Monday 31 October 2011

PULLEY


A pulley is a simple machine. It consists of a wheel mounted on an axis which is fixed to a frame called block. The wheel is free to rotate. With the help of pulley we can lift heavy loads very easily by applying little force and also change the direction of force.



FIXED PULLEY: -

If the block of the pulley is fixed to a strong beam or ceiling, the pulley will not move and is called a “Fixed Pulley”.

MECHANICAL ADVANTAGE OF FIXED PULLEY: -

In fixed pulley, the effort ‘P’ is applied which is equal to the load ‘W’, if we ignore weight of rope and force of friction between rope and pulley then:
effort = load
P = W


Dividing both sides by P
P/P = W/P
W/P = 1 Since [W/P = M.A]
So therefore M.A = 1
This shows that fixed pulley can only change the direction of force but it will lift load equal to the effort applied on it.

MOVEABLE PULLEY: -

In a moveable pulley, one end of the rope which passes around the pulley is tied to a firm support ‘O’ and effort ‘P’ is applied to the other end. The load is hung from the hook of the block. As the load is applied by two segments of rope, the effort becomes twice of the applied value. i.e.


EFFORT = 2 x P
In equilibrium condition we have
Load = Effort
W = 2P
Dividing both sides by P
W/P = 2
But [W/P = M.A]
Thus
M.A. = 2

This shows that a moveable pulley can lift a load double the effort.




Sunday 30 October 2011

LEVER


Lever 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 at one end of the bar and weight can be lifted from the other end.


TYPES OF LEVER: -

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

FIRST KIND OF LEVER: -

In the first kind of lever, the fulcrum F lies between effort (P) and load (W).


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

SECOND KIND OF LEVER: -

In the second kind of lever, load (W) lies between effort (P) and fulcrum (F).


Example: door, nutcracker, punching machine.

THIRD KIND OF LEVER: -

In the third kind of lever, effort (P) lies between load (W) and fulcrum (F).


Example: forceps, jaws, human forearm, fire tong.

MECHANICAL ADVANTAGE OF LEVER: -

Consider the example of a lever of 1st kind.


In equilibrium position torque of effort is always equal to the torque of load.
i.e.
Clockwise torque = Anti clockwise torque
Torque of effort = torque of load
OR
effort x effort arm = weight x weight arm
P x OA = W x OB
OA = W x OB/P
W/P = OA/OB
But [W/P = M.A.]
M.A = OA/OB
OR
M.A. = Effort arm / weight arm

This equation shows that mechanical advantage of lever can be increased:
·         By increasing effort arm.
·         By decreasing weight arm

Saturday 29 October 2011

MACHINES


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 force
Examples of simple machines are: Lever, pulley, inclined plane, wedge, screw etc.

EFFORT OR POWER: -

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 called mechanical advantage of the machine.
Greater the value of mechanical advantage of a machine, easier is the work done.
Mathematically,
M.A = load/effort
OR
M.A = W/P
UNIT: -

It has no unit.

INPUT: -

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

Input = effort x distance through which effort acts
OR
Input = P x d
OUTPUT: -

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

Output = load x distance covered by the load
OR
Output = W x D

EFFICIENCY: -

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

h = output/input
h = (W x D) / (P x d)
Efficiency in %:
h = (W x D) / (P x d) x100
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
Output = Input

Efficiency of an ideal machine is 100% because there is no loss of energy in an ideal machine due to friction or any other means that can waste useful energy.
M.A of an ideal machine is d / h.

Friday 28 October 2011

WORK, ENERGY, POWER

PHYSICAL DEFINITION OF WORK: -

"Work is said to be done if a force causes a displacement in a body in the direction of force".

OR

"The work done by a constant force is defined as the product of the component of the force and the displacement in the direction of displacement."

MATHEMATICAL DEFINITION: -

"Work is the scalar product of force and displacement".
OR
"Work 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- lb

CATEGORIES OF WORK: -

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


(i)                 ZERO WORK: -
If force and displacement are perpendicular to each other, work will be zero. i.e.
Since q = 90°
Work = 0
as
Work = F d Cos q
Work = F d Cos 90°
Work = (F)(d)(0)
Work = 0


NEGATIVE WORK: -

If force and displacement are in the opposite direction, work will be negative.


