The document discusses the principles of work and energy, including types of energy (kinetic, potential, elastic, chemical, etc.) and their equations. It explains the concepts of conservative and non-conservative forces, the work-energy principle, and the law of conservation of energy. Additionally, it provides examples and related calculations of potential and kinetic energy.

2. CONTENTS
 Principles of Work and Energy
 Work of Some Typical Forces
 Conservative Forces
 Non - Conservative Forces
 Concept of Energy,
 Kinetic Energy
 Gravitation Potential Energy
 ME of Motion
 ME due to Position
 Principle of Work and Energy for a Single Particle,
for a System of Particles
 Principle of Conservation of Energy of ME

3. INTRODUCTION
ENERGY
“It is the fundamental property of a particle or a system
referring to its potential to influence changes to other
particles by imparting work or heat.”
In short, energy is the capacity to do work.
Energy exists in many forms – Mechanical, electromagnetic, electrical,
nuclear, chemical and thermal.
Mechanical energy can be Kinetic Or Potential…..

4. W o r k
Work is a type of controlled energy transfer when one system is exerting
force in a specific direction and thus is making a purposeful change
(Displacement) of the other systems.
Work done on a particle or on a body is equal to the product of the force imparted on it
and the displacement along the line of action of the active force either forward or reverse
direction of motion.
Work = Force x Displacement
Unit of work = 1 Newton x 1 Metre = 1 Joule
It is a scalar quantity.

5. r
r1
r2
r + dr
Fα
dW = F . ds
Let the initial position vector of the particle at any time t be r and after a small time interval dt let its position vector
be r+dr. Therefore the displacement is dr. During the time interval dt it is assumed that a constant force F, inclined at
an angle α with the displacement vector acts.
Then the differential work dW is defined as
dW = F . dS =F . dr
1
2

6. K I N E T I C E N E R G Y
The kinetic energy of an object is the energy
which it possesses due to its motion. It is
defined as the work needed to accelerate a
body of a given mass from rest to its stated
velocity.
Having gained this energy during its
acceleration, the body maintains this kinetic
energy unless its speed changes.
The kinetic energy of an
object is related to its
momentum by the equation:
where:
Ek is momentum
m is the mass of the body

7. POTENTIAL ENERGY
Potential energy is energy which
results from position or
configuration.
The work of an elastic force is
called elastic potential energy.
The work of the gravitational force
is called gravitational potential
energy.
The work of the Coulomb force is
called electric potential energy;
The work of the strong nuclear
force or weak nuclear force acting
on the charge is called nuclear
potential energy.
The work of intermolecular forces
is called intermolecular potential
energy.
Chemical potential energy, such as
the energy stored in fossil fuels.

8. Gravitational Potential Energy
Gravitational potential energy is the energy stored in an
object as the result of its height. The energy is stored as the
result of the gravitational attraction of the Earth for the
object.
The gravitational potential energy of the ball (as shown) is
dependent on two variables - the mass of the ball (m) and
the height (H) to which it is raised.
H
m
Potential Energy = Mass (m) x Height (H) x g ( acc. due to gravity )
= m.g.H
Ram

9. Elastic Potential Energy
Elastic potential energy is the energy stored in
elastic materials as the result of their stretching or
compressing. Elastic potential energy can be stored in
rubber bands, bungee chords, trampolines, springs, an
arrow drawn into a bow, etc. The amount of elastic
potential energy stored in such a device is related to the
amount of stretch of the device - the more stretch, the
more stored energy.

