# IGCSE Physics Worksheet-Measurement

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### 1.1 Understanding Physics

Attempt the following questions on your own.

Phenomena & occurrence around us Field of study in physics 1. Car racing

2. Cooking in the kitchen 3. Rainbow in the sky 4. Shadow on the ground

5. Nuclear reactor and nuclear bomb 6. Light bulbs light up during night 7. Communication using mobile phone 8. Memory chip in computer

### 1.2 Base quantities and derived quantities

In learning Physics, we need to carry out investigations. We gather information through observations and taking measurements. We measure many types of physical quantities. A physical quantity is a quantity that can be _________. All physical quantities consist of a numerical __________ and a ______. Physical quantities can be classified in to two groups:

1. _______________________________ 2. ____________________________

What is Physics?

Physics is the study of the natural world around us-from the very large, such as the universe, to the very small, such as the atom. Physics is the science that deals with the ideas of _____________ and _______________.

3. _________________ Investigate the action of force and motion

1. _________________ Studies the influence of heat on different types of matter

Fields of study in Physics

2. _________________ Explains the different phenomena due to light

6. _________________ Understand the properties of different types of waves and their uses

5. _________________ Investigates the

interactions of electric and magnetic fields

4. _________________ Study of nuclear structure and their application

What are base quantities?

Base quantities are quantities that cannot be __________________ in terms

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2 There are seven base quantities. Fill in the blank in table below for the seven base quantities.

Base quantities Name of base unit Symbol for unit

Length metre m Mass Time Electric current Temperature Luminous intensity

Amount of substance mole mol

Determine the derived unit for the following derived quantities.

Derived quantity Formula (mathematical relationship with other

quantities)

Derived unit

area area = length × width m2

volume volume = length × width × height density density = mass/volume

speed speed = distance/time taken velocity velocity = displacement/time taken momentum momentum = mass × velocity

acceleration acceleration = change in velocity/time force force = mass × acceleration

pressure pressure = force/area

weight weight = mass × gravitational acceleration work work = force × displacement

power power = work/time

kinetic energy kinetic energy = ½ × mass × (velocity)2 gravitational

potential energy

gravitational potential energy = mass × gravitational acceleration × height

charge charge = electric current × time voltage voltage = work/charge

resistance resistance = voltage/current

Note that the physical quantities such as width, thickness, height, distance, displacement, perimeter, radius and diameter are equivalent to length.

Exercise 1

The extension of an elastic spring is directly proportional to the stretching force acting on it. It can be shown by the following formula.

𝐹 = 𝑘𝑥where F = the elastic spring force (unit N); k = spring constant and 𝑥 = the extension (unit m). Determine the unit of the spring constant.

What are derived quantities?

Derived quantity is one which obtained by ___________ base quantities by multiplication, division or both of these operations. Its unit is derived from similar combination of the base units.

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3 Exercise2

Write the following quantities in standard form:

a) Radius of the Earth = 6,370,000 m = ___________

b) Mass of electron = 0.000 000 000 000 000 000 000 000 000 000 911 kg = ___________ c) Speed of light in vacuum = 300,000,000 m/s = ______________

Fill in the blank of the table list of prefixes below:

Prefix Value Standard form

Tera 1,000,000,000,000 Giga 1,000,000,000 Mega 1,000,000 Kilo 1,000 Hecto 100 Deca 10 Deci 0.1 Mili 0.01 Micro 0.001 Nano 0.000 000 001 Pico 0.000 000 000 001 Exercise3

Convert the following to standard form:

a) 93 nm = _________ m c) 0.8 mg = ___________ kg b) 120 MJ = _________ J d) 59µs = _________s Exercise4

Convert the measurement into SI unit and in standard form:

a) Radio Caringin Frequency of radio wave is 101.4 MHz = ____________ b) Distance between the moon and the Earth is 383,000 km = ___________

c) Mass of the Earth is 60 000 000 000 000 000 000 000 000 000 g = _____________ d) The wavelength of a visible light is 0.00042 mm = ____________

Exercise5

The Body Mass Index (BMI) of a person is measured by taking the mass of the person divided by the square of his/her height. Use the information provided to work out the derived SI unit for BMI.

Express quantities using standard form

The values of measurements which is either very large or very small are written in standard form so as to be neater, brief and easier to read. Standard form: A × 10n, 1 < A < 10 and n = integer

Express quantities using prefixes

Prefix is used to simplify the expression of very big or very small numerical values of physical quantities.

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4 Attempt the following questions on your

own.

1. Which of the following physical quantities is not a base quantity? A. Weight C. Temperature B. Time D. Electric current 2. Which physical quantity has the correct

S.I. unit?

