasma physics 
• Medical physics 
• Particle physics 
• Spectroscopy 
• Low temperature physics and many more