MEASUREMENT

MEASUREMENT

Measurement is the process of assigning numbers to observations or events.

In physics measurement is done to physical quantities, Physical quantities are categorized as Fundamental physical quantities and derived physical quantities

Fundamental   physical quantities (Basic physical quantities)

These are physical quantities which cannot be obtained from any simpler physical quantities. These include Length, Mass, time, temperature, amount of substance, electric current and luminous intensity.

 Derived physical quantities

Derived physical quantities are those physical quantities which are obtained (derived) from other physical quantities. Example velocity, density, force, pressure and acceleration.

 For example.

Velocity (V)=distance/time  thus two basic physical quantities make the velocity which is categorized as derived physical quantities.

 Measurement of length.

Length is the distance or displacement between two points.

SI unit of length is metre (m).

Distance is the length measured between two points in unspecified direction, for example 20m.

Displacement is the distance measured between two points in specific direction,  for example  20m east. Height  and depth are also displacement.

Other units of distance includes kilometer(km),centimeter(cm),millimeter(mm),micrometer(µm),and nanometer(nm).

 Relationship between units

1km=1000m

1m=100cm

1cm=10mm

1mm=1000µm

1µm=1000nm

Instruments commonly used to measure length are

ü  Tape measure

ü  Vernier calliper

ü  Ruler

ü  Micrometer screw gauge

Using tape measure and ruler

Zero mark of the ruler or tape is placed on the desired initial mark of  object to be measured, in some ruler zero mark is the beginning of the ruler itself while other rulers have zero mark somewhere beyond the edge, the disadvantage of the former is that edge can be worn and ruler will give false readings especially when it is not calibrated into other smaller fractions to use this ruler is safe to measure starting one then subtract  it from the answer

                  

                                                                      

The ruler above reads 6.5 units, that is the length of object

To read correctly a ruler one must read at correct position to avoid parallax error

 The correct position to read the ruler is at point B,this avoids parallax error. Parallax error occurs when a point on an object is viewed from the remaining two  positions, A and B.

VERNIER CALLIPER

A vernier caliper measures the distance to accuracy of 0.01cm.

Vernier caliper    

 Parts of the vernier caliper                                                                                                                     

·         O-Outside jaws

·         I-Inside jaws

·         D-Depth probe

·         V-Vernier scale

·         M-Main scale

·         L-Locking nut

·         R-Retainer

Typical vernier caliper diagram

How to read vernier calliper

ü  Read the main scale

ü  Find where the vernier scale coincides with the main scale

ü  Take the position of the coincidence from vernier scale,

ü  Multiply with 0.01cm

ü  Add the answer from above to the main scale reading

Example 1.

What is the reading of  vernier caliper below

Solution

Main scale=6.6cm

Vernier scale=3 x 0.01cm=0.03cm

Reading on Main scale + Reading vernier scale

6.6cm+0.03cm=6.63cm.

6.63cm

Example 2.

What is the reading on vernier below,(units are in cm)

solution

Main scale reading=1.5cm

Vernier scale=7x0.01cm=0.07cm

Main scale +vernier scale

=1.5cm+0.07cm

1.57cm

Example 3

What is the reading on vernier calliper below

Solution

Main scale reading=10.2cm

Vernier scale reading=7x0.01cm=0.07cm

Main scale +vernier scale

10.2cm+0.07cm

10.27cm

MICROMETER SCREW GAUGE.

Micrometer screw gauge is used to measure length to the accuracy of 0.01mm(0.001cm).

When the thimble makes one complete revolution  the spindle moves in or out 0.5mm for 50 divisions of thimble or 1mm for 100 divisions of thimble,therefore 0.5mm/50=0.01mm and 1mm/100=0.01mm

             MICROMETER SCREW GAUGE

Parts of micrometer screw gauge

·         A-Anvil

·         C-Circular scale(thimble scale)

