physics - science curriculum office welcomes you to our ... · pdf fileby the end of the unit,...

Handling

physical

quantities

Physics

Grade 10 Advanced Level

Grade 10 Unit AP.1 – Handling Physical Quantities

2

UNIT 1: Handling physical quantities

Core Standards…………………………….…….. 3

Objectives………………………………………… 3

SI Units………………………………………….... 4

Accuracy and Precision......................................... 10

Vector and scalar quantities ……………………. 13

Question …………………………………………. 23

References………………………………………... 28

Contents

25.1

25.2

25.4


3

10A.25.1 Be familiar with fundamental and derived SI units and use appropriate prefixes, manipulate ranges of magnitude and express quantities correctly in standard form in SI format.

10A.25.2 Distinguish between precision and accuracy; know how to ensure both in physical procedures.

10A.25.4 Distinguish between vector and scalar quantities, manipulate them appropriately and interpret their meaning.

By the end of the unit, students are familiar with fundamental and derived SI units, and use appropriate prefixes for small and large measurements. They handle inaccuracies and uncertainties when taking and manipulating

measurements and distinguish between vector and scalar quantities.

Students who progress further include units along with the numerical values when manipulating physical quantities. They make sensible simplifying assumptions when analyzing experimental results and when solving problems.


4

Introduction:

Without a widely accepted system of units of measurement our civilization could not exist. Imagine the chaos if there were no standards for the measurement of mass, length and time, for example.

ان ؼاش ىتخ افضى إرا . مثي دذاخ اماط ال تغتطغ دضاستا أ تجذػا ظا تذ

.، ػى عث اثاياضطي ايماط اىتح

Scientists identify quantities which describe the natural world. In order to decide how much of a particular quantity a given object has, for example, MASS, it is necessary to compare that object to the masses of other objects which have known masses, defined in terms of an agreed standard.

، ػى اجغا ات ىاؼح ايوح ا ايلشس ى . ض اؼاء اىاخ ات تصف اؼا اطثؼ

، أ ماس جغ جي اىتح تجغ آخش ؼشف مذاس وتتضشسي ماسح ف اي، كتلةالعث اثاي،

. ادح ؼاس تفك ػشفتؼى آخش أ

The instrument used is called a BALANCE, shown above.

اجاص اغتخذ غى .، ضخ ف اشى أػالميزانإ

A PHYSICAL QUANTITY can be defined in terms of the operations necessary to measure it. For example, the length of an object can be determined by comparing it to an object of known length, such as a ruler.

ا ػى عث اثاي ، طي جغ . أي وح فضائح ى أ تؼشف ادح اؼاخ اضشسح ماعا

.غطشجاياطي، ث ؼشف ى أ مشس تماست إى جغ

25.1 SI Units وحدات القياس الدولية


5

A unit is an established standard for a physical quantity against which particular examples of that physical quantity can be compared. The act of comparing a physical quantity to a unit is called MEASUREMENT and the MEASURE of a particular physical quantity is the ratio of that physical quantity to the unit.

ػح. ؼح تغتخذ ماسح تىح ؼاس خصص ىح فضائح الىحدة دذج ب فضائحماسح وح إ

.إى ادذج فضائحته اىح اي غثح ؼح فضائحوح ي لاطإجشاء مقياس عىخ

The measure is a numerical value. When we calculate, we manipulate the measure, not the physical quantity.

Units are a very important part of scientific values and calculations. Without units, the numbers scientists talk about have no meaning. For example, saying "it is 20 outside today" doesn’t mean anything unless you attach a unit of measurement. "It is 20 degrees Fahrenheit outside today," means much more.

. تؼتثش ادذاخ ح ف اذغاتاخ اىاخ اؼح تذا تصثخ اىح تذ ؼى

SI Measurement

The International System of Units (which is abbreviated "SI", from the French "le Système International d' Unités") is the standard system of measurement used by many scientists. Using the same standards of measurement makes it easier for scientists to communicate with one another.

اص فا تادذاخ اذح ماط تغتخذ لث ؼظ اذاسع اؼاء دث تغ ػح ات

http://www.physchem.co.za/Basic%20Skills/Units.htm#measure


6

SI base units

The SI is founded on seven SI base units for seven base quantities assumed to be mutually independent, as given in Table 1.

