Scientific Learning

A scientific study looks at things in nature in a planned and organized way. It doesn’t trust opinions or guesses; it trusts evidence, things that can be observed and measured. Out of this evidence come scientific facts, theories and models.

Every event in nature has causes. The plant wilts because of something. A factor that is connected with an event, directly or indirectly, and can change, is called a variable.

Cause and effect

When something happens, we want to know why. Take the wilting plant. Maybe it lacks water; maybe the sun is too hot. To find out, we can move it into the shade, or water it, and watch what happens.

• The cause (lack of water, too much sun) is what makes something happen.
• The effect (wilting) is what happens.

The effect depends on the cause, and how much it depends matters. A stem stays stiff when it is full of water and goes limp as the water runs out. If we know how the size of the cause is linked to the size of the effect, we can predict: “If I forget to water it for two hot days, it will wilt.” Then we can act before it happens.

Finding these links, and in the end understanding how nature works, is the job of a scientist. And the way to find them is the experiment.

Activity 1.1: a rubber-band catapult

No rubber band at hand? Try the experiment here first.

What makes something a variable

In the catapult, you changed one quantity (the extension) and watched how another quantity (the distance) changed. Both are physical quantities, things you can measure, and both had a different value each time. That is why they are called variables: the quantities that change, or could change, in an experiment.

Other things could have changed too: the thickness of the rubber band, or the size of the paper bullet. So they are variables of this experiment as well, even if we chose not to change them.

To write about variables quickly, we give each one a symbol. If e is the extension and x is the distance, the result of the experiment can be written as

$$x \propto e$$

which is read “x is proportional to e”, and means: the more you stretch, the farther it flies.

Three kinds of variables

Variables are sorted into three kinds: independent, dependent and controlled. A simple way to remember them:

Kind	In plain words	In the catapult
Independent variable	what I change	the extension of the rubber band
Dependent variable	what I observe (measure)	the distance the bullet flies
Controlled variables	what I keep the same	the thickness of the band, the size of the bullet

a. Independent variable

The experimenter is free to choose its value: you decide to stretch the band 4 cm, then 6 cm. It is the cause you are testing. Its value does not depend on anything else in the experiment, which is why it is called independent.

In a plant-growth experiment, the amount of fertilizer, sunlight or water could each be the independent variable.

b. Dependent variable

You can’t decide how far the bullet will fly. You can only let go and measure it, because the distance depends on how much you stretched the band. A variable whose value depends on another variable, and that the experimenter cannot set directly, is the dependent variable. It is the effect.

If you study how sunlight affects a plant, the amount of sunlight is the independent variable, and the height or growth of the plant is the dependent variable.

c. Controlled variables

Most experiments have more than two things that could change, and each of them could affect the result. Suppose you used a thick band for the 4 cm shot and a thin one for the 6 cm shot. The bullet went farther the second time. Was it the stretch, or the band? You can’t tell. The result is worthless.

So every variable except the independent and dependent ones must be kept the same, or controlled, all through the experiment. That makes the results valid, reliable and accurate. Controlled variables are what make a test fair.

In the light-and-plants experiment of Figure 1.2, the plants should all be the same size at the start, and get the same air, water and manure, in the same kind of pot and soil. Those are the controlled variables.

Or suppose you study how the surface area of limestone affects how fast it reacts with acid (powder versus lumps). The surface area is the independent variable and the rate of reaction is the dependent variable. The concentration and amount of acid, and the mass of limestone, must stay the same: they are the controlled variables.

More examples

What is being studied	Independent variable (what I change)	Dependent variable (what I observe)	Controlled variables (what I keep the same)
How turning a tap’s knob affects the flow of water	how far the knob is turned (degrees)	water flowing out per minute (liters)	the water pressure
How electricity makes a solenoid magnetic	the electric current (amperes)	the number of pins the electromagnet picks up	the number of turns in the solenoid, the size of the pins
How heat affects how much sugar dissolves	the temperature of the water (°C)	the mass of sugar that dissolves completely (grams)	the amount of water (always 100 g)
How exercise affects the heartbeat right away	how long you exercise (minutes)	the number of heartbeats	the type of exercise, the time between stopping and counting

Now you try. Each of these is a real experiment.