·         F-Frame

·         S-Spindle

·         SL-sleeve

·         R-Ratchet

·         T-Thimble

Diagram of micrometer screw gauge

Reading micrometer screw gauge

ü  Read the sleeve scale

ü  Read the thimble scale

ü  The divisions in the thimble scale multiply by 0.01mm

ü  Add the thimble reading  to sleeve reading

Example 1

What is the reading on the micrometer screw gauge below

Solution

Sleeve reading =7.5mm

Thimble reading = 22 x 0.01mm = 0.22 mm

Sleeve reading + thimble reading = 7.5mm + 0.22 = 7.72mm

7.72mm

Example 2

What is the reading on the micrometer below

Solution

Sleeve reading = 5.5mm

Thimble reading = 30 x 0.01mm = 0.30mm

Sleeve reading + thimble reading = 5.5mm + 0.30mm

5.80mm

Example 3

What is the reading on the following micrometer

Solution

Sleeve scale = 14.5mm

Thimble reading = 29 x 0.01mm

Sleeve reading + thimble reading = 14.5mm + 0.29mm

14.79mm

MEASUREMENT OF VOLUME

Volume is the space occupied by a body. Volume of regular shapes can be found by mathematical calculation, Example of regular shapes includes  cylinder,rectangular,sphere,pyramid and cone

Cylinder

Sphere

cone

Example

Find the volume of a cylindrical tank of diameter 2m and height 20m.

Solution

V=πr²h

  =3.14 x 1²x20

  =62.8m³

Volume of irregular object

Volume of irregular objects can be obtained by using measuring cylinder as follows

ü  Fill the measuring cylinder with water and read the initial reading, reading should be taken at lower part of the meniscus.

ü  Tie an object with a thin thread

ü  Lower the object slowly by thread in the cylinder until it is completely immersed in water.

ü  Read the final volume of water

ü  Take the difference between the initial volume and the final volume

ü  The difference is the volume of irregular object.

What is the volume of irregular object above?

Solution

Initial reading = 32ml

Final reading  = 42ml

Volume=final reading – initial reading

            =42ml-32ml=10ml

Relationship between units

1m³   =1000litres

1litre = 1000cm³

1ml   = 1cm³

1dm³ = 1litre.

MEASUREMENT OF MASS

Mass is the quantity of matter contained in a body. The SI unit of mass is kilogram(kg). other commonly used units are ton and gram, ton (t) is mainly used in industries and gram in laboratory where small amounts of specimen are tested.

Relationship between units

1 kilogram = 1000grams

1ton           = 1000 kilograms

 Mass of an object does not change depending on place it is constant anywhere even on other planet.

The instruments used to measure mass include:

ü  Beam balance

ü  Electronic balance

ü  Triple beam balance

ü  Lever balance

·         F is fulcrum

·         M is standard mass

·         O is object

·         P is pointer

·         S is scale.

Measurement of mass by using beam balances is done by comparing (balancing) unknown mass against the standard mass.

The standard mass is known mass.

How to use beam balance

1.      Make sure the pointer points at the middle of scale when nothing is added.

2.      Put the unknown mass on a scale pan, pointer will shift

3.      Put the standard mass on another scale pan

4.      Add the standard masses until the pointer comes to the middle

5.      The total mass of standard masses is the mass of object (unknown mass).

WEIGTH

The weight of an object is the force of attraction of the earth on an object towards its Centre.

                                  Or

The weight of an object is the force an object exerts on anything which is freely supporting it.

The SI unit of weight is Newton (N)

The earth attracts objects towards its Centre by the pull of gravity.

The value of pull of gravity on earth’s surface is 9.8N/kg or approximately 10N/kg

Weight = mass x gravity pull

 W=mg.

Weight is measured by using spring balance.

                                      Spring balance

Parts of spring balance

ü  C- calibration

ü  S- spring

ü  P-pointer

ü  h-hook

Example 1

Find the weight of the mass of 30kg.

Solution

Weight=mass x gravity

W=30kg x 9.8N/kg

W=294N.

      294N

Example 2

What is the weight of an object of mass 50kg on the planet X where the gravity pull is one third of that of the earth?. What is the difference of the weight of an object on mass and on planet x?.

Solution

Mass of object=50kg

Gravity pull on earth= 9.8N/kg

Gravity pull on planet X =1/3 x 9.8N/kg

Weight on planet x = mass x pull of gravity on planet x

W=50 x1/3 x 9.8N/kg

    =163N.

 difference between the weight of an object on the earth and on planet x

weight on earth

          =50kg x9.3N/kg

          =465N

Difference = 465N-163N

                  =302N.

 Differences between mass and weight

·      mass is the quantity of matter contained in a body while weight is the force of attraction of  the earth on an object towards its Centre

·         the SI unit of mass is kilogram while SI unit of weight is Newton

·         mass does not change while weight changes

·         mass is fundamental physical quantity while weight is derived physical quantity

·         Mass is scalar quantity while weight is vector quantity.

·         mass is measured by beam balance while weight is measured by spring balance.