MAHATMA MONTESSORI SCHOOL BABA CBSE

(Affiliated to Central Board of Secondary Education – New Delhi)

Work:
Work is only done when the force acting on an object produces displacement in it in
the direction of force or in the direction of component of the force.
NOTE:
 There must be displacement of the object.
 There must be a component of force in the direction of the displacement.
Work Done by a Constant Force:
The work done on an object by the constant force is defined as the product of the
component of the force in the direction of the displacement and the magnitude of the
displacement.
Work done when the force acts along the direction of motion:
Force F displaces a body through a distance s parallel to the line of action of the force or in
the direction of force. W.D = Force X distance moved in the direction of the force W.D = F S
Work done when the force and displacement are inclined to each other:
Work done = component of force in the direction of displacement x magnitude of the
Displacement ; W.D = F cos θ X s; W.D = F s Cos θ ; W = F . S ;
Work done is the dot product of force and displacement vectors. Work is a scalar
quantity. Dimensions of work : [W] = M L T -2 X L [W] = M L 2 T -2. SI unit is Joule.
In CGS system erg. Unit of work done when a unit of force displaces a body through a
unit distance in the direction of the force.
Absolute unit of work done:
Work done is said to be one absolute unit if an absolute unit of force displaces a body
through a unit distance in the direction of the force.
One Joule:
One joule of work is said to be done when a force of one newton displaces a
bdoy through a distance of one metre in its own direction. 1J = 1N X 1 m ;1J = 1N m;
One erg:
If a force of one dyne displaces a body through a distance of one centimetre in its own
direction. 1 erg = 1 dyne x 1 cm;
Relation between Joule and erg:
1 joule = 1 newton x 1 m ; 1 joule = 10 5 dyne x 10 2 cm; 1 joule = 107 dyne cm;
Gravitational unit of work:
Kilogram metre 1 Kg m = 1 Kg wt = 9.8 N x 1 m ; 1 Kg m = 9.8 J ;
Gram centimetre: 1 g cm = 1 g wt x 1 cm = 980 dyne x 1 cm ; 1 g cm = 980 erg;
Types of work done:
Positive Work done:
Force acting on a body has a component in the direction of the displacement
then the work done is said to be positive work done.
Examples:
 When a body falls freely under gravity
 Horse pulls a cart
 Spring is stretched
Negative Work done:
Force acting on the body has a component in the opposite direction of
displacement, the work done is negative.
 Examples:
 When a body slides against a rough horizontal surface, its displacement is
opposite to the force of friction.
 When brakes are applied to a moving vehicle
 When a body is lifted, work done by the gravitational force is negative.
 When positive charge is moved towards another positive charge force of
repulsion is negative work done.
Zero Work done:
 If a body gets displaced along a direction perpendicular to the direction of the
applied force.
 If no force acts on an object
 If there is no displacement when a force is applied on an object
Exampls:
 Body moving in a circular path, centripetal force and displacement are
perpendicular to each other Work done in pushing an immovable stone is zero.
Unit of Work:
W = FS cos θ = (F cos θ) S = Force x Displacement. The SI unit of force is 1 N and that
of displacement is 1 m. Si unit of work = 1N x 1m = 1Nm or Joule.
1Nm or 1J is the amount of work done when a force of 1 N moves the body through a
displacement of 1 m in the direction of force.
Energy:
Energy of a body is defined as the ability (or capacity) of the body to do work.
NOTE:
 Energy of a body is the stored work, energy is a scalar quantity.
 Energy is measured in the same units as work i.e., joules.
 The dimensional formula of energy is [ML2T-2] i.e., the same as for work.
 Energy may appear in various forms such as mechanical energy, heat energy, sound
energy, light energy etc.
Energy has several forms:
Mechanical energy, Sound energy, Heat energy, Light energy, Chemical energy,
Atomic energy, Nuclear energy, Electric energy, Magnetic energy, Solar energy etc.
Mechanical energy :
Energy produced by mechanical means is called mechanical energy.
It has two forms (i) Kinetic energy (ii) Potential energy
Kinetic energy:
The energy possessed by an object by virtue of its motion is called its
kinetic energy. A moving object can do work. The amount of work done that a
moving object can do before coming to rest is equal to its kinetic energy .
Examples:
 Moving hammer drives a nail into the wood.
 A fast moving stone can break a window pane
 Bullet fired from a gun can pierce a target due to its kinetic energy.
 Kinetic energy of air is used to run wind mills.
 Kinetic energy of a fast stream of water is used to run water mills.
Potential Energy:
Potential energy is the energy stored in a body or a system by virtue of its
position in a field of force or by its configuration.
Examples of potential energy due to position:
1. A body lying on the roof of a building has some potential energy. When allowed
to fall down, it can do work.
 2. The potential energy of water stored to great heights in dams is used to run
turbines for generating hydroelectricity.
Examples of potential energy due to configuration:
1. In a toy car, the wound spring has potential energy. As the spring is released,
its potential energy changes into kinetic energy which moves the toy car.
