Engineering basic Science.pdf

7/28/2019 Engineering basic Science.pdf

1/10


2/10

2

Examples

a. 20 micrometer =1000000

20metre = 20x10

-6metre =20m

b. 40 gigasecond = 40 000 000 000 second = 40x109 second = 40Gsc. 500 millimetre =

1000

500metre =500x10

-3metre =500 mm =0.5 m

Exercise: Fill in the answers in the table below, one answer has been filled for you:Number and units of measure Standard powers of 10 or

Scientific notationshort form of prefix and unit ofmeasure

1100 metre 1.1x103m 1.1 km

0.000005 metre

1654 000 second

0.008 ampere

0.0000000092 metre

Dynamics

DefinitionVector

A vector is a quantity that is specified by two dimensions one of which is magnitudeand the other being the direction

Example1. The (x, y) coordinates in mathematics specify a location of point completely

by giving its magnitude and its direction.2. (-x, y) is another point absolutely specified by the two quantities Magnitude

and direction.3. If a police officer was chasing after a thieve and he disappeared, he asks for

the direction towards which the thief went and the means of transport he was

using, whether he was using a car or bicycle or running on foot. The last

information gives him the rate of covering of distance with respect to time.

ScalarIs a unit which is specified in one dimension in terms of magnitude only. In other

words only one quantity of measure is given.

ComparisonsQuantity Magnitude Direction Type

Speed range of a new car 220 km/hr None scalar

Velocity of wind in Mahe 15 km/hr North Vector

Mass sugar 10kg None Scalar

Weight of sugar on boys shoulder 10kg x 9.8=98N

Shoulder Vector

Weight of sugar on an astronaut at a certain point from theearth heading towards the morn

0 N Astronaut Vector

Acceleration 100m/s2

Forward Vector

Deceleration 100ms-2

Backwards VectorForce of vehicle wheel on the road 1kN Backwards Vector

Force of ground friction on the wheel 1kN Forward Vector

Definition of speed, velocity and accelerationQuantity Unit of

measure

definition

Speed m/s The distance travelled by a body in unit time or the rate at which distance iscovered with respect to time

Velocity m/s the rate at which distance is covered with respect to time in a specified


3/10

3

direction

Acceleration m/s2

The rate at which the velocity changes with respect to time

WavesWaves are caused by energy that changes from one form to the other at a point.

Examples of waves

Wave

type

Cause Effect

Waterwaves

Kinetic energyfrom a falling

stone or

disturbance

Spreading motion of water outward from the point of incidence. Thepattern of motion on the surface of water is wavy or curly or undulating

because of the following reasons: before the stone falls on water, water

particles were balanced by the container and the atmospheric pressuremaking water to be evenly distributed. When a stone falls on the surface

of water it exerts an excess force in addition to the atmospheric pressure

in that area. This force pushes water down but the ground opposing forcecauses the water in the pressed area to spread side ways. On the sidesthere are other water particles that resist the sideways motion as a result

the whole area pushes water up since the atmospheric pressure in the

area adjacent to the point where the stone hit is less than the pressureexerted by the stone plus the atmospheric pressure at the point of

incident. This generates the peak of the 1st wave. This peak is raised

above the normally water level and hence has potential energy which

causes pressure on the sides and generates another ripple. Hence manyripples are developed because of high pressure- low pressure areas along

the surface of the water.

Sound

waves

Kinetic energy

of thevibrating

sound

instrument

The effect is the same as above the only difference is that it only involves

air instead of water and that air is all over hence does not have a visiblesurface like water. The waves then spread in all directions as areas of low

and high pressure of air or compression and rarefactions.

Electro-magnetic

waves

Flow ofcurrent in a

conductor

A conductor of wire carrying current is surrounded by magnetic field. Ifthe current in the conductor is changing this is like agitation of water,

the surrounding magnetic field change in the like pattern. This energy istransmitted as a combination or interaction of electric and magnetic wave

through free space from the source of the disturbance. Speed of theseelectromagnetic waves i s 3x10

8m/s or 300m/s.

a

Sound wave vibrations

Electric or magnetic wave

only one of them shown ifthey are combined then oneof them is at 90 plane with

the other

Rarefaction Compression


4/10

4

The wave has the following properties

1. Wavelengththis measures the distance that it takes for a particular wave torepeat its pattern. It the shortest distance between any two identical points

along the wave in which the particles are in the same phase of their oscillation.

It is measured in metres.

2. Frequencythe number of complete waves forms that pass a given fixed pointin one second. It is the total number of wavelength that are produces in onesecond or the number of complete cycles that are made in one second.

Frequency is measured in Hz3. Amplitude shown as a in the diagram- the maximum displacement of any

particle from its mean position.4. Velocity the speed with which its outline is travelling in the direction of the

wave. V= f

5. Periodthe time taken to oscillate through one cycle. Period, T=f

1and its

measured in seconds. Hence V =T

lm/s

6. There are two main categories of waves namely, electromagnetic (light, radio,etc)which can travel through a vacuum and dynamical (sound, water, wavesetc)which can travel only through a material medium

7. All waves can be reflected just like mirrors reflect light or refracted i.e. its rayscan bend within or inside the second mediums when they are beamed from

one medium to the other in other words refraction is the change of velocity as

the wave pass from one medium to the other.

