Units and Measurements PDF

GENERAL PHYSICS 1 SUBJECT TEACHER: JACOB S. MERCADO, LPT AGENDA: 1. Routines/5S 3. Activities: Greetings Discussion Prayer Attendance 4. Wrap Up/5s 2. Motivation: Reminders/Announcements R...

GENERAL PHYSICS 1 SUBJECT TEACHER: JACOB S. MERCADO, LPT AGENDA: 1. Routines/5S 3. Activities: Greetings Discussion Prayer Attendance 4. Wrap Up/5s 2. Motivation: Reminders/Announcements Recalling measurements in Prayer their daily routine. Learning Outcomes: 1. Understand that physical quantities have numerical magnitude and a unit 2. Recall base quantities and use prefixes 3. Show an understanding of orders of magnitude  GREETINGS! PRAYER CHECKING OF ATTENDANCE Motivation: What are some daily activities that you measure length, mass, time and others? AGENDA: 1. Routines/5S 3. Activities: Greetings Subject Orientation Prayer Overview of Topics Attendance Checking of Reg. Form 4. Wrap Up/5s 2. Motivation: Reminders/Announcements Getting to know Prayer 1.1 Physical Quantities Quantitative versus qualitative Most observation in physics are quantitative Descriptive observations (or qualitative) are usually imprecise Qualitative Observations Quantitative Observations How do you measure What can be measured with the artistic beauty? instruments on an aeroplane? 1.1 Physical Quantities A physical quantity is one that can be measured and consists of a magnitude and unit.  70 4.5 m Measuring length km/h  SI units Vehicles Not are Exceeding common 1500 kg In today Unladen Weight 1.1 Physical Quantities Are classified into two types: Base quantities Derived quantities Derived quantity is like the house that was Base quantity build up from a collection is like the brick – the of bricks (basic quantity) basic building block of a house 1.2 SI Units SI Units – International System of Units Base Quantities Name of Unit Symbol of Unit length metre m mass kilogram kg time second s electric current ampere A temperature kelvin K amount of substance mole mol luminous intensity candela cd 1.2 SI Units This Platinum Iridium cylinder is the standard kilogram. 1.2 SI Units olume area v density speed n o a e e c t r i l Word Splash force Pressure 1.2 SI Units Example of derived quantity: area Defining equation: area = length × width In terms of units: Units of area = m × m = m2 Defining equation: volume = length × width × height In terms of units: Units of volume = m × m × m = m3 Defining equation: density = mass ÷ volume In terms of units: Units of density = kg / m3 = kg m−3 1.2 SI Units Work out the derived quantities for: distance Defining equation: speed = time velocity Defining equation: acceleration = time Defining equation: force = mass × acceleration 1.2 SI Units Work out the derived quantities for: Force Defining equation: Pressure = Area Defining equation: Work = Force × Displacement Work done Defining equation: Power =Time 1.2 SI Units Derived Relation with Base and Special Unit Quantity Derived Quantities Name area length × width volume length × width × height density mass  volume speed distance  time acceleration change in velocity  time force mass × acceleration newton (N) pressure force  area pascal (Pa) work force × distance joule (J) power work  time watt (W)  1.3 Prefixes Prefixes simplify the writing of very large or very small quantities Prefix Abbreviation Power 1. 2 Mb – 2,000,000 bytes 2. 5 Gb – 5,000,000,000 bytes nano n 10−9 3. 1 kg – 1,000 g micro  10−6 4. 500 mL – 0.5 L 5. 8 µm – 0.000008 m milli m 10−3 centi c 10−2 deci d 10−1 kilo k 103 mega M 106 giga G 109  1.3 Prefixes Alternative writing method Using standard form N × 10n where 1  N < 10 and n is an integer 600px-Andromeda_galaxy Scientific notation – 2.5 × 106 Real number – 2,500,000 light years Scientific notation = 4.5 x 10 −10 Real number – 0.00000000045 m Scientific notation = 6.9 x 1010 Real number – 69,000,000,000 m This galaxy is about 2.5 × 106 The diameter of this atom light years from the Earth. is about 1 × 10−10 m. 1. Scientific notation: 3.49 x 109 m Real Number: 3490000000. m 2. Real Number: 0.000000005.8 m Scientific Notation: 5.8 x 10 −9 m 1. A physical quantity is a quantity that can be measured and consists of a numerical magnitude and a unit. 2. The physical quantities can be classified into base quantities and derived quantities. 3. There are seven base quantities: length, mass, time, current, temperature, amount of substance and luminous intensity. 4. The SI units for length, mass and time are meter, kilogram and second respectively. 5. Prefixes are used to denote very big or very small numbers. 