.ثا اىح االعاعح دذج لاعا سض ادذج اغتخذ. اجذي اتا ث ادذاخ االعاعح اغثؼح

Table 1. SI base units

SI base unit

Base quantity Name Symbol

length meter m

mass kilogram kg

time second s

electric current Ampere A

thermodynamic temperature Kelvin K

amount of substance mole mol

luminous intensity candela cd

SI prefixes

The 12 SI prefixes used to form decimal multiples and submultiples of SI units are given in Table 2.

Table 2. SI prefixes

Factor Name Symbol

109 giga G

106 mega M

103 kilo k

102 hecto h

101 deka da

Factor Name Symbol

10-1 deci d

10-2 centi c

10-3 milli m

10-6 micro µ

10-9 nano n

10-12 pico p

10-15 femto f


7

SI derived units

Other quantities, called derived quantities, are defined in terms of the seven base quantities via a system of quantity equations. The SI derived units for these derived quantities are obtained from these equations and the seven SI base units. Examples of such SI derived units are given in Table 3, where it should be noted that the symbol 1 for quantities of dimension 1 such as mass fraction is generally omitted.

.تاعتخذا اما ااعثح األعاعحتؼشف خالي اىاخ أاىاخ اشتمح ى

“Staircase” Method

Draw and label this staircase every time you need to use this method, or until you can do the conversions from memory

Problem: Convert 6.5 kilometers to meters

Start out on the “kilo” step. To get to the meter (basic unit) step, we need to move three steps to the right. Move the decimal in 6.5 three steps to the right

Answer: 6500 m


8

PART A – SI UNITS

What type of measurement is indicated by each of the following units? Choices are in the last column.

.اىح افضائح ات تماط تا ادذاخ اتاح ا

.

1. g/mL

2. s

3. km

4. g

5. cm3

6. mm

7. mg

8. L

9. g/cm3

density length mass time volume

PART B – SCIENTIFIC NOTATION

Convert the following numbers into or out of scientific notation. Remember to keep the same number of significant figures.

1. 0.00003 cm

2. 8,600,000 g

3. 0.021 kg

4. 340 nm

5. 1.05 105 mm

6. 1.00 10-3 m

7. 7.20 x 10-6 s

8. 4.404 x 102 m/s

Exercises

SI Units


9

Compare using <, >, or =.

56 cm 6 m 7 g 698 mg 1,500 mL 1.5 L

536 cm 53.6 dm 43 mg 5 g 3.6 m 3 cm

Circle the two terms in each group that are related. Explain how the terms are related. .اثا و جػح تذث ىا تافما، فغش عثة زا اتافكدط

1. Celsius degree, mass, Kelvin

2. balance, second, mass

3. kilogram, liter, cubic centimeter

4. time, second, distance

5. decimeter, kilometer, Kelvin

Exercises

Metric conversion


10

Who is more accurate when measuring a book that has a true

length of 17.0cm?

Susan:

17.0cm, 16.0cm, 18.0cm, 15.0cm

Amy:

15.5cm, 15.0cm, 15.2cm, 15.3cm

Who is more precise when measuring the same 17.0cm book?

Susan:

17.0cm, 16.0cm, 18.0cm, 15.0cm

Amy:

15.5cm, 15.0cm, 15.2cm, 15.3cm

Precision: a measure of how close a series of measurements are to one

another. A measure of how exact a measurement is.

دسجح دلح اماط تاعتخذا أداخ اماط

Accuracy : a measure of how close a measurement is to the true value of the

quantity being measured.

.ت ت لاعامذاس تافك دلح اماط غ امح اصذذح ىح ا

25.2

Accuracy and Precision


11

Example 1: Evaluate whether the following are precise, accurate or both

Neither accurate nor precise

Precise but not Accurate

Precise AND accurate


12

ACCURACY AND PRECISION

Definitions:

Accuracy – how close a measurement is to ______________________________

Precision – how close a measurement is to _______________________________

Precision versus Accuracy: Look at each target and decide whether the “hits” are accurate, precise, both accurate

and precise, or neither accurate nor precise: (Note: An accurate “hit” is a bulls eye!)

Accurate?: Yes / No

Precise?: Yes / No

Accurate?: Yes / No

Precise?: Yes / No

Accurate?: Yes / No

Precise?: Yes / No

Exercises

Accuracy and Precision


13

The picture below shows a moving car.

Picture 1: A moving car

Look at the picture; think about all physical quantities you can find in the picture.

You can find mass, weight, speed, velocity, force of friction, distance, displacement.

Some of these quantities have magnitude (size) and direction we call them vectors, such

as displacement, weight, velocity and force of friction. Others only have magnitude (size)

such as mass, speed, we call them scalars.

