Physics. Grade 10 Advanced Level. Handling physical quantities

Transcription

1 Physics Grade 10 Advanced Level Handling physical quantities

2 Contents UNIT 1: Handling physical quantities Core Standards... 3 Objectives SI Units Accuracy and Precision Vector and scalar quantities. 13 Question. 23 References

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. 3

4 وحدات القياس الدولية 25.1 SI Units 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. تذ ظا ػا مث ي دذاخ ا م اط ال تغتط غ دضاست ا أ ت جذ. تخ ا ف ضى إرا ى ان ؼا ش م اط ا ىت ح ايط ي ا ض ػ ى عث ا ثاي. 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. ض ا ؼ اء ا ى اخ ا ت تصف ا ؼا ا طث ؼ. ى لش س ا ايو ح اي ؼ ح ا ت ى ا جغ ا ا ػ ى عث ا ثاي الكتلة ف ايضش سي ماس ح أ ماس جغ ج ي ا ىت ح تجغ آخش ؼش ف مذاس وت ت ت ؼ ى آخش أ ػش ف اد ح ؼ اس ت فك. The instrument used is called a BALANCE, shown above. إ ا ج اص ا غتخذ غ ى ميزان ضخ ف ا شى أػال. 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. أي و ح ف ض ائ ح ى أ تؼش ف اد ح ا ؼ اخ ا ضش س ح م اع ا. ػ ى عث ا ثاي ط ي جغ ا ى أ مش س ت ماس ت إ ى جغ ؼش ف ا ط ي ث اي غطشج. 4

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. الىحدة ؼ اس خصص ى ح ف ض ائ ح تغتخذ ماس ح تى ح ؼ ح. إ ػ ح ماس ح و ح خع ى مقياس إجشاء ل اط يو ح ف ض ائ ح ؼ ح غثح ت ه ا ى ح اي ف ض ائ ح إ ى ا دذج. ف ض ائ ح ب دذج 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. SI Measurement تؼتثش ا دذاخ ح ف ا ذغاتاخ ا ى اخ ا ؼ ح تذ ا تصثخ ا ى ح تذ ؼ ى. 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. ا دذاخ ا ذ ح م اط تغتخذ لث ؼظ ا ذاسع ا ؼ اء د ث تغ ػ ح ا ت اص ف ا ت 5

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. ا جذ ي ا تا ث ا دذاخ االعاع ح ا غثؼح. ث ا ا ى ح االعاع ح دذج ل اع ا س ض ا دذج ا غتخذ. Table 1. SI base units SI base unit SI prefixes 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 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 10 9 giga G 10 6 mega M 10 3 kilo k 10 2 hecto h 10 1 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 pico p femto f 6

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. Staircase Method ا ى اخ ا شتمح ى أ تؼشف خالي ا ى اخ األعاع ح تاعتخذا ا م ا ا اعثح. 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 7

8 Exercises SI Units PART A SI UNITS What type of measurement is indicated by each of the following units? Choices are in the last column. ا ا ى ح ا ف ض ائ ح ا ت تماط ت ا ا دذاخ ا تا ح.. 1. g/ml 2. s 3. km 4. g 5. cm 3 6. mm 7. mg 8. L 9. g/cm 3 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 cm 2. 8,600,000 g kg nm mm m x 10-6 s x 10 2 m/s 8

9 Exercises Metric conversion 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. د ط اث ا و ج ػح تذ ث ى ا ت افما فغش عثة زا ا ت افك. 1. Celsius degree, mass, Kelvin 2. balance, second, mass 3. kilogram, liter, cubic centimeter 4. time, second, distance 5. decimeter, kilometer, Kelvin 9

10 25.2 Grade 10 Unit AP.1 Handling Physical Quantities Accuracy and Precision Accuracy : a measure of how close a measurement is to the true value of the quantity being measured. مذاس ت افك دلح ا م اط غ ا م ح ا صذ ذح ى ح ا ت ت ل اع ا. 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 Precision: a measure of how close a series of measurements are to one another. A measure of how exact a measurement is. دسجح دلح ا م اط تاعتخذا أد اخ ا م اط 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 10

11 Example 1: Evaluate whether the following are precise, accurate or both Neither accurate nor precise Precise but not Accurate Precise AND accurate 11