Physical quantity S.I. unit A Temperature celcius B Time minute C Weight kilogram D Length metre 3. A 30 milliseconds is equivalent to … A. 3 × 10-6 seconds B. 3 × 10-5 seconds C. 3 × 10-3 seconds D. 3 × 10-2 seconds

4. Which of the following frequencies is the same as 106.8 MHz?

A. 1.068 × 10-4 Hz B. 1.068 × 102 Hz C. 1.068 × 106 Hz D. 1.068 × 108 Hz

5. The product of 2.4 × 10-2 and 5.0 × 10-4 is … A. 1.2 × 106 C. 1.2 × 10-6 B. 1.2 × 105 D. 1.2 × 10-5 6. What is 0.0455 kg expressed in standard form? A. 0.455 × 10-1 kg B. 4.55 × 10-2 kg C. 45.5 × 10-3 kg D. 455 × 10-4 kg

7. The prefixes according to their value in ascending order are …

A. Giga, mega, kilo, centi B. Micro, mili, centi, kilo C. Mega, giga, kilo, centi D. Centi, giga, micro, mili

8. Which of the following measurements is different?

A. 2.3 ×102m C. 2.3 ×106mm B. 2.3 × 104 cm D. 2.3 ×10-1 km 9. Which one of the following

measurements is the smallest? A. 1.5 ×102 kg C. 1.5 ×1012µg B. 1.5 × 107 g D. 2.3 ×109 mg

10. The volume of a metal sphere is 12 cm3. The volume in unit of m3 is …

A. 1.2 × 10-2 C. 1.2 × 10-5 B. 1.2 × 10-3 D. 1.2 × 10-7

11. The velocity of a car is 108 kmh-1. What is the velocity in unit of ms-1?

A. 20 C. 40

B. 30 D. 50

12. The acceleration of a trolley is 2000 cms-2. This acceleration in S.I. unit is? A. 0.002 C. 2

B. 0.02 D. 20

13. A car moves with an average speed of 75 kmh-1 from town P to town Q in 2 hours. By using this information, you may calculate the distance between two towns.

(a) Based on the statements given, state two basic quantities and their respective S.I. units?

_____________________________ _____________________________ (b) State a derived quantity and its S.I.

unit.

_____________________________ (c) Convert the value 75 kmh-1 to S.I.

unit

_____________________________ 14. Given the diameter of the Earth is about

1 × 107 m, how many Earth-sized planets can you place next to each other to fill the space between the Earth and the Sun which is 150 million km away? ________________________________ ________________________________ ________________________________ ________________________________ ________________________________

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### 1.3 Scalar and vector quantities

Studythe following description of events carefully and decide which events require magnitude, direction or both to specify them.

Description of events Magnitude Direction

1. Walk 500 m and you will find the shop

2. Walk 500 m left from the junction and you will find the shop

3. The room temperature is 300 C

4. The location of Sampoerna Academy is 17 km to the north of Ciawi

5. The power of light bulb is 25 W

6. A plane is travelling at 1200 km/hr from Jakarta to Bali

### Measurements

The knowledge of Physics we have today is the result of the work of many scientists over centuries. These scientists built and tested their ideas on matter and energy, and verified their ideas or theories by doing experiments.

When we do experiments, it is important to obtain reliable results. In order to obtain reliable results, accurate measurements must be made. This is why when we learn Physics we should understand some methods that we use to make accurate measurements.

When we measure a physical quantity, we need to consider its magnitude and then choose a suitable instrument. The magnitude of the quantity should not exceed the maximum capacity of the instrument, and the instrument must be sensitive enough to detect and give meaningful measurement of the quantity.

Activity 1

Measure these quantities in the table below, then record your observation in the table.

Physical quantities Instrument Readings

The length of laboratory table The length of the book The diameter of beaker The diameter of a copper wire The thickness of a paper The mass of a pencil

The time for 10 pulses of your heartbeat

1. What criteria do you consider when you choose an instrument to measure a quantity? __________________________________________________________________________ __________________________________________________________________________ 2. Suggest a suitable instrument when measuring the following quantities.

(a) The mass of a wooden block = ______________________________________________

Define scalar & vector

quantities

Scalar quantities are quantities that have magnitude but no direction. Vector quantities are quantities that have magnitude and direction.

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6 (b) The current that flows in a circuit = __________________________________________ (c) The voltage of a battery = __________________________________________________

Activity2

The diagram shows the result for four shooters A, B, C, and D in a tournament. Every shooter shot five times. The table below shows the conclusion. Write either high or low in the blank cell.

Shooter Consistency Accuracy

A B C D

The smallest scale division on the measuring instruments shows the sensitivity of the instruments. Thus, the more sensitive a measuring instrument, the smaller the scale divisions it has. For instance, a vernier calipers is more sensitive than a ruler. A sensitive instrument is not always an accurate instrument.

Activity 3

1. Check the smallest division of the following measuring instrument for length, and then decide its sensitivity (low or moderate or high).