Rules for variables

1. An experiment should have only one independent variable. Change two things at once and you can’t tell which one caused the effect.
2. It should have only one dependent variable: the one thing you measure.
3. All other variables are controlled.
4. In an equation, the dependent variable is usually written on the left, and the independent variable on the right. That is why they are sometimes called the left and right variables. In $s = vt$, the distance $s$ depends on the time $t$; the speed $v$ is kept the same. So $s$ is dependent, $t$ is independent, and $v$ is controlled.
5. On a graph, the independent variable goes along the horizontal x-axis, and the dependent variable up the vertical y-axis. So they are also called the x-variable and the y-variable. A graph shows how a change in the independent variable brings a change in the dependent one. (The catapult’s graph above is drawn this way.)

Every physical quantity is measured in a unit: length in meters, time in seconds. Units come in two types:

1. Fundamental (base) units
2. Derived units

Fundamental units

A fundamental unit stands on its own. It does not depend on any other unit and can’t be broken into simpler units. The meter (length), the kilogram (mass) and the second (time) are fundamental units.

The SI system (the International System of Units, used by scientists everywhere) has seven fundamental units:

Physical quantity	SI unit	Symbol
length	meter	m
mass	kilogram	kg
time	second	s
temperature	kelvin	K
luminous intensity (brightness of light)	candela	cd
electric current	ampere	A
amount of substance	mole	mol

Derived units

A derived unit does not exist on its own. It is made by combining two or more fundamental units.

The unit of density is kg/m³ (kilograms per cubic meter): it is made of the kilogram and the meter. The unit of force is kg m/s², made of three fundamental units, the kilogram, meter and second. Saying “kilogram meter per second squared” every time is tiring, so this combination has a short name of its own: the newton (N).

$$1\ \text{N} = 1\ \text{kg m s}^{-2}$$

In the same way, the unit of pressure, kg m⁻¹ s⁻², is called the pascal (Pa). Many derived units have special names like this. Some don’t: the unit of density is just kg m⁻³.

Quantity	Formula	Units according to the formula	Derived unit	Special name
area	length × breadth	meter × meter	m²
volume	length × breadth × height	meter × meter × meter	m³
density	mass ÷ volume	kilogram ÷ metre³	kg/m³
velocity	displacement ÷ time	meter ÷ second	m/s
acceleration	change in velocity ÷ time	meter ÷ (second × second)	m/s²
force	mass × acceleration	kilogram × meter ÷ (second × second)	kg m/s²	newton (N)
pressure	force ÷ area	(kg m/s²) ÷ metre²	kg m⁻¹ s⁻²	pascal (Pa)
work, energy	force × distance	(kg m/s²) × meter	kg m² s⁻²	joule (J)
power	work ÷ time	(kg m²/s²) ÷ second	kg m² s⁻³	watt (W)
frequency	1 ÷ time	1 ÷ second	s⁻¹	hertz (Hz)

Finding the fundamental units in a derived unit

Start from the formula that defines the quantity, and put in the unit of each part.

Fundamental unit	Derived unit
does not depend on other units	depends on fundamental units
there are only seven	there are many, all made from the seven

Here is the second tool, and it is a powerful one. Scientific study gives us formulas and equations. Units can tell us whether an equation could be right, and the rule is simple:

In a correct equation, both sides have the same units.

An example

Is $s = v \times t$ correct? (distance = speed × time)

• Left side: $s$ is a distance, in m.
• Right side: $v \times t$ is m s⁻¹ × s = m.

Both sides are meters, so the equation is valid.

Someone else says $s = v / t$. Check:

• Left side: m.
• Right side: m s⁻¹ ÷ s = m s⁻².

A distance can’t equal something measured in m s⁻². The equation is wrong.

Adding and subtracting

You can only add or subtract quantities with the same units. Two speeds can be added: $u + v$ is fine, as both are in m s⁻¹. You can’t add 5 meters to 3 seconds; the answer would mean nothing.

• $s - \tfrac{1}{2}at^2$ is possible: $s$ is in m, and $at^2$ is m s⁻² × s² = m.
• $s + at$ is not possible: $s$ is in m, but $at$ is m s⁻² × s = m s⁻¹, a speed.

So unit analysis is used to check whether an equation could be correct, to find how physical quantities are related, and to convert between different systems of units.

1. Choose the correct option

2. Give reasons

3. Differentiate between

4. Answer these questions