1.5 Measurement of Length and Time Accurate Measurement No measurement is perfectly accurate Some error is inevitable even with high precision instruments Two main types of errors – Random errors – Systematic errors 1.5 Measurement of Length and Time Accurate Measurement Random errors occur in all measurements. Arise when observers estimate the last figure of an instrument reading Also contributed by background noise or mechanical vibrations in the laboratory. Called random errors because they are unpredictable Minimise such errors by averaging a large number of readings Freak results discarded before averaging 1.5 Measurement of Length and Time Accurate Measurement Systematic errors are not random but constant Cause an experimenter to consistently underestimate or overestimate a reading They Due to the equipment being used – e.g. a ruler with zero error may be due to environmental factors – e.g. weather conditions on a particular day Cannot be reduced by averaging, but they can be eliminated if the sources of the errors are known 1.5 Measurement of Length and Time Length Measuring tape is used to measure relatively long lengths For shorter length, a metre rule or a shorter rule will be more accurate 1.5 Measurement of Length and Time Correct way to read the scale on a ruler Position eye perpendicularly at the mark on the scale to avoids parallax errors Another reason for error: object not align or arranged parallel to the scale 1.5 Measurement of Length and Time Many instruments do not read exactly zero when nothing is being measured Happen because they are out of adjustment or some minor fault in the instrument Add or subtract the zero error from the reading shown on the scale to obtain accurate readings Vernier calipers or micrometer screw gauge give more accurate measurements 1.5 Measurement of Length and Time Table 1.6 shows the range and precision of some measuring instruments Instrument Range of Accuracy measurement Measuring tape 0−5m 0.1 cm Metre rule 0−1m 0.1 cm Vernier calipers 0 − 15 cm 0.01 cm Micrometer screw gauge 0 − 2.5 cm 0.01 mm 1.5 Measurement of Length and Time Vernier Calipers Allows measurements up to 0.01 cm Consists of a 9 mm long scale divided into 10 divisions 1.5 Measurement of Length and Time Vernier Calipers The object being measured is between 2.4 cm and 2.5 cm long. The second decimal number is the marking on the vernier scale which coincides with a marking on the main scale. 1.5 Measurement of Length and Time Here the eighth marking on the vernier scale coincides with the marking at C on the main scale Therefore the distance AB is 0.08 cm, i.e. the length of the object is 2.48 cm 1.5 Measurement of Length and Time The reading shown is 3.15 cm. The instrument also has inside jaws for measuring internal diameters of tubes and containers. The rod at the end is used to measure depth of containers. 1.5 Measurement of Length and Time Micrometer Screw Gauge To measure diameter of fine wires, thickness of paper and small lengths, a micrometer screw gauge is used The micrometer has two scales: Main scale on the sleeve Circular scale on the thimble There are 50 divisions on the thimble One complete turn of the thimble moves the spindle by 0.50 mm 1.5 Measurement of Length and Time Micrometer Screw Gauge Two scales: main scale and circular scale One complete turn moves the spindle by 0.50 mm. Each division on the circular scale = 0.01 mm 1.5 Measurement of Length and Time Precautions when using a micrometer 1. Never tighten thimble too much – Modern micrometers have a ratchet to avoid this 2. Clean the ends of the anvil and spindle before making a measurement – Any dirt on either of surfaces could affect the reading 3. Check for zero error by closing the micrometer when there is nothing between the anvil and spindle – The reading should be zero, but it is common to find a small zero error –Correct zero error by adjusting the final measurement 1.5 Measurement of Length and Time Time Measured in years, months, days, hours, minutes and seconds SI unit for time is the second (s). Clocks use a process which depends on a regularly repeating motion termed oscillations. 1.5 Measurement of Length and Time Caesium atomic clock 1999 - NIST-F1 begins operation with an uncertainty of 1.7 × 10−15, or accuracy to about one second in 20 million years 1.5 Measurement of Length and Time Time The oscillation of a simple pendulum is an example of a regularly repeating motion. The time for 1 complete oscillation is referred to as the period of the oscillation. 1.5 Measurement of Length and Time Pendulum Clock Measures long intervals of time Hours, minutes and seconds Mass at the end of the chain attached to the clock is allowed to fall Gravitational potential energy from descending mass is used to keep the pendulum swinging In clocks that are wound up, this energy is stored in coiled springs as elastic potential energy. 