Since q = 180°
Work =  negative
as
Work = F d Cos θ
Work = F d Cos 180°
Work = (F)(d)(-1)
Work = - F d

ENERGY: -

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

UNITS OF ENERGY: -

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

TYPES OF ENERGY: -

There are numerous types of energy such as:

  • ·       Heat Energy 
  • ·          Light Energy 
  • ·          Sound Energy 
  • ·          Nuclear Energy 
  • ·          Chemical Energy  
  • ·          Electrical Energy 
  • ·          Solar Energy 
  • ·          Wind Energy 
  • ·          Kinetic Energy 
  • ·          Potential Energy etc. etc.
POTENTIAL ENERGY: -

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’".

FORMULA: -

Consider a body of mass "m" placed at a height of "h" from the surface of earth.
                                              Force = Weight = W
                                       But displacement (d) = h



Work done = F d 

  OR 
Work done = W h 

[but W = mg]

                                                          Work done = m g h

We know that the work done in lifting the body is stored in the body in the form of Potential Energy. Thus

                                                        P.E. = m g h

KINETIC ENERGY: -

"Energy posses by a body by virtue of its motion are referred to as ‘Kinetic Energy’".

FORMULA: -
K.E. = ½ mv2


  • Kinetic energy depends upon the mass and velocity of body.
  • If velocity is zero than K.E. of body will also be zero.
  • Kinetic energy is a scalar quantity like other forms of energies.
DERIVE: K.E = ½ m v 2: -

PROOF: -

Consider a body of mass "m" starts moving from rest. After a time interval "t" its velocity becomes V.
If initial velocity of the body is Vi = 0, final velocity Vf = V and the displacement of body is "d". Then


First of all we will find the acceleration of body.

Using equation of motion
2aS = Vf2 – Vi2 

Putting the above mentioned values 

2ad = V– 0

a = V2/2d
Now force is given by

F = ma 

Putting the value of acceleration

F = m(V2/2d) 

As we know that 

Work done = F d
Putting the value of F

Work done = (mv2/2d)(d)

Work done = mV2/2

OR
Work done = ½ mV2
Since the work done is motion is called "Kinetic Energy" i.e.

K.E. = Work done
OR
K.E. =1/2mV2.

LAW OF CONSERVATION OF ENERGY: -

According to the law of conservation of energy:
                       "Energy can neither be created nor it is destroyed, however energy can be                                            converted from one form energy to any other form of energy"

SHOW THAT THE MOTION OF A SIMPLE PENDULUM IS ACCORDING TO THE LAW OF CONSERVATION ENERGY.
                                                                      OR

PROVE THE LAW OF CONSERVATION WITH 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 At Point ‘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. = m g h.

Energy total = K.E. + P.E

Energy total = 0 + m g h

Energy total = m g h

This shows that at point A total energy is potential energy.

Energy Conservation At Point ‘M’: -

If we release the bob of pendulum from point ‘A’, velocity of bob gradually increases, but the height of bob will decreases from point to the point. At point ‘M’ velocity will become maximum and the height will be nearly equal to zero.
Thus,
K.E. = maximum = ½ mV2 but P.E. = 0.

Energy total = K.E. + P.E

Energy total = ½ mV2 + 0

Energy total = ½ mV2

This shows that the P.E. at point is completely converted into K.E. at point ‘M’.

Energy Conservation At Point ‘B’: -
           
At point M the bob of Pendulum will not stop but due to inertia, the bob will moves toward the point ‘B’. As the bob moves from ‘M’ to ‘B’, its velocity gradually decreases but the 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. = m g h.

Energy total = K.E. + P.E.

Energy total = 0 + m g h

Energy total = m g h

This shows 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. the motion of the bob of simple pendulum is according to the law of conservation of energy.

POWER: -

"The rate of work done of a body is called Power".

AVERAGE POWER: -

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

MATHMATICALLY: -

Power = Work done / time
Power = Work / t
But [work = F d]
Therefore
Power = F d / t

UNITS OF POWER: -

(i)         Watt                             [1 watt = 1joule/sec]
(ii)        Kilo watt                       [1Kw = 1000 watt]
(iii)       Mega watt (Mw)           [1Mw = 106 watt]
(iv)       Horse power                 [1Hp = 746w]








Thursday 27 October 2011

GRAVITATION


Every object in our universe attracts the other object with certain fore towards its center. This force of attraction is known as GRAVITATIONAL FORCE and the phenomenon is called GRAVITATION. This is gravitational force which is responsible for the uniformity or regularity in our daily astronomical life. The whole system of the universe is in order only due to this force. Due to gravitation, the system of our universe is working uniformly and smoothly. A Planet around the earth or around the sun moves in an orderly motion due to gravitation.