Sound- is pressure changes in an elastic medium, these pressure changes can travelthrough gases, liquids and solids. Audible Sound occupy the frequency range 15Hz to

20 KHz. Sound travels at different speed in different mediums; 335 m/s in standardatmospheric conditions, 1220 m/s in lead, 4880m/s in glass and 5190 m/s in

aluminium.

Momentum

An impelling force that is defined as: The product of mass and velocity.

Any moving body gather a forward propelling force or momentum.

Momentum = mass x velocity

= m [kg] x v [m/s]

= mv [kg m/s]

kg m/s = N for Newton

ReflectionRefraction


5/10

5

Sir Isaac Newton

The man who studied and produced the Law of motion. He defined three laws of

motion. These areLaws Mathematical Meaning

Law1

Every body continues to be in a state of motion with uniform velocity, wherevelocity can be any values {V, 0, +V}, unless acted upon by the resultantforce

Law

2

F = ma Change of momentum per second is proportional to the resultant force on the

body and the change of momentum takes place in the direction and sense ofthe resultant force

Law

3

Faction =

Freaction

Action and reaction are always equal and opposite i.e. if body A exerts a force

F, on body B then it follows that body B is exerts a force of equal magnitude

and direction but opposite sense to F.

The absolute unit of force is Newton. A Newton is the force which cause a mass of

1kg to accelerate at 1m/s2.

Law II

Momentum = mv

Change in momentum = mvbmva

Butt

mumv - Fresultant

)(t

uvm

-

Fresultant

giving F ma F = (constant) x ma [kg m/s2]

But we can choose a constant to be 1, then the units of measurement becomes

Newton instead and the equation becomesF = ma

Law III

Law I

Earth pull

on the body

or gravity

Reaction or bodysown pull on the earth

If this reaction or opposing

force is Zero the bodykeeps moving with constant

forward velocity

Constant forward velocity


6/10

6

AccelerationIs the rate of change of velocity and is a vector quantity. An easy to understand

example of acceleration is the operation of a motor vehicle. The car is said to be

accelerating if the velocity is changing. Example of vehicle acceleration are given

belowVelocity/speed Gear effect

From 0 km/ to 10 km/hr 1 AccelerationFrom 10km/hr to 25 km/hr 2 Acceleration

From 25km/hr to 40km/hr 3 Acceleration

From 40 km/hr to 60km/hr 4 Acceleration

From 60km/hr to 120 km/hr 5 Acceleration

Travelling at 120km/hr 5 No acceleration oracceleration =0

Reaching the destination applying brakes to

stop the vehicle

Change down from 5 to

1 in steps

Deceleration or negative

acceleration

Acceleration is measured in SI standard, in m/s2.

Weight is the force that is exerted by the pull of the earth (or any large mass) on a

body of a certain mass. It is equal to the product of the mass of that body that is being

pulled and the acceleration due to gravity of the earth (or large mass).Mass is the numerical measure of the inertia or resistance of an object to change in itsstate of motion .

Work

Work is the total effort done by a force, F, in moving an object for a distance ofs

metres. Its mathematical definition is given below:

Work done by the force = Force applied to the object x distances moved by the

object in the direction and sense of the force

W = Fs [Nm]

ExamplesForce Direction of effort Distance moved

by the bodyWorkdone

Man pushing a wall In line with the applied

force

Zero Zero

Man balancing a scaffold so that it does

not move

In line with the applied

force

Zero Zero

Pull of the earth on a satellite as itmakes circular orbits around the earth

Perpendicular to themovement of body

Many km Zero

A stationary boy holding a kite string asthe kit move

Perpendicular to themovement of kite

Some meters Zero

A book slides as the table is pushed Perpendicular to the

movement

Zero (book

stationary)

Zero

20N weight stone falls down 2m In line with the applied

force

2m +40J

30 N Friction resistance on a booksliding on a table as book moves 3m

Same direction butopposite sense

3m -90J


7/10

7

Joules1 joule is the work done by a force of 1 N when it moves a distance of 1 m in the

direction and sense of the force. Joule is the SI unit of Work.

PowerPower is the rate of doing work.

Mathematical,

Power =workdototakentime

forcebydonework

P =][sec

][

ondst

JoulesW

1 watt (W) is the rate of working when one of joule of work is done in 1 second.

Energy

Energy is the ability to do work. If a body has the ability to do some work it hasenergy. The work done is a measure of how much energy has been transferred or

interchanged between two bodies. The energy that is lost by one body is gain by theother body that receives it.

We say a body can do work when it has energy.

There are many forms in which energy can exist in a body and forms of transfer also.The forms of energy are listed below.Form of

energy

Expansion

Kinetic The energy that a body possesses when in motion. Change in the bodys K.E. =workdone by the forces on the body. If work done is 40J then the body gained 40J K.E. K.E

is also = mv2

Potential Energy possessed by the body by the reason of its position above the ground level.

