LSC S1:Measurements, Density

Introduction
In our everyday life, we often take decisions involving physical quantities. For instance, when planning to visit a friend, several questions come into your mind. Such questions include: how far, how long and probably what would be the shortest route to reach his or her place.
In this chapter, you will basically understand the meaning and importance of measurements, how to take measurements of physical quantities and express them in appropriate units.
3.1: Meaning and Application of Measuring
Measuring substances is an important aspect in the study of science. We constantly measure physical quantities.
A physical quantity is any property of a system that you can measure. But what is the meaning of measurement? In Activity 3.1 , you will discover the meaning and application of measurements.

Measuring is an important aspect in the study of science. We constantly measure physical quantities.

Fundamental Quantities and Instruments
Classification of physical quantities is based on how they relate with one another. For instance, quantities expressed in terms of the other are referred to as derive d quantities. While independent physical quantities are basic. You will do Activity 3.2 in order to be able to classify physical quantities.

3.2: SI units of a Physical Quantity
Measuring doesn’t always involve counting. For instance, when you are buying milk, you have to specify what quantity of milk you need.
Therefore, a standard known unit is required to describe physical quantities. In this context, an international system of units commonly referred to as the SI unit was adopted.
Activity 3.3: Identifying various Sl units for physical quantities
What you need: notebooks, stylus, slate, and perkins brailler and braille papers.
What to do:

1. In a group, analyse table 3.2 and write down the missing Sl units of physical quantities together with their symbols..

Hint: Use the relationships in activity 3.2 to generate the Sl units for volume, area and density.

2. Research about other Sl units for physical quantities and write down their symbols.
3. Present your work to class.

Measuring of a Physical Quantity
Measuring is a scientific technique used to quantify different properties of objects. In this section, you will learn how to numerically represent the size or magnitude of different physical quantities such as length, mass, time, area, volume and density.
Length
Length is a physical property which tells us how far a certain point is from any given reference point.
Various instruments for measuring length express this quantity in different units. Therefore, one should know how to change the results into the required units (standard units). Let us carry out activity 3.4 to measure length and express it in standard units.
Activity 3.4: Measuring the length of objects

What you need: A wooden table, ruler, tape measure, notebooks, stylus, slate, and Perkins brailler and braille papers

What to do
I. In groups, identify and name the instruments in Figure. 3.2 used to measure the length of
an object.

2. Suggest the best instrument used to obtain length of the different dimensions for the table
   in Figure. 3.3. Hence determine the length for each dimension.
3. Use the standard scale to express the quantity measured in its standard units.
   Repeat the steps above to determine the length ofthe dimensions for your desk.
   Note: Length is sometimes obtained using instruments which don’t give readings
   in standard units. Table 3.3 shows how you can convert length measured in one
   scale to another.

1. Using a metre ruler, measure the length and width of your a) Class room b) teacher’s table c) classroom door
2. Using a tape measure, the width of your waist and height.

Mass
Mass is a physical quantity which basically tells us about how much matter is contained in a body or a system. Observe the Figure. 3.4 and identify which bear has more matter as compared to the other.
Compare the mass of a pen to that of a car.

Do you think one can really use the same instrument to determine the quantity of matter contained in each body?
Therefore, in this section, you will learn how to identify a suitable instrument for measuring mass of a specific body.
Activity 3.5: Determining the mass of a body
What you need: notebooks, stylus, slate, and perkins brailler, braille papers, weighing scales, cups and basins

What to do:

1. In groups, identify and name the instruments a,b,c,d and e in Figure. 3.5 used to measure mass of a body.
2. Suppose that you have the objects in Figure. 3.6. Identify and name the best instruments for measuring their masses. Discuss and state reasons
3. to support your answers in step (3).
   Hint: The standard unit of measurement of mass is kilogram written as kg. Note that values recorded in kg should be written to 3 decimal places and the conversion factors for measuring mass are as shown in the Table 3.4:
   Time
   Time is simply a measurement of the duration taken by an event. For example, how long you take to move from home to school is the time for that event. The Sl unit (system international of unit) of time is seconds written with a symbol
   S. Time values obtained using a stop clock should be recorded to a 1 decimal place or zero decimal places.
   Time values measured using a stop watch should be recorded with 2 decimal places.

Activity 3.6: Determining the time taken to move from one point to another
What you need: stop clock or stop watch, classroom, notebooks, stylus, slate,
and perkins brailler and braille papers.
What to do
In groups:
1.Assign roles to your selves which include, moving from one corner of the class to another and timing the motion of a colleague.
2.Ask a group member to start moving from one corner to another as the other immediately starts the stop clock.
3.Stop the clock and note the time taken to complete the defined distance.
4.Interchange the roles and repeat steps 2 and 3 to determine the time for another colleague.
5.Calculate the average time and ensure that the value obtained is expressed in its standard units.
Hint: Values recorded using a stop watch should be recorded to two decimal places while values recorded using a stop clock should be recorded to one decimal place.

Area
Area is a physical quantity used to describe two dimensional shapes such as squares, rectangles, triangles, circles among others. The Sl unit of area is metres squared (m2). Do Activity 3.7 to investigate how the area of an object is determined.

Note: In determining the area of an object, we always deal with only two Imens,ons of the body under investigation.
Exercise 3.2:

1. Identify the dimensions of the teacher’s table. Determine their length using an appropriate instrument. Calculate the area of the teacher’s table and express it in appropriate units.
   Volume
   In the previous section, you learnt about a two dimensional quantity used to describe objects in two dimensions. What physical quantity do you think can be used to ri e an object in three dimensions? How should we then define volume.

4. Write down or braille about what you understand by the statement ” a 500 m/ mineral bottle”.
   Hint: Volume is obtained by multiplying the area and height of an object. Volume of liquids is obtained using gradualed apparatus such as a measuring cylinder, pipette, burette among others.