1.5 Measurement of Length and Time Watch also used to measure long intervals of time most depend on the vibration of quartz crystals to keep accurate time energy from a battery keeps quartz crystals vibrating some watches also make use of coiled springs to supply the needed energy 1.5 Measurement of Length and Time Stopwatch Measure short intervals of time Two types: digital stopwatch, analogue stopwatch Digital stopwatch more accurate as it can measure time in intervals of 0.01 seconds. Analogue stopwatch measures time in intervals of 0.1 seconds. 1.5 Measurement of Length and Time Errors occur in measuring time If digital stopwatch is used to time a race, should not record time to the nearest 0.01 s. reaction time in starting and stopping the watch will be more than a few hundredths of a second an analogue stopwatch would be just as useful 1.5 Measurement of Length and Time Ticker-tape Timer electrical device making use of the oscillations of a steel strip to mark short intervals of time steel strip vibrates 50 times a second and makes 50 dots a second on a paper tape being pulled past it used only in certain physics experiments 1.5 Measurement of Length and Time Ticker-tape Timer Time interval between two consecutive dots is 0.02 s If there are 10 spaces on a pieces of tape, time taken is 10 × 0.02 s = 0.20 s. Counting of the dots starts from zero A 10-dot tape is shown below. 1. The metre rule and half-metre rule are used to measure lengths accurately to 0.1 cm. 2. Vernier calipers are used to measure lengths to a precision of 0.01 cm. 3. Micrometer are used to measure length to a precision of 0.01 mm. 4. Parallax error is due to: (a) incorrect positioning of the eye (b) object not being at the same level as the marking on the scale 5. Zero error is due to instruments that do not read exactly zero when there is nothing being measured. 6. The time for one complete swing of a pendulum is called its period of oscillation. 7. As the length of the pendulum increases, the period of oscillation increases as well. Metric Units and Conversions What is a Unit Conversion?  A unit conversion is a changing of one unit to another.  Unit Examples: ▪ meters ▪ grams ▪ inches ▪ feet ▪ pounds ▪ seconds  Any time you write down a number in physics, you should have a unit written after it!!! What is a Metric Unit? Metric units are the universally excepted units around the world (except for the US). They are the easiest to convert. Metric Unit Examples: meters liters grams Base Units – all other metric units are based off of these (km, cm, ml, kg) Dimensional Analysis Common Metric Units (Prefixes) Abbreviation Mega- M kilo- k hecto- h deka- da or D Base- m, l, g deci- d centi- c milli- m micro- µ nano- n Metric Conversion Factors Knowing these conversion 1 km= 1000 m factors makes calculating 100 cm= 1 m conversions easy! 1000 mm = 1 m These also work for liters and 10 mm = 1 cm grams. Just replace the base unit (m) with a (g) or (l). Conversion Factor Cards Each group has a set of cards with common conversion factors on them that you will be using for the next two days. Front Back 1m 100 cm 100 cm 1m Dimensional Analysis A mathematical way to convert one unit to another. This works for metric units and non-metric (English) units. This works by taking the unit you are given and multiplying it by a conversion factor. Example 1: Convert 3m to cm 3m For meters to cancel out, meters 100 cm in the conversion factor must be 1m on the opposite side of the fraction (fence). Given Conversion Factor Multiply every number on top of the fence and divide by = 300cm the bottom. Example 2: Convert 1516 g to kg 1516 g 1 kg 1000 g conversion factor = 1.516 kg Whiteboard Problem 1 Convert 1200 cm to m. Whiteboard Problem 1 Convert 1200 cm to m. Whiteboard Problem 2 Convert 5200 mL to L. Whiteboard Problem 2 Convert 5200 mL to L. Example 3: Convert 7200mm to km 7200 mm 1 cm 1 km 10 mm 100,000 cm =.0072 km Whiteboard Problem 3 Convert 3 m to mm. Whiteboard Problem 3 Convert 3 m to mm. Non-Metric (English) Unit Conversions Common Conversion Factors 5280 ft = 1 mile 12 in = 1 ft 1 mile = 1600 m English to Metric conversion factors 1 in = 2.54 cm 3 ft = 1 yard Example 4: Convert 2 miles to ft 2 mi 5280 ft 1 mi = 10,560 ft Whiteboard Problem 4 Convert 3.2 ft to inches. Whiteboard Problem 4 Convert 3.2 ft to inches. Example 5: Convert 5 ft to cm 5 ft 12 in 2.54 cm 1 ft 1 in = 152. 4 cm Whiteboard Problem 5 Convert 50 inches to m. Whiteboard Problem 5 Convert 50 inches to m. Warm-Up: Solve using Dimensional Analysis 1. Convert 45 inches to cm. 2. Convert 8 m to inches. Warm-Up: Using Dimensional Analysis 1. Convert 10ft to cm. 2. Convert 5 km to in.