لمعرفتها تسمى كمات واتجاههناك كمات فزائة تحتاج مقدار أن مالحظةمن خالل الصورة الموضحة مكن

.للمقدار فقط لمعرفتها تسمى كمات عددة حتاجمتجهة، ومنها ما

25.4

Vectors and scalars المتجهة اتالكميو العددية اتالكمي

Scalar:

A quantity with magnitude only.

.فقطه الكمة الت كف لتحددها مقدار : الكمة العددة

Vector:

A quantity with magnitude and direction.

.ه الكمة الت لزم لتحددها مقدار واتجاه: الكمة المتجهة

.


14

Question: Identify the quantity either it is vector or scalar.

Quantity Vector Scalar

(تغاسع) Acceleration

(غادح) Area

(وثافح) Density

(طالح0 Energy

Gravitational field strength

(شذج جاي اجارتح)

(وتح) Mass

(دسجح اذشاسج) Temperature

Vectors are represented by a bold letter F or an arrow above

the symbolF

, whereas scalars are represented by a normal letter, F= 50 N due south represents vector but F = 50 N represents the magnitude only.

.ددة فتمثل برمز فقطاما الكمة الع. تمثل المتجهات اما برمز بخط غامق وسمك او برمز فوقة سهم

In the diagram a vector is represented by an arrow.

Representing vectors

تمثل المتجهات


15

1. The length of the arrow, drawn to scale, represents its magnitude. 2. The direction of the arrow is the direction of the vector.

Note:

For vectors confined to one dimension, positive or negative sign with magnitude of vector indicate the direction of vector.

You can decide which direction to be positive but in general (right +, left -), (north +, south -), (up +, down -).

Example: (Scale: 1 cm represents 5ms-1)

Figure 1 vector representing

:التمثل البان للمتجهات

:تم تمثل المتجهات برسم سهم بمقاس رسم مناسب بحث أن

.المتجهةمثل طول السهم مقدار الكمة -1 .اتجاه السهم ف نفس اتجاه الكمة المتجهة -2

: حظةمال

عند التعامل مع المتجهات ف بعد واحد لتدل على اتجاه ( -، ) + مكن استخدام اإلشارات -1 .الكمات المتجهة

مكن اختار أي اتجاه لكون االتجاه الموجب لكن عادة االتجاهات المن والشمال واألعلى -2 .واالتجاهات السار والجنوب واألسفل + تأخذ إشارة


16

Question: Draw the vectors ارسم المتجهات التالية

1. A man walks 20m due east. تش جح اششق 20سج ش

2. A plan flies 100km due north. و تش شاال 100طائشج تذك

3. A boat travels 15 km at a direction of 20 north of east. دسجح شاي اششق 20و تش ف اتجاج 15لاسب ثذش

4. A car travels 80 Km/hr at a direction of 20 south of west. دسجح جب اغشب 20و تش ف اغاػح تاتجاج 80عاسج تتذشن تغشػح


17

The figure below shows some paths you could take from your home to school.

Picture 2 your displacement from home to school is the same regardless of which route you take

.مقدار ثابت اإلزاحة أنوف كل الحاالت نالحظ . من البت للمدرسة للتوجهالشكل وضح عدة مسارات

You could first walk 2 km south and then 4 km west and arrive at school, or you could

travel 1km west then 2km south, and then 3km west. In each case, the displacement

vector d is the same. This displacement is called a resultant vector.

Addition of vectors (resultant of vectors):

(المحصلة إيجاد ) جمع المتجهات

A resultant is a vector that is equal to the sum of two or more vectors.

.ه متجه وحد مساوي لحاصل الجمع أالتجاه لمتجهن أو أكثر :المحصلة


18

There are two methods to find the resultant vector:

To find the addition of two vectors by drawing

1- Choose the scale for drawing. 2- Draw the first vector. 3- Use the protractor to measure the angle between the first and second vector. 4- Draw the second arrow from the head of the first arrow.

تج تطشمح اشع الجاد اجغ االتجا

اعتخذ امح ماط اضاح ت اتجح االي اثا -3. اسع اتجح االي -2.اختش ماط اشع ااعة -1

اسع عا ث اتجح اثا -4

To find the resultant draw an arrow from the tail of first vector to the head of second

vector. Measure the length of resultant vector by ruler to find the magnitude and

measure the angle between first vector and the resultant vector to find the direction.

