Jamb physics tutorial S01

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INTRODUCTION

Welcome to the first series of this Jamb physics tutorial we will be starting off this jamb physics tutorial series by first looking at MEASUREMENT AND UNITS. This is probably the question you will see first before any other.

Grab your writing material (Biro and jotter). Also, make sure you get a glass of chilled fruit drink or water to refresh yourself as we start up with this Jamb physics tutorial series. 

AIM OF THIS TUTORIAL SERIES

In this Jamb Physics Tutorial series one we will achieve the following objectives:

  • Why measurement and units
  • What Fundamentals and Derived quantities with their S.I units
  • Know the Prefix of S.I units and their factors
  • Understand physical dimension
  • Know how to convert derived units to their dimensions
  • Know how to use temperature dimension(CHECK OUT EXAMPLE 5)
  • Measurement of length (know how to read vernier calipers and micrometer and also their accuracy)
  • Measurement of mass
  • Measurement of volume
  • Lastly, you will take a short quiz based on this topic to be sure that you are 100% ready for it

For those of you, that feel you are done this topic, you can jump right ahead to take the quiz which is at the end of the article by clicking the button below.

Mind you if you fail any question I recommend you come back to read this enriched write-up

WHY MEASUREMENTS AND UNITS?

Measurement and units is one of the rudimentary topics in physics. This is because without measurement there is no physics. Studying physics involves using quantities which are quantified by different measuring devices for example, Ruler for length, the barometer for pressure.

Units is a unique name we assign to measures of a particular quantity.

We have two types of quantities in physics:
1.Fundamental Quantities

Fundamental quantities are physical quantities which other quantities depend on for their definition, that is, they are the basis for which all other quantities are built on. In other words, fundamental quantities can exist alone and still make sense.

2.Derived Quantities

Derived Quantities are physical quantities which depend on fundamental quantities for their definition. In other words, derived quantities are gotten from fundamental quantities. 

Below shows some examples of fundamental quantities and derived quantities and their S.I units,

FUNDAMENTAL QUANTITIES
S.I UNITS

MASS

Kilogram (Kg)

LENGTH

Metre (m)

TIME

Second (s)

CURRENT

Ampere (A)

AMOUNT OF SUBSTANCE

Mole (mol)

LUMINOUS INTENSITY

Candela (Cd)

TEMPRATURE

Kelvin (K)

DERIVED UNITS
DERIVATION/FORMULA
SI UNITS

AREA

Length x breadth

m2

VOLUME

Length x breadth x height

m3

DENSITY

Mass / volume

Kg/m3

FORCE

Mass x acceleration

Kg.m/s2(Newton)

ENERGY or WORK

Force x distance

Joule

POWER

Workdone / time

N.m/s (watt)

MOMENTUM

Mass x velocity

Kg.m/s

MOMENT

Force x perpendicular distance

N.m

PRESSURE

Force / area

N/m2

WEIGHT

Mass x acceleration due to gravity

Newton

ELASTIC CONSTANT

Force / extension

N/m

STRESS

Force / Area

N/m2

VELOCITY

Displacement / time

m/s

ACCELERATION

Velocity / time

m/s2

ELASTIC CONSTANT

Stress / strain

N/m2

Prefix of S.I units

The prefix of S.I units is a method used by students, scientist, and engineers to represent extremely large or extremely small values.

For example, if the mass of a spec of dust was measured to be;

mass of dust = 0.000000001 g

imagine writing that or saying it out “zero point zero zero zero zero zero zero zero zero one gram” it’s quite odd.

However, Scientist and engineers decided to come up with a system of representing this using prefix

Let’s write out the mass in the standard form

mass = 1 x 10^{-9} g

Leaving it in this format makes a lot of sense.

Now, using the prefix system; 10^{-9} has a prefix of nano-

Therefore, students, scientist or physicist can now write the mass as

mass = 1 nanogram

Now it looks more “tushed” to write and to pronounce

You can check out other factors and their corresponding prefix below

Measurement and units
The dimension of Physical quantities

The dimension of a physical quantity is simply how that quantity is related to the 7 fundamental quantities. Most textbooks will say 3 important fundamental quantities which are mass, length and time.

In the above write up, we were made to know that derived units are gotten from the combination of two or more fundamental units.

However, we must know how to represent the fundamental unit with the correct letters.

Mass is represented with M

Length is represented with L

Time is represented with T

Temperature is represented with θ

Current is represented with I

Let’s work with some examples:

Example 1: Find the dimension of Area.

