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Slide 1:

Measurements and Units

2.1 Measurements in Daily Life:

2.1 Measurements in Daily Life We often make measurements in our daily lives, either accurately or by estimations. Measuring ingredients in recipes is one such example. It is important, however, to use standard units to take accurate measurements.

2.2 Units of Measurements:

2.2 Units of Measurements Physical quantities are quantities that can be measured. E.g. length, area, volume, mass and time

2.2 Units of Measurements:

2.2 Units of Measurements Measurements are expressed in two parts – the numerical value and the unit . The numerical value tells us how much there is of something. The unit tells us the standard that we are comparing the value to. numerical value unit

2.2 Units of Measurements:

2.2 Units of Measurements Systeme International d’Unites or S.I. units are the most commonly used system of units in science. Common S.I. units: Physical Quantity S.I. Unit Symbol Length metre m Mass kilogram kg Temperature Kelvin K Time second s

2.2 Units of Measurements:

2.2 Units of Measurements For larger or smaller quantities, prefixes are used. Some examples: Prefix Value Symbol giga One billion G mega One milion M kilo One thousand k deci One tenth d centi One hundredth c milli One thousandth m micro One millionth μ nano One billionth n

2.3 Measuring Length:

2.3 Measuring Length Length is the distance between two specified points. Examples of measurements of length: height, depth, width, thickness and circumference S.I. unit of length is metre . The symbol for the metre is m .

Instruments for measuring length:

Instruments for measuring length Metre rule Exactly 1 m long Used to measure straight edges shorter than 1 m long. Accuracy: 0.001 m (or 1 mm)

Instruments for measuring length:

Instruments for measuring length Metre rule To measure the length of an object using a metre rule, place one end of the object against the zero mark, and read off the mark on the rule at the other end of the object When your eye is in the wrong position for viewing the measurement, parallax error occurs. We can avoid parallax error by turning up the ruler instead of lying it flat. PARALLAX ERROR

Instruments for measuring length:

Instruments for measuring length Parallax error Parallax error: this error in reading arises when the line of sight is not properly aligned with the reading on the scale. How to avoid parallax error : always read the scale with the line of sight perpendicular to the scale. turn the ruler up if possible, so the scale is at right angles to the edge . Use a thin ruler so the scale is touching the measured object

Instruments for measuring length:

Instruments for measuring length Measuring tape A measuring tape is used for measuring lengths greater than 1 m. A special property of the measuring tape is that it is soft and flexible, and are often used in measuring the diameters of round objects.

Instruments for measuring length:

Instruments for measuring length External and internal calipers External calipers can measure the external diameter of a round object. Internal calipers can measure the internal diameter of a round object. http://en.wikipedia.org/wiki/Image:OutsideCalipers.jpg http://en.wikipedia.org/wiki/Image:InsideCalipers.jpg 3 pairs of external calipers 2 pairs of internal calipers

Instruments for measuring length:

Instruments for measuring length Vernier calipers Vernier calipers are able to measure short lengths and diameters of objects of up to 10 cm. They are more accurate than the metre rule since the smallest division on the vernier scale is 0.01 cm compared to 0.1 cm on the metre rule. http://en.wikipedia.org/wiki/Image: Messschieber.jpg A pair of vernier calipers

Instruments for measuring length:

Instruments for measuring length Using the vernier calipers Step 1 : Close the jaws of the vernier calipers. Make sure that the zero marking on the vernier scale is in line with the zero marking on the main scale. Step 2 : Place the object within the jaws of the vernier calipers and clamp it firmly in place. Step 3 : Read the length.

Instruments for measuring length:

Instruments for measuring length Using the vernier calipers

Instruments for measuring length:

Instruments for measuring length Using the vernier calipers Zero error Positive zero error occurs when the jaws of the vernier calipers are closed and the zero marking on the vernier scale falls on the right of the zero marking on the main scale. Negative zero error occurs when the jaws of the vernier calipers are closed and the zero marking on the vernier scale falls on the left of the zero marking on the main scale.

Zero error:

Zero error Positive error is always expressed as +0.0__ cm or +0.__ mm Negative error is always expressed as - 0.0 __ cm or -0 .__ mm

Corrected reading:

Corrected reading If there is zero error in the vernier calipers, your raw reading needs to be ‘’corrected’. Corrected reading = vernier caliper reading – zero error

Corrected reading:

Corrected reading Correct reading = vernier caliper reading – zero error E.g., to measure the diameter of a tube, if the raw reading on the VC is 1.67 cm, and the zero error is +0.05 cm Corrected reading = 1.67 – (+0.05) = 1.62 cm

Corrected reading:

Corrected reading Correct reading = vernier caliper reading – zero error E.g., to measure the diameter of a marble, if the raw reading on the VC is 2.31 cm, and the zero error is -0.04 cm Corrected reading = 2.31–(-0.04) = 2.35 cm

Instruments for measuring length:

Instruments for measuring length Choosing instruments Length to be measured Instrument to use Accuracy of instrument Between 0 and 10 cm Vernier calipers To the nearest 0.01 cm 10 cm – 100 cm Metre rule To the nearest mm 5 cm and above Measuring tape or contractor’s rule To the nearest mm (short lengths) To the nearest cm (very long lengths)

2.4 Measuring Area:

2.4 Measuring Area Definition: area is the measure of the size or extent of a surface. S.I . unit for area is square metre and represented by the symbol m 2 . Other common units for area are square millimetre (mm 2 ), square centimetre (cm 2 ) and square kilometre (km 2 ).

