MEASUREMENT

All measurements in physics, even of such things as density, are related to the three chosen fundamental quantities of length,mass, and time.until about the year 1800 ,workers in various countries used different systems of units. Thus ,while the English used inches, a continental scientist would measure lengths in centimeters. Fortunately, this situation has now changed by the efforts of various international committees of scientists who have met for discussion regularly over many years.

When we measure something ,we are determining its size or magnitude.

To carry out any measurement we need to know :

1.the quantity being measured.

2.the unit for measuring it.

 

In 1960 ,scientist agreed on one international system of units to be used, International System of Units ,shortened to SI units ,in all languages.

There are seven basic physical quantities and units from which other quantities can be derived. The seven basic quantities ,their symbols and SI units are given in Table 1.1 below.

Other quantities can be formed from these quantities for example;area ,volume ,density,acceleration and charge. These quantities are called derived physical quantities.

LENGTH

Length is a measure of distance between two points. Breadth ,width,height,radius,depth and diameter are all lengths. THE SI unit of length is the metre(m).

Example : convert the following;a)1000 km into mb)270 Hm into dmc)100 m into mmd)100 mm into Hm

Measurement of Length

Length can be determined by estimation or accurately by using a measuring instrument. There are various instruments for measuring length. Some instruments used to measure length are metre rule and tape-measure.

Metre RulesThey are graduated in centimetres and

millimeters.

When using a metre rule:•Place the metre rule in contact with the object•Place the end of the object against the zero mark on the scale.•Position your eye perpendicularly above the scale.

Figure shows the inaccurate use of the rule. The arrangement will not give us affair result because:•The rule is not in contact with the object.•The object is not aligned to the zero mark on the scale•The position of eye is not perpendicular to the scale.

Example 1

What are the readings indicated by arrows P1, P2, and P3 on the metre rule in figure 2.3? (Diagram not to scale)

HW:EXERCISE 2.1

Tape Measure

There are several types of the tape measures,ie:tailor`s carpenter`s and surveyor`s types. The choice of tape measure is determined by the nature of the distance to be measured.

Always ensure that the tape measure is taut when measuring.

Measurement of Curved Length

Curved lengths such as roads and railways lines on a map or dimensions of some containers can be measured using a thread. For curved surfaces such as a cylinder,a thread is closely wrapped around the surface a number of times.

EXPERIMENT 2.1:To measure the circumference of a cylinder

using a cylinder using a thread.

•Measure the length between the ink marks and call it a1 . repeat three times,

recording the readings as a2 and a3 to ensure accuracy of your measurement. Find

the average length a;

Divide the average length by 10 to find the length of one turn. This gives the circumference of the cylinder. Thus;

Estimation of Length

One may to wish to know which of several objects is the largest. This could be established by comparing the sizes of the object directly. At times ,it is better to compare all of them with that of a chosen basic length called a standard length.

The estimation of sizes of various objects such as the height of tree,flagpost or the length of rope possible by comparing with standard lengths.

EXPERIMENT 2.2:

To estimate the height of tree

The height of the tree is estimated from the relation:

Example 2:

Hamad found that the width of her desk was approximately 10 palm-lengths. If his palm was 15.0 cm long ,what was the width of her desk in centimetres?

HW:EXERCISE 2.2

AREA

Area refers to the measure of surface.It is derived quantity of length.The SI unit of area is the square metre,written as m2 .It can also be measured in multiples and sub-multiples of m2,for example ; cm2 and km2

Example:

Example

Measurement of Area

Area of regularly-shaped objects

The area of regularly-shaped surfaces such as rectangles,triangles and circles can be obtained by applying the appropriate formula.

Rectangle

AREA=length x width

A=l x w

Triangle

Circle

Trapezium

Area of irregularly-shaped surfacesThe area of an irregular shaped surface can be estimated by dividing it into smaller regular shapes for example squares whose sides are 1 cm in length.

A=no. of complete squares+1/2 (no. of incomplete squares)

Example :

Calculate the area of the trapezium above:

HW:EXERCISE 2.3

Volume Volume is the amount of space occupied

by matter. The SI unit of volume is the cubic

metre(m3). 1 m3=1m x 1m x 1m = 100 cm x 100 cm x 100 cm = 1000 000 cm3

Other units like litres (l) and millilitres (ml) are also used.

1ml= 1cm3

1000 ml=1litre 1m3=1000 000 cm3

Example 6:

Example 7:

Volume of Regularly-Shaped SolidsThe volume of regularly-shaped solids can be obtained by applying the appropriate formula.

Cuboid

Volume = area of cross-section x height

=(ab)c

= abc

Cylinder

Volume = area of cross-section x height

=(∏ r2 ) h

= ∏ r2 h

Triangular prism

Volume = area of cross-section x length = ½(bhl)

Sphere

Example 8:

Homework Exercise 2.4

Measurement of Volume of Liquids

Liquids have no definite shape, but assume the shapes of the containers in which they are put.