Sometimes called gravitational potential. P.E. increases but its sign is ve, when a bodymoves up and decreases when the body moves down towards the earth

W=20N

Work done by force of gravity

to bring the stone down= 20N x 2 = 40N

2m

W=10N W=10N

2m

Work done by the effort to lift

the block to a hight of 2m= 10N x 2 = 20N in both cases

Block

Friction = 10N

Effort = 20N

5 m

Work done by

effort = +100J

Work done byfriction = -50J


8/10

8

Internal Friction and sometimes sound are internal energy of a body

Elastic

potential

The energy possessed by a stretched spring or elastic material which has the elastic

properties that pulls it back on release.

Heat The energy supplied by hot objects

Chemical The energy released by chemical action or chemical reaction

Radiant The energy released by radiation

Electro

magnetic

Electrical energy from the power supply that generate voltage which is as a result of

electron current flow. MagneticNuclear Energy produced by nuclear reaction

Principle of conservation of energy

There is no change in the total energy in the universe. Energy is only being transferred

from one form to the other. As work is being done by the system one body gainenergy and while the other loses the same amount of energy to the body that receives

energy. Energy cannot be created or destroyed.

Energy transfers

System Originalenergy

Energytransfer

Final state

A bullet fired with 10J of energy

into a block of wood and is

embedded.

Kinetic =

10J

Friction =

-10J

KE=0, Friction = 10J

Water of weight 5N at a height of30M on a water fall.

PE = 150J KE =150J At the bottom KE=0 PE = 0 Reaction= 150J

Electric iron 120J as a lady ironscloth 20J

Chemical =20J

Electrical=120J

KE = 20JHeat =

120J

Cloth and environment received heat=120J and reaction force received =

20J

Engine rotation KE Heat Motion and heat

Electricalenergy Heater Element

converts electrical intoheat energy

Heater system

Electrical energy tocharge batteries

Batteries convert

electrical into chemical

Batteries convert their

stored chemical energyinto electrical

Electrolysis

processelectricalinto chemical and

heat

+V -V


9/10

9

Efficiency

Is the ratio of useful power output to overall power input. Example if the car engine is

supposed to turn the wheel and drive the vehicle forward and the input chemicalpower is 100J while the output power that actually drives the engine forward is 75J

the other 25J is lost as heat energy. Then efficiency is the measure of useful energyconversion

= 75/100 = 75%

STATICS

A force is a vector because it has magnitude and direction

As a revision determine if the following quantities are scalar or vectorQuantity Vector or scalar Quantity Vector or scalar

Acceleration Time

Energy Density

Displacement Distance

Coefficient of friction Work done

Electric current Volume

Weight

Representation of force as a vector

A vector has magnitude and direction. It can be represented by a straight line as

follows:1. The length of the line represents to scale, the magnitude of the quantity

2. The direction of the line is parallel to the line of action of the forceExamples

Electric

Motor

Electric motor converts electrical tomechanical energy

Electric

Generator

Electric generator convertsmechanical to electrical energy

Electricalpower output

a

b

F =force of gravity = mg

F

O

A

B

Force OA = OB + BA

P

W

T


10/10

10

1. The first diagram shows one force represented in terms of magnitude and direction.

2. The second diagram above shows that one force acting in a certain direction can be

broken down into to components one acting in the x- direction and one in the y-

direction. This is called resolution of a force into its components.

Parallelogram of forces

To find the resultant of two forces P and Q1. If we have scalar quantities like 5kg of mass and 10 kg of another mass we can

calculate their total when put together = 5 kg +10 kg = 15 kg2. And if we have two forces acting together in the same direction we can simply

add their effect. Like

3. But if we have two forces acting in different directions simple addition is notpossible. But a different approach can be made as shown below.

A parallelogram of forces can be drawn as shown on the right hand side. R is theresultant of the two forces Q and P. If P and Q are drawn accurately and

proportionally, using the correct directions then R can be measured aftercompleting the parallelogram, to give the resultant force. Also mathematical

calculations can be performed to come up with the same answer. If Q is right

angled then Pythagorass theorem can be used to find the resultant.

The resultant of two forces acting at an angle oq between them can be found by

completing a parallelogram out of the two forces magnitude and direction, with

the diagonal between the two forces giving the required resultant.

Triangle of forces

The diagram below shows three coplanar forces (forces acting on a common plane or

same layer) act on a body and keep it in equilibrium, then the forces can berepresented in terms of magnitude, direction and sense to form a triangle. The

arrangement of which must be such that the line directions form a continuous flow inone direction around the triangle. The resultant triangle is called the triangle of forces.

It simplifies calculations involving balanced forces.

m = 30kg

F=mg=300N

100N

-30N

Resultant = 300N-300N = 0 N

Resultant = 100N-30N = +70N

P

Q

P

QR

Engineering basic Science.pdf

Documents

Transcript of Engineering basic Science.pdf