12 Exercises Accuracy and Precision 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 12

13 25.4 Vectors and scalars Grade 10 Unit AP.1 Handling Physical Quantities العددية الكمي ات والكمي ات المتجهة 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. من خالل الصورة الموضحة مكن مالحظة أن هناك كم ات ف ز ائ ة تحتاج مقدار واتجاه لمعرفتها تسمى كم ات متجهة ومنها ما حتاج للمقدار فقط لمعرفتها تسمى كم ات عدد ة. Scalar: A quantity with magnitude only. الكم ة العدد ة: ه الكم ة الت كف لتحد دها مقدار فقط. Vector: A quantity with magnitude and direction. الكم ة المتجهة : ه الكم ة الت لزم لتحد دها مقدار واتجاه. 13

14 Question: Identify the quantity either it is vector or scalar. Quantity Vector Scalar Acceleration )تغاسع ) Area ) غادح ) Density )وثافح ) 0 طالح Energy ) Gravitational field strength )شذج جاي ا جارت ح ) Mass )وت ح ) ( Temperature دسجح ا ذشاسج ) Representing vectors تمث ل المتجهات 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. تمثل المتجهات اما برمز بخط غامق وسم ك او برمز فوقة سهم. اما الكم ة العدد ة فتمثل برمز فقط. In the diagram a vector is represented by an arrow. 14

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. التمث ل الب ان للمتجهات: تم تمث ل المتجهات برسم سهم بمق اس رسم مناسب بح ث أن: - مثل طول السهم مقدار الكم ة المتجهة. - اتجاه السهم ف نفس اتجاه الكم ة المتجهة. 1 2 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 -). مالحظة: - مكن استخدام اإلشارات ( + - ) عند التعامل مع المتجهات ف بعد واحد لتدل على اتجاه الكم ات المتجهة. - مكن اخت ار أي اتجاه ل كون االتجاه الموجب لكن عادة االتجاهات ال م ن والشمال واألعلى تأخذ إشارة + واالتجاهات ال سار والجنوب واألسفل. 1 2 Example: (Scale: 1 cm represents 5ms -1 ) Figure 1 vector representing 15

16 Question: Draw the vectors 1. A man walks 20m due east. ارسم المتجهات التالية سج ش 20 تش ج ح ا ششق طائشج تذ ك 100 و تش ش اال north. 2. A plan flies 100km due 3. A boat travels 15 km at a direction of 20 north of east. لاسب ثذش 15 و تش ف اتجاج 20 دسجح ش اي ا ششق 4. A car travels 80 Km/hr at a direction of 20 south of west. ع اسج تتذشن تغشػح 80 و تش ف ا غاػح تاتجاج 20 دسجح ج ب ا غشب 16

17 Addition of vectors (resultant of vectors): ) جمع المتجهات ( المحصلة إيجاد 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 الشكل وضح عدة مسارات للتوجه من الب ت للمدرسة. وف كل الحاالت نالحظ أن اإلزاحة مقدار ثابت. 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. A resultant is a vector that is equal to the sum of two or more vectors. المحصلة: ه متجه وح د مساوي لحاصل الجمع أالتجاه لمتجه ن أو أكثر. 17

18 There are two methods to find the resultant vector: 1- Scale drawing (head to tail method): الطريقة البيانية إليجاد المحصلة 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. ال جاد ا ج غ االتجا تج تطش مح ا شع 1- اختش م اط ا شع ا اعة. 2 - اسع ا تجح اال ي. 3- اعتخذ ا م ح م اط ا ضا ح ت ا تجح اال ي ا ثا 4- اسع ع ا ث ا تجح ا ثا 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. ال جاد ا ذص ح اسع ع ا ج تذاي اال ي ا ح ا ثا. ى ط ي زا ا غ مذاس ا ذص ح تغد ضشتح ت م اط ا شع. تى ا ضا ح ت ا تجح اال ي ا ذص ح اتجا ا. 18

19 2- Calculation: الطريقة الحسابية إليجاد المحصلة 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. ا وا ا تج ا ف فظ االتجاج فا ذص ح ج ؼ ا. ا ا ا وا ا ف اتجا تؼاوغ فا ذص ح حاص طشد ا b- If the angle between two vectors is 90 : To find the resultant magnitude use Pythagoras s theory R 2 = A 2 + B 2 and to find the direction of resultant use trigonometry θ = tan 1 B A ا وا ا تج ا تؼا ذا ف غتخذ ظش ح ف ثاغ س ط ال جاد ا ذص ح. 19