Measuring instrument Smallest division (cm) Sensitivity (low-moderate-high) Ruler

Vernier caliper

Micrometer screw gauge

2. The sensitivity of different types of ammeter.

Double-scale ammeter Range: 0-1 A/0-5 A

Milliammeter Range: 0-50 mA

Double-scale ammeter

Sensitivity of upper scale: _____

Explain accuracy & consistency

Consistency is the degree of uniformity of the measurements. Another

word, consistency is the degree of a measuring instrument to record consistent reading for each measurement by the same way. When we say the measurements are consistent, we mean that all the values of the measurements are close together.

Accuracy is the degree of closeness of the measurements to the actual or accepted value.

When we say the measurements are accurate, we are actually saying that the values of the measurements are close to the true or accepted value.

A B C D

Explain sensitivity

Sensitivity of an instrument is the ability to detect a small change in the

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7 What is the sensitivity (smallest

division)? __________________

What is the sensitivity (smallest division)? __________________

Sensitivity of lower scale: _____ Which is more sensitive: ___________________________________ Reading: ___________________ Measuring time Sensitivity: ___________________ Reading: _____________________ Measuring temperature Sensitivity: __________________ Exercise6 Group A Group B Reading 1 = 14.01 s Reading 1 = 14.37 s Reading 2 = 13.15 s Reading 2 = 14.15 s Reading 3 = 14.36 s Reading 3 = 14.36 s Reading 4 = 12.99 s Reading 4 = 14.29 s Reading 5 = 15.34 s Reading 5 = 14.34 s

Any measurement of a physical quantity has errors or uncertainty.There are two types of errors.(a) Systematic errors (b) Random errors

Systematic errors

Systematic errors are errors in

themeasurement of a physical quantity due toinstruments, the effects of

surroundingconditions and physical constraints of theobserver.

Sources of systematic errors are:

(i) Zero errors or end errors

Zero errors occur when the instrumentgives a non- zero reading when in fact theactual reading is zero.It can be corrected by adjusting the zeroadjuster on the

instrument or bysubtracting zero error from any readingtaken from the instrument.

(ii) Personalerror of the observer

Physical constraints or limitations of

theobserver can cause systematic errors.An example is the reaction time

Systematic errors can be eliminated orreduced by improving the procedure of takingthe measurements, using a

differentinstrument or getting somebody else tomakethe measurements.

Explain types of experimental error and use appropriate techniques to reduce errors

Group A and group Bdo an experiment to measure the period of a simple pendulum five times and the results are shown in the table. State which group’s mesurements are more consistent and explain why.

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Random errors

The main source of random error is due tothe carelessness of the observer whenmaking a measurement.

Examples of random errors are:

(i) Parallax errors – occur when the positionof the eye is not perpendicular to thescale.

(ii) Different pressures are applied whenclosing the gap of the micrometer screwgauge when it

is used to measure thediameter of a wire.

(iii) Changes in the temperature during anexperiment. (iv) Recording the wrong reading.

(v) Mistake in counting

To eliminate or reduce random errors,repeated readings are taken.To avoid parallax

errors:The position of the eye must beperpendicular to the plane of the scale (Fig. 1.4.1 (a) &

(b)).To overcome parallax errors ininstruments with a scale and pointer, e.g.avoltmeter often have a mirror behindthe pointer (Fig. 1.4.2). The correct reading isobtained by making sure that the eye isexactly in front of the pointer, so that the reflection of the pointer in the mirror isbehind it.

Every measurement of a quantity is an attempt to find its true value and is subject to error arising from limitations of the apparatus and the experimenter. The number of figures, called significant figures, given for a measurement indicates how accurate we think it is and more figures should not be given than is justified.

For example, a value of 4.5 for a measurement has two significant figures; 0.0385 has three significant figures, 3 being the most significant and 5 the least, i.e.it is the one we are least sure about since it might be 4 or it might be 6. Perhaps it had to be estimated by the experimenter because the reading was between two marks on a scale.

When doing a calculation your answer should have the same number of significant figures as the measurements used in the calculation. For example, if your calculator gave an answer of 3.4185062, this would be written as 3.4 if the measurements had two significant figures. It would be written as 3.42 if the measurement had three significant figures. Note that in deciding the least significant figure you look at the next figure. If it is less than 5 you leave the least significant figure as it is (hence 3.418 becomes 3.4 for two significant figures) but if it equals or greater than 5 you increase the least significant figure by 1 (hence 3.418 becomes 3.42 for three significant figures). If a number is expressed in standard notation, the number of significant figures is the number of digits before the power of ten. For example, 2.74 × 103 has three significant figures.

Significant figures

Figure 1.4.2Voltmeter scale withmirror mounted under the needle Figure 1.4.1 (b) Inaccurate measurement

due to parallax errors Figure 1.4.1 (a) No parallax errors

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