2. A stretched bow possesses potential energy. As soon as it is released, it shoots
the arrow in the forward direction with a large velocity. The potential energy of
the stretched bow gets converted into the kinetic energy.
3. Due to the potential energy of the compressed spring in a loaded gun, the bullet
is fired with a large velocity on firing the gun.
Different types of potential energies:
Three common types of potential energies are as follows:
1. Gravitational potential energy. It is the potential energy associated with the
state of separation of two bodies, which attract one another through the
gravitational force.
2. Elastic potential energy. It is the potential energy associated with the state of
compression or extension of an elastic (spring like) object.
3. Electrostatic potential energy. The energy due to the interaction between two
electric charges is electrostatic potential energy.
Gravitational Potential Energy:
The gravitational potential energy of a body is the energy possessed by the body by
virtue of its position above the surface of the earth. U = m g h
Conservation and non-conservative forces:
Conservative Force:
A force is conservative if the work done by the force in displacing a particle from one
point to another is independent of the path followed by the particle and depends only on the
end points. Mathematically, we can write WAB (along path 1) = WAB (along path 2)
Work done on the particle along the path 2 from A to B = - Work done on the particle along
the path 2 from B to A i.e., WAB (along path 2) = - WBA (along path 2) we have, WAB (along
path 1) = - WBA (along path 2) or WAB (along path 1) - WBA (along path 2) = 0 or W closed path = 0
Hence a force is conservative if the work done by the force in moving a particle around any
closed path is zero. Examples: Gravitational force, electrostatic force and elastic force of a
spring are all conservative forces.
Einstein’s Mass energy Equivalence:
E = m c2. Mass can be converted in to energy and vice versa.
Principle of conservation of energy:
Energy can neither be created nor be destroyed. It may be transformed from one form to
another. The total energy of an isolated system remains constant. As the entire universe may
be regarded as an isolated system, the total energy of the universe is constant. If the one
part of the universe loses energy another part must gain an equal amount of energy.
Power:
Rate of doing work or rate at transfer of energy. P = W / t or E / t SI unit is W (watt)
1 W = 1 J /s; Scalar quantity. Dimensional formula M L2 T-3 . Bigger units are
measured in Kilowatt . Other unit is measured in Horse Power (HP) ; 1 HP = 746 W ;
Instantaneous Power:
The power of an agent may not be constant during a time interval. The
instantaneous power is defined as the limiting value of average power as the
time interval approaches zero. P = lim ∆w
∆t0 ∆t ;
P = dw / dt ; dW = F. dr ; P = dW / dt ; P = F. dr/dt; P = F.v ;1 Kwh=3.6x106;
Kilowatt hours is also called as commercial unit of electrical energy or BOT
(Board of Trade).
Conservative Force:
A force is said to be conservative if the amount of work done in moving an object against
that force is independent of how the object moves from the initial position to the final
position. A force is conservative if the total work it does on an object is zero when the object
moves around any closed path returning to its initial position. Work done by a conservative
force is recoverable.
Non – Conservative Force:
A force is non-conservative if the work done by that force on an object moving between two
points depends on the path taken between the points. Force of friction is an example of
non-conservative force.
Elastic Potential Energy:
The energy possessed by a spring due to change in its shape is called elastic potential energy
of the spring.
Spring Constant.
Spring constant (or force constant) of a spring is numerically equal to the force required to
produce unit displacement (compression or stretch) in the spring.
Mechanical Energy:
The mechanical energy (E) of a body is the sum of kinetic energy (K) and potential energy (U)
of the body i.e., Mechanical energy , E = K + U
o The kinetic energy (=mv2/2) of a body is always positive because both m and v2
are positive.
o The potential energy may be positive or negative.
o A body may have negative mechanical energy i.e., K + U may be negative.
Law of Conservation of Energy:
The total energy neither increases not decreases in any process. Energy can be transformed
from one form to another: and transferred from one body to another but the total amount
remains the same.
Collision:
A collision is a short-time event and is said to have occurred if tow (or more) bodies
physically collide against each other or even when the path of motion of one particle is
affected by the other.
CONCLUSIONS:
o The linear momentum is always conserved in a collision.
o The total energy is always conserved in a collision.
o The kinetic energy in a collision may or may not be conserved. If kinetic energy
(K.E) is conserved in a collision, it is called elastic collision. If kinetic energy is
not conserved in a collision, it is called inelastic collision.
Elastic Collision:
A collision in which kinetic energy is conserved is called an elastic collision.
Therefore, an elastic collision has the following characteristics:
o The linear momentum is conserved.
o The total energy of the system is conserved.
o The kinetic energy is conserved.
Inelastic Collision:
A collision in which kinetic energy is not conserved is called an inelastic collision.
Therefore, an inelastic collision has the following characterisitics:
o The linear momentum is conserved.
o The total energy of the system is conserved.
o The kinetic energy is not conserved.
Perfectly Inelastic Collision:
A collision in which the two objects stick together after the collision is called a
perfectly inelastic collision.