ENGINEERING SCIENCEBB101

TOPIC 4: ENERGY

CONSERVATION OF ENERGYThe 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.

KINETIC ENERGYKinetic energy of an object is the energy due to its

motion.The SI unit : kgm2s-2 or Joule or JKinetic 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 = massv = velocity

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

POTENTIAL ENERGYThe 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 = mghm = massg = gravitationalh = height

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

The Principle of Conservation of EnergyThe 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.

Potential energy = mgh 0Kinetic energy = 0

Potential Energy =Kinetic Energy mgh 1 =1/2 mv 2

(if h 1 =1/2 h0 )

Potential Energy =Kinetic EnergyKinetic Energy=1/2 mv 2

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

ExerciseA 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.

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 fall2. meter under free fall3.Right after its touched the ground

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.

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.