3.3: Irregular Objects
In the previous section, you learnt how to determine the volume of an object whose dimensions such as length, height are clearly established. How about the volume of a body whose shape is undefined? What methods should we use to determine the volume of such a body?
Carry out activity 3.9 to determine the volume of an irregular object.

3.4: Density
Suppose you have a piece of wood and a metal pin of the same mass. What do you think will happen if both objects are dropped into water, as shown in Figure 3.12? The piece of wood will float on
top of the water as the pin shall sink into water. But again, how can this happen yet both
objects have the same mass?

Therefore, by the end of this section, you will be able to determine e ensl substances so as to explain such scenarios.

Meaning of Density
Density is a qualitative measurement of the compactness of a substance or a system in a given space. It’s a property described by two physical quantities which include; the mass of the substance and its volume.
Do activity 3.10 to understand more the meaning of density.

Activity 3.10: Understanding the meaning of density
What you need: Notebooks, Stylus, Slate, and Perkins brailler, braille papers, tin of water in different states (solid – ice, liquid – water and water vapour – gases), source of heat and cylinder.
What to do:
In groups,

1. Suppose that cylinders A, B, and C have the same volume, and that the mass of the substances is the same, identify which substance is more compact than the others.

2.Basing on your answer in step (1 ), state the cylinder with the highest density.
3.What do you think will happen to the compactness of cylinder B when the volume of cylinder B is increased?
4.Write down the relationship between the density of a substance and the volume it occupies.
5. Since the mass of a substance remained a constant for change in volume, write down the formula for calculating density. State the Sl units of density.
Solids have a higher density as compared to liquids and gases whose molecules are more spaced. This explains why most solids sink in water. However, solids whose density is less than 1000kgm-3 such as wood, float on water.

Density and Relative Density
Relative Density
Closely packed molecules are denser than those with a greater separation in the same amount of space. For instance, solids are said to be denser than liquids because their molecules are closer to one another.
Our interest in this section is to measure the density of one substance relative to another whose value is already known. Such substances whose density is known include water paraffin among others.
Let us do Activity 3.11 to determine the relative density of a substance.

Activity 3.11: To determine the relative density of a substance
What you need: Two beakers, water, cooking oil, measuring cylinder, notebooks,
stylus, slate, and perkins brailler and braille papers.
What to do
In groups
1.Measure any suitable volume (V c”) of water and place it in one of the
beakers provided to you.
2.Determine the density of the measured volume of water.
3.Repeat the steps (1 ) and (2) but this time using the same volume of cooking oil.
4.Determine the relative density of cooking oil and hence state it’s Sl units.

5. Conclude about what is observed when:
   a) Substances with a relative density greater than 1 are placed on water.
   b) Substances with a relative density less than 1 are placed on water.
6. Do you think the relative density of an object can be zero? Explain your answer.

1. Consider the following diagrams to state which substance has the highest and lowest values of relative density.

2. Calculate the relative density of silver with a density of 10500 kgm-3. Determine whether silver floats or sinks in water.

Density of Solids and Liquids
Density of Solids
In this section, solids shall be classified basing on shape. Solids with a definite shape such as cubes, spheres among others are regular while those whose shape can’t easily be defined are called irregular objects. Let us learn how to determine the density of both irregular and regular solids.

What to do
1. Use a weighing scale to determine the mass of an irregular object (stone).
2 Fill the over flow can with water and use it to determine the volume of a stone.
3 State some assumptions made in this Activity. Use the formular to determine density of substance.

Activity 3.13: Determining the density of a regular object
What you need: ruler/tape measure, three dimensional object (cube), beam balance,
notebooks, stylus, slate, and perkins brailler and braille papers.
What to do
1.In your respective groups, use the available resources to discuss:
2.Area of a cube
3.Volume of a cube
4.Mass of a cube

2. Use the previously learnt skills to determine the density of the cube. Hint: Since regular objects have a definite shape, it becomes easy to establish its dimensions from which its volume can be calculated.

1. Calculate the density of an irregular object with mass 5 kg given that it is displaced 20 cm3 of the liquid in which it is immersed.
2.Calculate the density ofa sphere whose radius is 4cm and has mass of 20g. 3.Ice has a density of 0.9 gcm•3. State what will happen when it is placed on water. Explain your observation.

What you need: measuring cylinder, 4 beakers, paraffin, cooking oil, water,
beam balance, notebooks, stylus, slate, and perkins brailler and braille papers
What to do: In groups
1.Discuss and determine the density of the same volume of each of the liquids
provided to you.
(Ask your teacher to guide you on how to use the beam balance in the
process of determining mass of different liquids)
2.Arrange the three liquids in an increasing order of their densities.
3.Suppose that all the liquids were placed in the same container, draw a diagram to represent their layers of separation.

Materials that Float and Sink
Suppose that you have two objects, how will you tell which of the two floats or sinks in water. When do you think shall a given object sink or float on water?

Activity 3.15: Discovering materials which sink or float in water
What you need: spoon, safety pins, pencils, cooking oil, palm oil, pen, beaker, 500 cm3 of water, stone and a piece of chalk.

What to do
I.Hint:
1 Predict whether each of the materials provided to you will sink or float on water.

2 Categorise the substances as those which float or sink in water. Using the knowledge of density, what does it mean when a substance:

floats on water?

sinks in water?
3.Why do some liquids mix together easily, for example passion juice and
water, when others don’t mix together at all?
4.At home, you have accidentally added water instead of paraffin to the stove.
5.Describe what would happen. How can you obtain the water from paraffin?
6.Compare your results with other groups to explain the differences which exist.
Since regular objects have a definite shape, it becomes easy to establish its dimensions from which its volume can be calculated.