NEWTON’S LAW OF GRAVITATION: -

In order to explain the gravitational force between two bodies, Newton formulated a fundamental law known after his name i.e. "NEWTON'S LAW OF GRAVITATION"
Newton’s law of gravitation states that every object in the universe 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 ∞ m1 x m2 ------- (1)
 (2) The gravitational force of attraction between two bodies is inversely proportional to the square of the distance between their centres.

F ∞ 1 / r2----------- (2)
 Combining the above two equations we get

F ∞ m1 x m2 / r2

F = G m1m2 / r2

Where G = universal gravitational constant and in S.I system its value is G = 6.67 x 10-11 Nm2/kg2
MASS OF THE EARTH: -

Consider a body of mass ‘m’ placed on the surface of the earth. Let the mass of the earth is ‘Me’ and radius of earth is ‘Re’.
Gravitational force of attraction between earth and body is
F = G m Me/ Re2
 We know that the force of attraction of the earth on a body is equal to weight the weight of body.
 i.e
F = W
 therefore
W = G m Me/ Re2
 But W = mg
mg = G m Me/ Re2
or
g = G Me/Re2
or
Me = g Re2/G
 From astronomical data:
 g= 9.8 m/s2
 R= 6.4 x 106 m
 G = 6.67 x 10-11 N-m2/kg2
 Putting these values in the above equation.
Me = 9.8 (6.4 x 106)2/6.67 x 10-11

or 




Wednesday 26 October 2011

CIRCULAR MOTION


UNIFORM CIRCULAR MOTION: -

If a body moves in a circular path with constant speed or uniform speed then the motion of the body is said to be "uniform circular motion"

CENTRIPETAL ACCELERATION: -

When a body moves around a circle with constant speed, the direction of its velocity continuously changes.  Due to change in direction, its velocity changes. A changing velocity imparts acceleration in the body.  The direction of this acceleration is always towards the centre of circle. This acceleration is known as “CENTRIPETAL ACCELERATION".
        According to 2nd law of motion
F c = ma c.......... (1)

But

F c = mv2 / r........ (2)

From (1) and (2) we get

ma c = mv2 /r
Or
ac = v2/r

CENTRIPETAL FORCE: -

Centripetal force is defined as the force necessary to move a body in a
circular path and is always directed towards the centre of the circular path.
OR
When a body moves in a circular path with uniform velocity, it experiences a force,
directed along the radius towards the centre of the circle. This force is called CENTRIPETAL FORCE.

MATHEMATICAL REPRESENTATION: -

 Centripetal force depends upon the mass of body, velocity of body and the radius of circular path.


CENTRIFUGAL FORCE: -

When a body of moves around circle, centripetal force acts upon it. According Newton’s third law of motion another force equal to centripetal force but opposite in direction also acts upon it. This force is referred to as CENTRIFUGAL FORCE.

The force acting in the opposite direction of centripetal force is called centrifugal force





Tuesday 25 October 2011

ADVANTAGES AND DISADVANTAGES OF FRICTION - METHODS OF REDUCING FRICTION


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 move on ice, it     becomes difficult to walk due to low friction of ice.
2. We cannot fix nail in the wood or wall if there is no friction. It is friction which holds the nail.
3. A horse cannot pull a cart unless friction furnishes him a secure Foothold.

DISADVANTAGES OF FRICTION: -
 
Despite the fact that the friction is very important in our daily life, it also has some disadvantages 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 REDUCING FRICTION: -

There 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 lubricated by using oils and lubricants of suitable viscosity.

USE OF GREASE: -

Proper greasing between the sliding parts of machine reduces the friction.

USE OF BALL BEARING: -
In machines where possible, sliding friction can be replaced by rolling friction by using ball 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.

Sunday 23 October 2011

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
P = m V
   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 OF MOMENTUM: -
 The law of conservation of momentum states that:
"When some bodies constituting an isolated system act upon
one 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 momentum after collision."

Consider an isolated system of two bodies 'A' and 'B' as shown. The masses of bodies are ma and mb 
MATHEMATICAL REPRESENTATION: -
 Consider two bodies of mass m1 and m2 moving initially with velocities u1 and u2 as shown in the figure.
 Total momentum before collision = m1u1 + m2u2


Let after collision their velocities become v1 and v2 as shown in the figure.



 Total momentum after collision = m1v1 + m2v2
According to the law of conservation of momentum
m1u1 + m2u2 = m1v1 + m2v2