One of the methods which can be used to measure the volume of a liquid is to pour the liquid into a container with a uniform cross-section ,as shown in figure 2.8.

The height of the liquid,h is measured.The volume of the liquid is then obtained by applying the formula;

The graph of V against h is the a straight line,indicating that height increases with the increase of volume V.

Measuring devices which are marked off like this are called measuring cylinders. They are used to measure volumes of liquids.

Measuring cylinders are made of glass or transparent plastic and graduated in cm3 or ml.

Note:1.The scale of the burette begins from zero at

the top and increases downwards to the maximum value.

2.The reading of volume is taken with the eye positioned in level with the bottom of the meniscus,see figure 2.11.

Measuring the Volume of an Irregularly-Shaped Solid

Volumes of irregular solids are measured using the displacement method.The method works with solids that are not soluble in water, do not absorb water, do not react with water and sink in water.

EXP.2.5:To determine the volume of an irregularly-shaped object

a)Using a measuring cylinder

Apparatus:Measuring cylinder,stone,thread and Eureka can.

Result: the volume of the stone V=V2-V1

b) Using Eureka canA eureka or displacement can is a

container with a spout from the side.It is used to measure volumes by displacement method.It is also known as an overflow can.

Result: The volume of water collected in the measuring cylinder is the volume of the object.

EXP.2.6: To determine the volume of an object that floats on water using the displacement can

Apparatus : Eureka can,measuring cylinder,floating object and a sinker(small metal block).

When finding the volume of an object that floats on water,e.g.,a cork, another object that sinks in water is attached to it so that both are totally submerged. This object is known as a sinker.

Results :The water collected in the

measuring cylinder is the volume of sinker and cork. Call it V2.so, the volume of the cork V=V2-V1

HOMEWORK: EXERCISE 2.5

MASSThe mass of an object is the

quantity of matter in it.Matter is anything that occupies space.The mass of an object depends on its size and the number of particles it contains.

The SI unit of mass is the kilogram(symbol kg).The commonly used sub-multiples and multiples of kilogram are given table 2.6.

The mass of an object is the same everywhere because the number of particles in an object remains constant.

Measurement of Mass There are two common types of

balances for measuring mass,namely,the electrical and the mechanical types.

HOMEWORK: EXERCISE 2.6

DENSITY

The density of a substance is defined as its mass per unit volume.Its symbol is rho(p) and its SI unit is kilogram per cubic metre (kg/m3).Another commonly used unit is gram per cubic centimetre(g/cm3).

From definition, the density of a substance is given by:

Measurement of Density

To measure the Density of a Solid

The density of the object is then calculated from the formula:

Exp 2.8: To find the density of a liquid

Apparatus : clean dry beaker, balance, measuring cylinder, a burette or a pipette.

Result :

Density Bottle

A density bottle is a small glass bottle fitted with glass stopper which has a hole through which excess liquid flows out.

Normally, the density bottle has its capacity indicated on the side.

To find the density of a liquid using a density bottle

Measure the mass m1 of a clean dry density bottle with its stopper.

Fill the bottle with liquid and replace the stopper.

Dry the bottle on the outside.Measure the mass m2 of the bottle plus the

liquid.If the capacity of be is V, then Density of liquid= (m2-m1)/V

Exp :2.10: to measure the density of a solid using a density bottle

This method is used for solids in form of grains,beads or turnings.

Apparatus :Density bottle Lead shotBeam balance

Procedure :

1.Measure the mass m1 of a clean dry empty density bottle.

2. Fill the bottle with lead shot and measure the mass m2.

3. Fill up the bottle with water up to the neck and measure its mass m3.

4. Empty the bottle and rinse it.

5. Fill it with water and replace the stopper . Wipe the outside dry and measure the mass m4 of the bottle filled with water.

mass of water = (m4-m1) gVolume of water =m4-m1(density of water is 1g/cm3)Volume of bottle =(m4-m1) cm3Mass of lead shot =(m2-m1)gMass of water present when bottle is filled with lead shot

and water = (m3-m2)gVolume of water =(m3-m2)cm3Volume of lead shot =(m4-m1)-(m3-m2)

It should be noted that this method is unsuitable for solids which are either soluble in water or react with it.

Densities of mixtures

A mixture is obtained by putting together two or more substances such they do not react with one another. It is assumed that the volume of the mixture is equal to the sum of the volumes of the individual constituents.

Time

Time is a measure of duration of an event. The SI unit of time is second(s).

Multiple and Sub-multiple units of the secondMicrosecond µs 0.000001 secondsMillisecond ms 0.001 secondsMinute min 60 secondsHour hr 3600 secondsDay day 86400 secondsWeek wk 604800 seconds

Measurement of Time

In laboratories ,intervals of time are measured using either a stopwatch or stop-clock,depending on the accuracy required.

Homework :

Exercise 2.7 and Revision Exercise 2