We have two ways of tackling this:

1. Via the definition of the physical quantity.

2. Via the unit of the physical quantity.

we will apply these two methods to this question

Via method 1;

The area is defined as length x breadth since both quantities are used to measure length.

Area = L x B = L  x L =  L^{2}

via method 2;

The unit of area is  m^{2}

since m indicate meter which is used for measuring length we can replace it with L, making it L^{2}

Example 2: We will look at the physical dimension for density

Using the definition method

Density = \frac{mass}{volume}

mass can be represented as M

While volume is defined as Length x Breadth x Height. Which can be represented by a dimension of L cubed, L³

Therefore, Density =\frac{M}{L^{3}}

Example 3: Let’s repeat this for velocity

using the unit method, the unit of velocity is in m/s

since m indicates Length(L) and seconds indicates time(T)

velocity=\frac{L}{T}

Example 4: What does x,y,z represent for acceleration in M^{x}L^{y}T^{z}

Going with the definition of Acceleration: acceleration is the rate of change of velocity with time.

Acceleration = \frac{Velocity}{time}, but velocity = \frac{L}{T}

Replacing velocity with its dimension gives:

Acceleration = \frac{(L/T)}{T}

simplifying the expression gives: Acceleration = \frac{L}{T^{2}}

writing it out using the laws of indices

Acceleration = LT^{-2}

comparing it with M^{x}L^{y}T^{z};

LT^{-2}=M^{x}L^{y}T^{z}

Since the left-hand side of the equation do not have M, we can say that the power of M in the right-hand side of the equation is 0, Therefore;

x = 0

The power of L in the right-hand side of the equation is 1, Therefore;

y = 1

The power of T in the right-hand side of the equation is -2, Therefore,

z = -2

x = 0, y = 1, z = -2

Example 5: Let us find out the dimension of specific heat capacity

specific heat = \frac{Heat energy}{mass * temperature change}

c = \frac{Q}{Mθ}

since the dimension of Heat energy is the same as work or energy, therefore;

Let us do the dimension for energy;

energy/work = force x distance

energy/work = \frac{ML}{T^{2}} x L

energy/work = \frac{ML^{2}}{T^{2}}

going back to the specific heat

c = \frac{ML^{2}}{T^{2}} / Mθ

The mass term will cancel out giving us

c = \frac{L^{2}}{θT^{2}} or {L^{2}T^{-2}θ^{-1}}

DERIVED UNITS
DERIVATION/FORMULA
Physical Dimension
AREALength x breadthL2
VOLUMELength x breadth x heightL3
DENSITYMass / volume \frac{M}{L^{3}} or ML^{-3}
FORCEMass x acceleration \frac{ML}{T^{2}} or MLT^{-2}
ENERGY or WORKForce x distance \frac{ML^{2}}{T^{2}}or ML^{2}T^{-2}
POWERWorkdone / time\frac{ML^{2}}{T^{3}}or ML^{2}T^{-3}
MOMENTUMMass x velocity \frac{ML}{T}or MLT^{-1}
MOMENTForce x perpendicular distance\frac{ML^{2}}{T^{2}}or ML^{2}T^{-2}
PRESSUREForce / area \frac{M}{LT^{2}}or ML^{-1}T^{-2}
WEIGHTMass x acceleration due to gravity  \frac{ML}{T^{2}} or MLT^{-2}
ELASTIC CONSTANTForce / extension  \frac{M}{T^{2}} or MT^{-2}
STRESSForce / Area \frac{M}{LT^{2}}or ML^{-1}T^{-2}
VELOCITYDisplacement / time \frac{L}{T}or LT^{-1}
ACCELERATIONVelocity / time \frac{L}{T^{2}}or LT^{-2}
YOUNG’S MODULUSStress / strain  \frac{M}{LT^{2}}or ML^{-1}T^{-2}
Measurement of length

Devices used for measuring lenght includes:

  • Metre rule
  • Calipers
  • Micrometer screw gauge

The  Metre rule has an accuracy of up to 0.05cm or 0.5mm

The Vernier calipers has an accuracy of up to 0.01cm or 0.1mm

The Micrometer has an accuracy of up to 0.001 cm or 0.01mm

The Metre rule is used for measuring short distances such as the length of your book while cylindrical objects can be measured with the aid of calipers and metre rule.

The vernier calipers is used to measure the diameter of rods and that of internal diameter of tubes and depth of cavities.

The micrometer is used for measuring diameters of small objects like wires,small balls.

Micrometer is used when greater accuracy is expected.