د ضشتح تماط ى طي زا اغ مذاس اذصح تغ. االي اح اثا جالجاد اذصح اسع عا تذاي

.تى اضاح ت اتجح االي اذصح اتجاا. اشع

1- Scale drawing (head to tail method):

الطريقة البيانية إليجاد المحصلة


19

a- If the vectors are in one dimension. If the two vectors in the same direction, to find the resultant vector simply add them and

the direction of resultant is the same direction of the vectors.

If the two vectors are in opposite direction, to find the resultant vector simply subtract

them.

اص طشدااا ا واا ف اتجا تؼاوغ فاذصح ح. ا وا اتجا ف فظ االتجاج فاذصح جؼا

b- If the angle between two vectors is 90: To find the resultant magnitude use Pythagoras’s theory R2 = A2 + B2 and to find the

direction of resultant use trigonometry θ = tan−1 B

A

.الجاد اذصحا وا اتجا تؼاذا فغتخذ ظشح فثاغسط

2- Calculation:

الطريقة الحسابية إليجاد المحصلة

http://www.clker.com/clipart-2265.html


20

A negative vector is the opposite direction to a positive vector, we can subtract vector B

from vector A by changing the direction of vector B and adding it to A.

A – B = A + (-B)

Question: A car moving east at 45 km/h turns and travels west at 30 km/h. What

are the magnitude and direction of the change in velocity?

Two vectors may be added together to produce a single resultant. It follows that a single

vector may be split up, or resolved, into two vectors or components.

Components at right angles:

A vector (A) is broken up or resolved into two perpendicular components, Ax a horizontal

component parallel to x-axis, and the other Ay vertical component parallel to y-axis.

Ax= A cos Ay= A sin

Subtraction of vectors

طرح المتجهات

Resolution of vectors

تحليل المتجهات


21

Figure 2 the components of vector A

Question: A bus travels 23.0 km on a straight road that is 30 north of east. What

are the east and north components of its displacement?

ا لح اشوثت تاتجاج اششق . دسجح ف اتجاج اشاي اششل 30وتش تطشك غتم 23تتذشن دافح

اشاي زج االصادح؟

تم تحلل المتجه إلى مركبتن متعامدتن ، المركبة السنة الموازة للمحور السن والمركبة الصادة

.الموازة للمحور الصادي


22

Two or more vectors (A,B,C,...) may be added by:

1- Resolving each vector to its x-and y-components.

2- The x-components are added to form the x-component of the resultant, Rx.

3- The y-components are added to form the y-component of the resultant, Ry.

4- Find the magnitude of resultant, 𝑅 = 𝑅𝑥2 + 𝑅𝑦

2

5- Find the direction of the resultant, 𝜃 = 𝑡𝑎𝑛−1 𝑅𝑦

𝑅𝑥

ى جغ تج ا اوثش

د و تجح اى شوثتح اغح اصادح -1

اجغ اشوثاخ ػى اذس اصادي -3اجغ اشوثاخ ػى اذس اغ -2

𝑅الجاد اذصح اعتخذ اؼاللح -4 = 𝑅𝑥2 + 𝑅𝑦

2

𝜃الجاد اتجاج اذصح اعتخذ اؼاللح -5 = 𝑡𝑎𝑛−1 𝑅𝑦

𝑅𝑥

Question: three forces act on an object 3N due east, 4 N due north and 5N at 30 due north of west. What is the resultant force on the object?

Addition of vectors by the method of components

جمع المتجهات باستخدام طرقة التحلل


23

1. For each of the following commonly used measurements, indicate its symbol. Use the symbols to complete the following sentences with the most appropriate unit. Units may be used more than once or not at all.

.(ى اعتخذا اشض أوثش شج.) اوتة سض ادذج اغتخذ ىاخ اتاح ، ث اعتخذ تى اج اتاح

_____ milliliter _____ kilogram _____ meter

_____ milligram _____ millimeter _____ kilometer

_____ millisecond _____ liter _____ centimeter

_____ gram _____ second

1. Colas may be purchased in two or three _____ bottles.

2. The mass of a bowling ball is 7.25 _____.

3. The length of the common housefly is about 1 _____.

4. The mass of a paperclip is about 1 _____.

5. One teaspoon of cough syrup has a volume of 5 _____.

6. Stand with your arms raised out to your side. The distance from your nose to your outstretched fingers is about 1 _____.

