Class:
form one: Subject:
Physics
Chapter 7
WORK,POWER, ENERGY AND SIMPLE MACHINES
7.1 work
Definition
Work is done when a force causes an object to move in the same
direction that the force is applied.
We therefore measure work by
measuring the applied force and distance covered.
Work=force applied x distance
moved in direction of the force.
W=fd
The unit of work is joule(j).Finance
Only
Example 7.1
If you have to pull with a force
of 50N to move a create steady 3m in the direction of the force, find the work.
Solution
Work= f x d
= 50Nx3m= 150Nm = 150N
Example 7.2
A car weighing 1000kg and
traveling at 30m/s stops at distance of 50m decelerating uniformly.
What is the force exerted on it
by the brakes? What is the work done by the brakes?
Solution
Given
Initial speed, u =30m /s , Final speed, v - 0 (The car stops) , Acceleration, a- ? Distance, s = 50 m
We know that;
So, (0)2=(30)2+2xax50
100a= -900
a=-900/100
Thus, Acceleration, a= -9m /s
The force exerted by the brakes
can now be calculated using the formula
F= mxa
Here, Mass, m = 1000 kg And, Acceleration, a= -9m /s (Calculated
above)
So, Force, F =1000x(-9)
F=-9000N
The work done by the brakes can
be calculated by using the relation: W = Fxd
Here, Force, F= 9000 N Distance,
d = 50m
So, Work done, W= 9000 x 50 J
= 450000 J
= 4.5 x 105 J
Thus, the work done by the brakes
is 4.5 x 10 joules.
7.1.1 Work done against the gravity
The amount of work done is equal
to the product of weight of the body and the vertical distance through which
the body is lifted.
Now, Work done in lifting a body
= Weight of body x Vertical distance
W=m x g x h
where; W = work done.
m = mass of the body. g = acceleration due to gravity. and h = height through which the body is
lifted.
Example 7.3
Calculate the work done in
lifting 200 kg of water through a vertical height of 6 metres (Assume g = 10
m/s?).
Solution
Given: m=200kg h=6m, g=10m/s w=?
W=mgh
W = 200kg x 10m /s x 6m
W=12000j
7.2 power
Definition: Power is the rate at
which work is done or the rate at which energy is transferred from one place to
another.
Mathematically, it can be denoted
as follows;
p=power w=work be time
Unit of power
The SI unit of power is Watt in
honor of the Scottish mechanical engineer, James Watt, Watt is most famous for
inventing an improved steam engine.
W= j/s
Other units of power are
Kilowatt (Kw) =1000W Megawatt
(Mw) =106w Horsepower (Hp)
=746W=750W
Example 7.4
An elevator with an operator weighs 5000 N. If it is raised to a height
of 15.0 min 100s, how much power is developed?
Solution
Given;
F = 5000 N s = 15.0m t = 10.0 s P = ?
W =FxS =5000N x15.0m =75000 J
P =W/t = 75000J/10s = 7500w
Example 7.5
The power expended in lifting an 825N girder to the top of a building
100 m high is
10.0 hp. How much time is required to raise the girder?
Solution
Given: F = 825 N d = 10m P = 10.0 hp
w = Fxd
W =825x10m =8250J
P=10hp =10x7461 =7460
P = w/t
T=w/p =82501/7460w = 1.11 seconds
Example 7.6
The mass of a large steel wrecking ball is 2000 kg. What power is used
to raise it to
height of 40.0 m if the work is done in 20.0 s? (g=9.8m/s?)
Solution
Given:
m = 2000 kg d = 40.0m t= 20.0 s g=9.8m/s?) P=?
W =mgh =2000kg x40m x9.8m /s2=784000J
P=W /1=784000/ 20s =39, 200W =39.2Kw
7.3 Energy
Definition: Energy is the
ability to do work.
Energy transfer is needed to
enable people, computers, machines and other devices to work and to enable
processes and changes to occur.
Scientists have learned how to
change energy from one form into another to make our lives more comfortable.
7.3.1 Forms (Types) of energy
a) Chemical Energy
Food and fuels like oil, gas,
coal and wood, are concentrated stores of chemical energy.
b. Electrical energy
Electrical energy is produced by
energy transfers at power stations and in batteries
c. Mechanical energy
Mechanical energy is the sum of
potential energy and kinetic energy that is the energy associated with the
motion & position of an object.
There are different forms of
energy. All forms of energy are grouped into two main categories.
a) Kinetic energy. That's energy of motion.
b) Potential energy. That's energy stored in an object due to its
position.
1. Potential Energy
It is the energy stored in an
object and is measured by the amount of work done.
Examples of potential energy
a) Stretched rubber band
b) A raised weight
c) A river water at the top of
water fall
"d) The stretched bow
Mathematically, it denoted as follows:
Potential energy =mgh
M=mass of the object in kg h= height in meters , g acceleration due to the gravity
Example 7.7
A body of mass 4kg is lifted from
the ground and placed at table 5m high from the ground. Calculate the potential
energy stored in the body? (Useg=10m/s).
Solution
M= 4kg; h =5; mg=10m/s'; P.E=?
P.E = mgh
P.E =4kg x10m /s2x5m
P.E = 200J
Elastic potential Energy
Another common potential energy
is elastic potential energy, sometimes called strain.
The amount of elastic potential
energy stored in the spring depends on
a) The force applied
b) The a distance moved
. Elastic Potential energy=1/2FX
F= force in N
X= extension of spring in m
Therefore the elastic potential
energy can be obtained as follow:
EPE = 1/2 kx2 where k is spring constant
Example 7.8
A force of 100N causes a spring
to extend by 40cm. Calculate the energy stored in the spring?
Solution
Given: F=100N x= 0.4m EPE = ?
EPE= 1/2x100Nx0.4= 20j
2- Kinetic Energy
Any moving body has kinetic
energy (K.E.) and the faster it moves, the more K.E. it has
So that the energy in motion is
known as kinetic energy.
Equation of kinetic energy
K.E= 1/2mv2
Example 7.8
A bullet of mass 12g travels at
415m/s. find k.E.
Solution
Given
M=12g = 0.012kg v= 415m/s K.E=?
K.E= 1/2mv2
= 1/2x0.012x(415)2
7.3.2 Sources of Energy
i) Heat energy: Used for cooking food, warming up, etc.
in) Energy from fuels: Used for running cars, buses, etc.
lil) Electric energy: Used for lighting bulbs and tubes, and to run
radio, television and household appliances.
Definition
A source of energy is one which
can provide adequate amount of energy in a convenient form over a long period
of time.
Types of energy sources
All sources of energy can be
categorized into two main parts:
a) Non-renewable sources of
energy and
b) Renewable sources of energy.