The vernier caliper

The vernier calipers consist of two scales:

  • Main scales
  • vernier scales
Vernier caliper

Example 1; Read the vernier caliper below

Jamb Physics Tutorial

The vernier calipers main scale is calibrated in cm, from point 0 to the next point which is 0.1 cm.

To read off the main scale, the point where the zero mark of the vernier scale coincides with the main scale is the reading of the main scale.

Therefore, point 0 of the vernier scale is between 1.1 cm and 1.2 cm on the main scale. we will use the smallest value which is 1.1 cm because this value is to the immediate left of the vernier 0 scale.

The vernier scale reading is where the vernier scale coincides with the main scale. From our diagram above, it coincides at point 6 which should be taken  as 0.06 cm

final reading= main scale + vernier scale

final reading =1.1 cm+0.06 cm = 1.16 cm 

Example 2: (Jamb physics 1994)

The main scale reading is 1.3 cm. This was gotten by checking the point on the main scale to the immediate left of the 0 mark of the vernier scale.

The vernier scale coincides with the main scale at vernier mark 9. Therefore, the vernier scale reading is 0.09 cm

Therefore, final answer = main scale reading + vernier scale reading

answer = 1.3 + 0.09 = 1.39 cm

explanation

Example 3: (Jamb 2003)

Jamb physics tutorial

I believe you should be able to read off the vernier caliper here. Anyways we will do this one together before we move on to the next sub-topic.

The reading on the main scale is 1.6 cm because it is directly at the immediate left of the 0 mark of the vernier scale.

The reading on the vernier scale is 0.04 cm because point 4 on the vernier scale coincides with the main scale

Vernier caliper reading = 1.6 +0.04 = 1.64 cm.

Do you find it hard to concentrate while reading click here to see the steps you can take to discipline yourself to study well.

The Micrometer screw gauge

Like the vernier calipers, the micrometer screw gauge has two scales

  • Main scale: which is located on the sleeve
  • Vernier scale: which is located on the thimble. The vernier scale on the micrometer might also be called micrometer scale.
Reading the Micrometer

Example 1: Read the micrometer below

The reading of the micrometer is not too different from the vernier calipers.

For the micrometer, the main scale is calibrated in mm and its value can be read off by checking the value closest to the thimble.

From the diagram below the main scale value is 5.5 mm

micrometer

The vernier scale can be read off by considering where the mid line of the main scale coincide at the vernier scale.

The vernier scale here is 0.42 mm

micrometer

Hence, the final reading of the micrometer becomes:

Answeer = main scale + vernier scale

Answer = 5.5 + 0.42 = 5.92 mm

Therefore, the micrometer reading is 4.92 mm

Example 2: What is the reading of the micrometer below?

micrometer

I hope think from the previous example, you should be able to tackle this question with ease.

It is quite clear that the main scale reading is 2.5 mm

Main scale = 2.5 mm

The vernier scale reading is on the ”37” mark which represent 0.37 mm.

Micrometer reading = 2.5 + 0.37 = 2.87 mm

Check the image below for clarificatton

Example 3: What is the micrometer reading below?

Micrometer reading

Its quite clear. The main scale reading is 12 mm.

While the vernier reading is on the mark ”40” which represent 0.40 mm.

micrometer reading = 12 + 0.4 = 12.4 mm

Measurement of mass

The mass of a body can be measured using any of the device below:

  • Spring balance
  • Beam balance (Single beam balance, double beam balance and triple beam balance)
  • Chemical beam balance.

The balance with the highest accuracy is the chemical beam balance which has an accuracy of 0.001 gram

Measurement of volume

The volume of regular shapes can easily be measured using the formula to calculate its volume depending on the shape.

However, if the body is irregular a number of ways can be used to determine its volume by:

  • Immersing the body in a volumetric cylinder and then noticing its increase in volume
  • Using the Eureka can for measurement.

Quiz Section

You can check out your understanding of this topic by clicking the button below to take the quiz

Philip Obhenimen

Hello world, first I want to thank you for visiting my blog and hope you find the content useful. My name is JOHN PHILIP OBHENIMEN the CEO of poschools.com I am currently studying mechanical engineering in a reputable university. I am very passionate about educating young people on academics,career and skill acquisition. I pray that the Almighty God help assists me in accomplishing the above.

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15 Responses

  1. felicia umoren says:

    thanks bigger bro! i find it interesting to educate my self here. thanks.

  2. Great Oriahi says:

    Awesome tutorial. Keep up with this, keep giving people good value. Kudos!

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