7. The body mass of a flea is about 0.5 _____.

8. On a statistical basis, smoking a single cigarette lowers your life expectancy by 642,000 _____, or 10.7 minutes.

Questions


24

Metric Conversions

2. Fill in the boxes in the stair step diagram.

3. Try these conversions, using the ladder method.

1000 mg = _______ g 1 L = _______ mL 120 mg = _____ g

160 cm = _______ mm 14 km = _______ m 5.6 m = _____ cm

109 g = _______ kg 250 m = _______ km 8 mm = _____ cm

2000 mg = _______ g 5 L = _______ mL 16 cm = _______ mm

104 km = _______ m 198 g = _______ kg 2500 m = _______ km

480 cm = _____ m 75 mL = _____ L 65 g = _____ mg

5.6 kg = _____ g 50 cm = _____ m 6.3 cm = _____ mm


25

4. Match the terms in Column II with the descriptions in Column I. Write the letters of the correct term in the blank on the left.

Iغ اصف ااعة ف اؼد IIلات اىح ف اؼد

Column I Column II

_____ 1. distance between two points

a. time

_____ 2. SI unit of length

b. volume

_____ 3. tool used to measure length

c. mass

_____ 4. units obtained by combining other units

d. density

_____ 5. amount of space occupied by an object

e. meter

_____ 6. unit used to express volume

f. kilogram

_____ 7. SI unit of mass

g. derived

_____ 8. amount of matter in an object

h. liter

_____ 9. mass per unit of volume

i. second

_____ 10. temperature scale of most laboratory thermometers

j. Kelvin

_____ 11. instrument used to measure mass

k. length

_____ 12. interval between two events 1. Balance

_____ 13. SI unit of temperature

m. meter stick

_____ 14. SI unit of time

n. thermometer

_____ 15. instrument used to measure temperature o. Celsius


26

5. Evaluate whether the following are precise, accurate or both.

6. A car travels 30 km east then 40 km north. Draw a scale diagram to represent these two vectors and use it to find the car’s resultant from its starting point.

استخدم الطرقة البانة إلجاد محصلة المسافات الت . شماالكبلومتر 40كبلومتر شرقا ثم 30سارة تتحرك

قطعتها السارة

7. A car travels 30 km east then 40 km north. Find the car’s resultant from its starting point by calculation.

.الحسابةاوجد المحصة بالطرقة . كبلومتر شماال 40كبلومتر شرقا ثم 30سارة تتحرك


27

8. A group of students worked in separate teams to measure the length of an object.

الكمال الفراغات التالة ف الجدولاستخدم البانات. مجموعة الطلبة عملوا كفرق منفصلة لحساب طول جسم ما

Here are their data:

• The average length is------------------------------------------------------------------cm.

This is the mean or average.

• Subtract the highest value from the lowest value---------------------------------------- cm.

This is the range or spread.

• Divide this number by 2: --------------------------------------------------------cm.

This is the approximate ± range from the average.

• The precision of the measurement can be shown as average ± range.

The precision of the measurement was ________±_____ cm.

Team 1 Team 2 Team 3 Team 4 Team 5 Team 6 Team 7

2.65 cm 2.75 cm 2.80 cm 2.77 cm 2.60 cm 2.65 cm 2.68 cm


28

Resources:

Books:

1- Mee, Chris, and WENDY BROWN. AS/A2 PHYSICS. HODDER & STOUGHTON, 2000.

2- ZITZEWITZ, PAUL, and NOEL GUITRY. GLENCOE PHYSICS PRINCIPLES AND PROBLEMS. USA: GLENCOE/MCGRAW HILL, 1999.

Websites:

1. http://www.physchem.co.za/Basic%20Skills/Units.htm

2. http://www.nwr1biology.com/pdfs/I%20Metric%20Conversion%20Worksheet.pdf

3. http://sciencespot.net/Media/metriccnvsn2.pdf

3- Picture1: http://www.flickr.com/photos/quicklunarcop/3746082148/

4- Picture2: http://www.physicsclassroom.com/Class/vectors/U3L1a.cfm

http://www.physchem.co.za/Basic%20Skills/Units.htm

http://www.nwr1biology.com/pdfs/I%20Metric%20Conversion%20Worksheet.pdf

http://sciencespot.net/Media/metriccnvsn2.pdf

http://www.flickr.com/photos/quicklunarcop/3746082148/

http://www.physicsclassroom.com/Class/vectors/U3L1a.cfm

physics - science curriculum office welcomes you to our ... · pdf fileby the end of the unit,...

Documents