Introduction to Physics and Measurement of Physical Quantities

Lessons

Senior 1 · Physics

Introduction to Physics and Measurement of Physical Quantities

5 lessons

Lesson 1 of 5

Physics and How Scientists Investigate

22 min

A question from the playground

Two swings hang side by side in a school playground in Huye. One has long ropes, the other short ropes. The pupils notice that the long swing goes back and forth more slowly than the short one. Is it the length of the rope that matters? The mass of the child? How high the swing is pulled back?

You could argue about it for a long time. A physicist would do something simpler: change one thing, measure the result, and let the numbers decide. That is what this lesson is about: what physics studies, and the skills scientists use to find answers they can trust.

Definition

Physics is the branch of science that studies matter and energy and how they act on each other: motion, forces, heat, light, sound, electricity and magnetism.

A physical quantity is a property that can be measured and written as a number multiplied by a unit. Example: the length of the rope is $l = 1.5\,\mathrm{m}$ , where 1.5 is the number and $\mathrm{m}$ (metre) is the unit.

Experiment: what decides how long one swing takes?

A small swing, called a simple pendulum, can be built in any classroom from a stand, a string and a small heavy ball (the bob). One complete swing, from one side to the other and back again, is called an oscillation. The time for one oscillation is the period, $T$ , measured in seconds.

Figure 1.1: Apparatus for the pendulum investigation. The length l is measured from the point of suspension to the centre of the bob.

Method

Clamp the string between two halves of a split cork so that the point where it swings from does not move.
Set the length $l$ to 20.0 cm, measured from the cork to the centre of the bob.
Pull the bob aside through a small angle (less than about 10°) and let it go. Do not push it.
Start the stopwatch as the bob passes the marker, and count 10 complete oscillations. Stop the watch on the tenth.
Repeat for lengths of 40, 60, 80 and 100 cm. Keep the same bob and the same small angle every time.

Important

Safety. Weigh down or clamp the base of the stand so it cannot tip over. Swing the bob gently and keep your face out of its path. Use a bob of wood or metal, never glass.

One class's results

Length $l$ (cm)	Time for 10 oscillations (s)	Period $T$ (s)
20.0	9.0	0.90
40.0	12.7	1.27
60.0	15.5	1.55
80.0	18.0	1.80
100.0	20.1	2.01

The class then kept $l = 60.0\,\mathrm{cm}$ and changed only the bob. Bobs of 50 g, 100 g and 200 g gave 15.6 s, 15.5 s and 15.6 s for 10 oscillations: the same, within the timing error.

Conclusion: a longer pendulum has a longer period, but the mass of the bob makes no measurable difference. The playground's long swing is slow because its ropes are long, not because of who sits on it.

Worked example 1: the period from many swings

A pupil times 20 oscillations of a pendulum and gets 31.2 s. Find the period.

The period is the time for ONE oscillation, so divide the total time by the number of oscillations:

T = \frac{\text{total time}}{\text{number of oscillations}} = \frac{31.2\,\mathrm{s}}{20} = 1.56\,\mathrm{s}

Worked example 2: the mean of repeated readings

Three timings of 10 oscillations are 15.4 s, 15.7 s and 15.5 s. Find the mean time and the period.

\text{mean} = \frac{15.4 + 15.7 + 15.5}{3} = \frac{46.6}{3} = 15.53\,\mathrm{s} \approx 15.5\,\mathrm{s}

T = \frac{15.5\,\mathrm{s}}{10} = 1.55\,\mathrm{s}

Repeating a reading and taking the mean reduces the effect of small, random timing mistakes.

The skills behind the experiment

The pendulum investigation used the science process skills, the steps every scientist follows when they want an answer they can trust.

Figure 1.2: The steps of a scientific investigation. If the results do not support the hypothesis, the scientist forms a new hypothesis and tests again.

Skill	What it means	In the pendulum investigation
Observing	Using your senses and instruments carefully	The long swing moves more slowly
Hypothesising	Suggesting a testable explanation	"A longer rope gives a longer period"
Measuring	Using instruments and units	Metre rule for $l$ , stopwatch for time
Experimenting	Changing one variable and controlling the others	Only the length changed
Recording	Tables and graphs with units	The results table
Analysing and concluding	Finding the pattern and saying what it means	Longer $l$ gives longer $T$ ; mass has no effect
Communicating	Reporting so others can check	A written report to the class

Definition

A hypothesis is a possible explanation that can be tested by an experiment.

