1. ENGINEERING SCIENCE
BB101
TOPIC 4: ENERGY

2. CONSERVATION OF ENERGY
 The energy of a body is a measure of its ability to do
work
 The SI unit for energy is joule ( J )
 Energy can exist in various forms ; potential energy ,
kinetic energy, heat energy, electrical energy, sound energy
and nuclear energy.
 When energy changes from one from to another, work is
done.

3. KINETIC ENERGY
 Kinetic energy of an object is the energy due to its motion.
 The SI unit : kgm2s-2 or Joule or J
 Kinetic energy is the energy possessed by a moving
object. Only moving object possess kinetic energy.
 Consider an object moves at a distance , s with constant
acceleration , a.
 The formula for kinetic energy is Ek=1/2mv2
 m = mass
 v = velocity

4. Example:
Calculate how much kinetic energy is required for 80.0kg
man accelerate from rest to3.5ms-1 .
solution
Ek = 1/2mv2
= ½(80)(3.5) 2
= 490J

5. POTENTIAL ENERGY
 The potential energy of an object is the energy stored in
the object because of its position or state.
 The gravitational potential energy is equal to the work
done to raise an object to a particular height.
 Work done, W = F x s
 Gravitational potential energy, Ep = mgh
 m = mass
 g = gravitational
 h = height

6. Example:
A package of 5 kg is lifted vertically through a distance
10m at a constant speed. Taking the acceleration due to
gravity to be 9.81ms-1 , what is the gravitational potential
energy gained by the package ?
solution
Ep =mgh
=(5)(9.81)(10)
= 500J

7. The Principle of Conservation of Energy
 The principle of conservation of energy states that
energy can be converted from one form to another, but the
total energy in an isolated system never changes.
 Ex: When a ball mass , m kg fall from a height of h
meters to the ground, it loses its gravitational potential
energy which is changed into kinetic energy of
motion.
 If air resistance is ignored , the kinetic energy of the
ball just before it hits the ground is equal to its
potential energy at the beginning.

8. Potential energy = mgh 0
Kinetic energy = 0
Potential Energy =Kinetic Energy
mgh 1 =1/2 mv 2
(if h 1 =1/2 h0 )
Potential Energy =Kinetic Energy
Kinetic Energy=1/2 mv 2

9. Example:
A jackfruit falls from a height of 22m. What is the
velocity of the jackfruit just before it hits the ground ?
[Assume that g = 9.81ms-1 ]
solution
kinetic energy of the jackfruit just before it hits the
ground = maximum potential energy of the jackfruit.
1/2mv2 = mgh
v2 = 2gh
= (2)(9.81)(22)
= 431.64
v =20.8ms-1

10. Exercise
 A car with a mass of 1200 kg moves with a velocity of 25
m/s. Calculate the kinetic energy possessed by the car.
 Jacob, the former platform diver for the Jumbo's Circus,
had a kinetic energy of 12 000 J just prior to hitting the
bucket of water. If Jacob's mass is 40 kg, then what is his
speed?
 A ball of mass 2 kg falls from a height of 1.25 m. Calculate
the gravitational potential energy possesses by the ball.
 A lift with its passengers has a total mass of 1350 kg.
Calculate the gravitational potential energy gained by the
lift by moving upwards to a height of 25 m.

11.  An object of 30 kg mass was lifted as high as 3 m from
the ground and was let to fall under the gravitational
reaction. Calculate the gravitational potential
energy and the kinetic energy possess by the object
under these situations:
1.Before it was let to fall
2. meter under free fall
3.Right after its touched the ground

12.  A cutter is used to cut a rim of paper. What is the
length of the knife of the cutter if the force used is 240
N with an angle of 25o? The work is done 20 J.
 An escalator is used to move 20 passengers every
minute from the first floor of a department store to the
second. The second floor is located 5.2 m above the
first floor. The average passenger's mass is 54.9 kg.
Determine the power requirement of the escalator in
order to move this number of passengers in this
amount of time.

13.  A pendulum bob with a mass of 15 g is initially at rest
at position A. It is released and starts swinging. Its
lowest position is at position B which is 10 cm lower
than position A.
1.State the transformation of energy when the pendulum
bob swings from position A to position B.
2.Calculate the speed of the pendulum bob at position B.