10. EXAMPLES

11. Q & A
Q .1
A cart is loaded with a brick and pulled at constant speed
along an inclined plane to the height of a seat-top. If the mass
of the loaded cart is 3.0 kg and the height of the seat top is
0.45 meters, then what is the potential energy of the loaded
cart at the height of the seat-top?
Ans. 1
PE = m x g x h
PE = (3 kg ) X (9.8 m/s/s) X (0.45 m)
PE = 13.2 J

12. Q & A
Q . 2
If Ram is pushing a 12 N box at a constant speed of 35 m/s and
Shyam is pushing another box weighing 35 N but with the speed
12 m/s. Which of the box has higher Kinetic Energy ?
RAM
SHYAM
ANS .2
RAM’s Box
K.E1 = ½ m v2
= 0.5 x 12 x 35 x 35
= 7350 J
SHYAM’s Box
K.E2 = ½ m v2
= 0.5 x 35 x 12 x 12
= 2520 N
K.E1 > K.E2

13. CONSERVATIVE
FORCES
Illustration :

14. POINTS TO REMEMBER :
1. Conservative Forces are reversible forces, meaning that the
work done by a conservative force is recoverable.
2. When an external agent is applied to change the state of a
system that is also acted upon by conservative force then the
system can be restored to its initial state without using any
other external agent.
3. Each type of conservative force is associated with it a potential
energy.
4. Conservative forces are path independent.
5. The work done by a conservative force can be transformed into
a change in potential energy.

15. Non-Conservativeforce
The work done by a non-
conservative force does
depend upon the path
taken.
EXAMPLE : Friction

16. Conservative force and Potential energy
Potential energy is always associated with a conservative force. It is not defined with respect to a non
conservative
Force.
Potential energy can be expressed as the integral form of a conservative force as
U(x) =- ⨜F(x)dx + U(x0 )
The constant of integration shown in the equation is an arbitrary one showing that any constant can be
added to
The potential energy . Practically it means that the initial or the reference point of computation of
potential energy
Can be set at any convenient point.
The potential energy U(x) is equal to the work necessary to move an object from x0 reference point to
the position
x in the conservative force field.
Differentiating the above equation wrt to x we get
F(x) = - dU(x)
dx
This means F(x) is the negative of the slope of the potential energy curve.

17. Work-Energy Principle for particle
Let us assume that the velocity of travel of a mass for a differential displacement be v, then
dW= F . dr
Integrating the equation
2
1
Therefore, the principle of work-energy can be stated as : the work done due to movement is equal with the
change in Kinetic energy.
Work-Energy Principle for Rigid Body
Total work done by a rigid body will be the summation of work done by the net forces acting at the mass centre
and the work done by the net moment about the mass centre and is represented by the equation.
W= [ ½ m (VC
2)2 - ½ m (VC
2)1 ] + [ ½ IC w2
2 – ½ IC w1
2 ]
Similarly the change in kinetic energy of a rigid body is the summation of change in kinetic energy due to translation
and due to rotation.
ΔΚE = [ ½ m (VC
2)2 - ½ m (VC
2)1 ] + [ ½ IC w2
2 – ½ IC w1
2 ]

18. Principle of Conservation of Energy
The law of conservation of energy states that
the total energy of an isolated system cannot
change—it is said to be conserved over time.
“ Energy can be neither created nor destroyed,
but can be changed into one form to another
form. ”

19. Principle of Conservation of Energy
Let us assume that a particle subjected to a system of conservative forces only
Then,
WC = -Δ P.E
Applying Work-Energy Principle
WC = Δ K.E
Equating the two equations,
Δ K.E = -Δ P.E
Δ K.E + Δ P.E = 0
Einitial = Efinal
i.e. the mechanical energy of the system remains constant if only conservative forces act
on the system.

20. Q. 1
A sphere of mass m and radius r allow to roll down without
slipping along an α inclined as shown in the figure.
Derive the expressions for the velocity for rolling down a
distance s. α
Ans. 1
Mg sin α
Mg cos α
Normal
Reaction
force
Static
friction

21. Power
Power is defined as the rate of change of work done per unit time by the body .
If the total work done during a differential time interval Δt is ΔW, then the average power
can be expressed as,
Pavg = ΔW/ Δt
Pinstantaneous = dW/dt = (F . dS)/dt = F . V