A variable is anything that can change in an experiment:

the independent variable is the one you change on purpose (here, the length $l$ );
the dependent variable is the one you measure (here, the period $T$ );
the control variables are kept the same so the test is fair (the bob, the angle, the stopwatch).

Tip

I change the Independent variable; the Dependent variable Depends on it. Change only ONE thing at a time, or you cannot tell which change caused the result.

Warning

Common mistake: timing a single oscillation. Your reaction time when starting and stopping a stopwatch is about 0.2 s. For one swing of 1.5 s that is an error of more than 10%. For 20 swings (about 30 s) the same 0.2 s is less than 1%. Always time many oscillations and divide.

Physics in Rwanda: the other sciences and technology

Physics is the base on which the other sciences and most technology are built. You will meet it all around you:

Field	How physics is used	A Rwandan example
Energy	Turning the energy of falling water and of sunlight into electricity	Hydropower stations on the Nyabarongo River; the solar field at Rwamagana
Chemistry	Gases, pressure and heat	Methane gas taken from deep water in Lake Kivu to generate electricity
Medicine and biology	X-rays, ultrasound, how the eye and ear work	X-ray and ultrasound scans at the University Teaching Hospital of Kigali (CHUK)
Weather and the Earth	Measuring temperature, rainfall, wind; studying earthquakes	Weather stations of Meteo Rwanda
Communication	Radio waves, electronics	Mobile phones and mobile money; RwaSat-1, Rwanda's first Earth-observation satellite, launched in 2019
Engineering and building	Forces, loads and materials	The dome of the Kigali Convention Centre

What Is Physics? (GPB Education, Physics in Motion). Watch for the list of topics physics covers, and notice how each one is studied by measuring.

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Practice

Name the science process skill in each case. (a) Mutesi notices that water in a pot with a lid boils sooner. (b) She says, "The lid stops heat escaping." (c) She heats two identical pots of water on identical stoves, one with a lid and one without, and times both.
A pupil times 20 oscillations of a pendulum and records 28.6 s. Calculate the period.
Three timings of 10 oscillations are 17.9 s, 18.2 s and 18.0 s. Find the mean time and then the period.
Keza investigates how the height of a ramp affects how far a marble rolls across the floor. Name the independent variable, the dependent variable and two control variables.
Give one use of physics in each of these in Rwanda: (a) medicine, (b) communication, (c) electricity supply.
Explain why the class timed 10 oscillations instead of one.
Use the results table to predict the period of a pendulum 50 cm long. Explain how you decided.

Show answersHide answers

(a) Observing. (b) Hypothesising. (c) Experimenting (a fair test).
$T = \frac{28.6\,\mathrm{s}}{20} = 1.43\,\mathrm{s}$
Mean $= \frac{17.9 + 18.2 + 18.0}{3} = 18.03\,\mathrm{s} \approx 18.0\,\mathrm{s}$ ; $T = \frac{18.0\,\mathrm{s}}{10} = 1.80\,\mathrm{s}$ .
Independent: the height of the ramp. Dependent: the distance the marble rolls. Controls (any two): the same marble, the same floor, releasing from the same point without pushing, the same ramp surface.
(a) X-ray or ultrasound scans at hospitals such as CHUK. (b) Mobile phones use radio waves. (c) Hydropower from rivers such as the Nyabarongo, solar power at Rwamagana, or methane from Lake Kivu.
Reaction time adds an error of about 0.2 s at the start and the stop. Spread over 10 oscillations, this error becomes a much smaller fraction of the time measured, so the period is more accurate.
About 1.4 s. The period for 40 cm is 1.27 s and for 60 cm is 1.55 s, so 50 cm, half-way between, gives a period between them. The middle value is about 1.41 s.

Key points

Physics studies matter and energy: motion, forces, heat, light, sound, electricity and magnetism.
A physical quantity is a number times a unit, such as $l = 1.5\,\mathrm{m}$ .
A fair test changes one independent variable, measures the dependent variable and keeps the control variables the same.
The period of a pendulum depends on its length, not on the mass of its bob. Time many oscillations and divide.

Sources and credits

Photo: An aerial of Kigali Convention Center on June 19, 2019. Photo by Emmanuel Kwizera.jpg by Emmanuel Kwizera, Wikimedia Commons, licensed under CC BY-SA 4.0.
Video: What Is Physics? | Physics in Motion, GPB Education, embedded from YouTube.

Written by Ganzaa: the lesson text, the pendulum investigation and its results, the diagrams and the practice exercises.

1A question from the playground

2Experiment: what decides how long one swing takes?