2.4 Measuring Area:

2.4 Measuring Area Regular figures: use the right formula to calculate area a a b a b h r h Square Area = a x a Rectangle Area = b x a Triangle Area = ½ x b x h Circle Area = π r 2 Parallelogram Area = b x h b

2.4 Measuring Area:

2.4 Measuring Area Irregular figures Estimation of its area can be done with the help of a square grid whose sides are of known lengths. For example, if the sides are each 1 cm in length, the area of the square is 1 cm x 1 cm = 1 cm 2

2.4 Measuring Area:

2.4 Measuring Area Estimating the area of irregular figures: Step 1 : Trace the figure on a piece of graph paper and shade the area covered by the figure. Step 2 : Tick all the shaded areas that take up more than half a square. Any area that is over half a square is considered to be one unit. Any areas less than half a square are to be left out. Step 3 : Count the total number of ticks, and multiply with the unit square area. This gives you an estimate of the total area.

2.5 Measuring Volume:

2.5 Measuring Volume The volume of an object is the amount of space it occupies. The S.I. unit for volume is cubic metre and represented by the symbol m 3 . Other common units for volume are the cubic centimetre (cm 3 ), cubic decimetre (dm 3 ), litre (L or l ) and the millilitre (mL or m l ).

2.5 Measuring Volume:

2.5 Measuring Volume Liquids The volumes of liquids can be accurately measured using the measuring cylinder, burette or pipette.

2.5 Measuring Volume:

2.5 Measuring Volume Liquids Reading the meniscus In narrow glass cylinders, the liquid level is curved into a shape called the meniscus (see diagram in the next slide). Position your eye at the same level as the bottom of the meniscus to get the correct reading and avoid parallax error.

2.5 Measuring Volume:

2.5 Measuring Volume Liquids Reading the meniscus meniscus

2.5 Measuring Volume:

2.5 Measuring Volume Regular solids: use the right formula to calculate volume l Cube Volume = l x l x l l l b l h Cuboid Volume = l x b x h r h Cylinder Volume = π r 2 h r Sphere Volume = 4/3 π r 3 Cone Volume = 1/3 π r 2 h r h

2.5 Measuring Volume:

2.5 Measuring Volume Irregular solids The volume of a small, irregular solid can be measured by displacement . This can be done with the aid of a measuring cylinder or a displacement can.

2.6 What is mass?:

2.6 What is mass? Mass is a measure of the amount of matter in a body. S.I. unit of mass is kilogram , and represented by the symbol kg . Other common units for mass are grams (g), milligrams (mg), and tonnes (t).

Measuring mass:

Measuring mass Balances are used to measure mass. A beam balance uses known masses to measure the mass of an unknown object. An electronic balance measures the mass of an object when the object is placed on the metal pan and the reading is displayed. Electronic balance Beam balance

2.7 What is density?:

2.7 What is density? The density of a substance is the mass per unit volume of a substance. Density = Mass Volume

2.7 What is density?:

2.7 What is density? Let’s consider this: A 1 cm 3 steel cube has a mass of 8 g. Thus, the density of steel is 8 g/cm 3 . A 1 cm 3 wooden cube has mass of 0.9 g. Thus, the density of steel is 0.9 g/cm 3 . Since the steel cube has a higher density than the wooden cube, we can say that steel is denser than wood, and wood is less dense than steel.

Floating and sinking:

Floating and sinking Usually, a denser substance will sink while a less dense substance will float. The wooden block, which is less dense than water, floats in water. The paper clip, which is denser than water, sinks in water.

Floating and sinking:

Floating and sinking Another example: Look at the diagram on the right. Oil is the least dense of the three and will float at the top. Mercury is the densest substance, and will sink to the bottom. Water has a density between those of oil and water, and hence is suspended between the other two substances. oil water mercury

2.8 Temperature:

2.8 Temperature Temperature is a measurement of how hot or cold something is. The S.I. unit for temperature is Kelvin and is represented by the symbol K. However, for practical reasons, most thermometers measure temperature on the Celsius scale.

2.8 Temperature:

2.8 Temperature Instruments to measure temperature: A laboratory thermometer can measure temperatures between –10  C to 110  C. A thermocouple can measure temperatures from –200  C to 1200  C. An infrared thermometer allows us to measure temperatures from a distance (–55  C to 280  C) A digital thermometer displays the temperature on a digital display (35.5  C to 41.1  C)

Miscellaneous:

Miscellaneous http://physics.nist.gov/cuu/Units/ http://www.unc.edu/~rowlett/units/ http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=52 http://www-istp.gsfc.nasa.gov/stargaze/Smass.htm http://en.wikipedia.org/wiki/Mass http://en.wikipedia.org/wiki/Density