20 Subtraction of vectors طرح المتجهات 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? Resolution of vectors تحليل المتجهات 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, A x a horizontal component parallel to x-axis, and the other A y vertical component parallel to y-axis. A x = A cos A y = A sin 20

21 Figure 2 the components of vector A تم تحل ل المتجه إلى مركبت ن متعامدت ن المركبة الس ن ة المواز ة للمحور الس ن والمركبة الصاد ة المواز ة للمحور الصادي. 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? تتذشن داف ح 23 و تش تطش ك غتم 30 دسجح ف اتجاج ا ش اي ا ششل. ا ل ح ا شوثت تاتجاج ا ششق ا ش اي زج االصادح 21

22 Addition of vectors by the method of components جمع المتجهات باستخدام طر قة التحل ل 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, R x. 3- The y-components are added to form the y-component of the resultant, R y. 4- Find the magnitude of resultant, R = R x 2 + R y 2 5- Find the direction of the resultant, θ = tan 1 R y R x ى ج غ تج ا اوثش 1- د و تجح ا ى شوثت ح ا غ ح ا صاد ح 2- اج غ ا شوثاخ ػ ى ا ذ س ا غ 3- اج غ ا شوثاخ ػ ى ا ذ س ا صادي R = R x 2 + R y 2 θ = tan 1 R y R x 4- ال جاد ا ذصح اعتخذ ا ؼاللح 5- ال جاد اتجاج ا ذص ح اعتخذ ا ؼاللح 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? 22

23 Questions 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. اوتة س ض ا دذج ا غتخذ ى اخ ا تا ح ث اعتخذ تى ا ج ا تا ح.) ى اعتخذا ا ش ض أوثش شج(. 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 The length of the common housefly is about The mass of a paperclip is about One teaspoon of cough syrup has a volume of Stand with your arms raised out to your side. The distance from your nose to your outstretched fingers is about The body mass of a flea is about On a statistical basis, smoking a single cigarette lowers your life expectancy by 642,000, or 10.7 minutes. 23

24 Metric Conversions 2. Fill in the boxes in the stair step diagram. 3. Try these conversions, using the ladder method 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 24

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. لات ا ى ح ف ا ؼ د II غ ا صف ا اعة ف ا ؼ د I Column I 1. distance between two points 2. SI unit of length 3. tool used to measure length 4. units obtained by combining other units 5. amount of space occupied by an object 6. unit used to express volume 7. SI unit of mass 8. amount of matter in an object 9. mass per unit of volume 10. temperature scale of most laboratory thermometers 11. instrument used to measure mass 12. interval between two events 13. SI unit of temperature 14. SI unit of time 15. instrument used to measure temperature Column II a. time b. volume c. mass d. density e. meter f. kilogram g. derived h. liter i. second j. Kelvin k. length 1. Balance m. meter stick n. thermometer o. Celsius 25

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. س ارة تتحرك 30 كبلومتر شرقا ثم 40 كبلومتر شماال. استخدم الطر قة الب ان ة إل جاد محصلة المسافات الت قطعتها الس ارة 7. A car travels 30 km east then 40 km north. Find the car s resultant from its starting point by calculation. س ارة تتحرك 30 كبلومتر شرقا ثم 40 كبلومتر شماال. اوجد المحصة بالطر قة الحساب ة. 26

27 8. A group of students worked in separate teams to measure the length of an object. مجموعة الطلبة عملوا كفرق منفصلة لحساب طول جسم ما. استخدم الب انات ف الجدول الكمال الفراغات التال ة Here are their data: Team 1 Team 2 Team 3 Team 4 Team 5 Team 6 Team cm 2.75 cm 2.80 cm 2.77 cm 2.60 cm 2.65 cm 2.68 cm 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. 27

28 Resources: Books: 1- Mee, Chris, and WENDY BROWN. AS/A2 PHYSICS. HODDER & STOUGHTON, ZITZEWITZ, PAUL, and NOEL GUITRY. GLENCOE PHYSICS PRINCIPLES AND PROBLEMS. USA: GLENCOE/MCGRAW HILL, Websites: Picture1: 4- Picture2: 28