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MEASUREMENTS AND UNITS PHYSICAL QUANTITY It is a quantity that can be measured with an instrument such as length. A physical quantity has a magnitude and a unit. For example:

length of 20 m Unit

Physical quantity

Magnitude

SI units (Systeme Internationale) It is a system of units that is used worldwide by all the scientists. It is a common system of units used to prevent confusion and time consuming conversions. For example, length has a unit of metre (m) which everyone recognizes. If another unit such as yard or inch is used not everyone knows what it is. So using a SI unit is best.

REMEMBER:

use SI units whenever you use a formula.

PHYSICAL QUANTITIES AND THEIR UNITS Physical quantity 1. Length

Name of SI unit metre

Symbol of unit m

2. 3.

Time Mass

second kilogram

s kg

4. 5. 6.

Temperature Current Amount of matter

Kelvin Ampere mole

K A mol

Instrument Measuring tape, metre rule, half metre rule, vernier callipers, micrometer screw gauge Stop watch Beam balance, electronic balance, top pan balance Thermometer Ammeter --------------------------

We are going to study just the first two physical quantities in this chapter i.e. length and time.

LENGTH There are many instruments used to measure length depending on the range and accuracy of the measurement. Instrument Measuring tape Metre rule Half metre rule Vernier callipers

Range Several metres 50 cm - 100 cm 10 cm - 50 cm 2 cm - 10 cm

Accuracy 0.1 cm ( 1 mm ) 0.1 cm ( 1 mm ) 0.1 cm ( 1 mm ) 0.01 cm ( 0.1 mm)

Micrometer screw gauge

Less that 2 cm

0.001 cm ( 0.01 mm)

REMEMBER:

Example Length of a room Length of a chair Length of a book Diameter of a coin, internal diameter of a test tube Diameter of a wire, thickness of a coin

even if the measurement is in cm if it is less than 2 cm use a micrometer. For example 0.2 cm should be measured with a micrometer not a vernier calliper.


USING MEASURING TAPE/METRE RULE/HALF METRE RULE When using measuring tape, metre rule or the half metre rule remember to use the correct method of measurement.

You can see that the line of sight of the eye is incorrect. It does not pass through the edges perpendicularly so the measurement of length of the box you get is inaccurate. This type of error is called parallax error.

PARALLAX ERROR: 1. It is an error caused by the wrong position of your eyes when measuring from an instrument. The correct way of taking the measurement is as follow:

This is the correct way of looking at the scale when taking a measurement. Your eyes should always be perpendicular or vertically opposite to the scale on the instrument. Now the line of sight passes perpendicularly through the edges of the box and gives you an accurate value of its length. How to avoid parallax error? Always look perpendicular (vertically opposite) to the scale on the measuring instrument. 2. Parallax error can also occur when you take measurement from a distance. example:

metre rule When you place the rule far and try taking a measurement it will be inaccurate. The reason for this is that the markings on the rule are too close so the reading you get may be incorrect. This is also a parallax error.


To avoid such a parallax error you should place the rule as close as possible to the object and use a set square as shown below.

Using a set square this way will ensure that you get an accurate reading.

Set square

Set square can also be used to ensure that an object is perpendicular to the ground. metre rule

set square ground

VERNIER CALIPERS

1. 2. 3. 4.

Take the reading on the main scale just before the ‘0’ of the vernier scale. Look at the vernier scale and take the reading of the line that coincides with the main scale. Divide the vernier reading by 100 (when the scale is in mm then divide the reading by 10). Add up the two readings. vernier scale (6th line coincides with the main scale)

main scale (5th line just before ‘0’ the of vernier scale). Example: Main scale reading = 5 mm Vernier reading = 6 / 10 = 0.6 mm (we divide 6 by 10 because the main scale is in mm). Total reading = 5 + 0.6 = 5.6 mm.


MICROMETER SCREW GAUGE

1. 2. 3. 4.

Take the main reading on the main scale. Look at the thimble scale and take the line that coincides with the datum line. Divide it by 100. (We divide by 100 because the thimble scale readings are 1/100 of a mm) Add up two readings.

Example: 0

1 23

Main scale reading = 1.5 mm Thimble scale reading = 23 / 100 = 0.23

total reading = 1.5 + 0.23 = 1.73 mm.

ZERO ERROR It is an error that occurs when the instrument scale does not start from “0”. 1. Micrometer

when fully closed the 0 on the thimble scale must 0

coincide with the datum line. NO ZERO ERROR!

datum line There are two types of errors on the micrometer:

NEGATIVE ZERO ERROR

‘0’ is ABOVE the datum line 0

when fully closed, the 0 does not coincide with the datum line so there is a ZERO ERROR.

Each line on the thimble scale represents 0.01 mm so the zero error is 0.01 (there is one line below 0). Do not look at the number shown in the thimble scale just count the no. of lines.

Correction of zero error. As the scale is starting one line below zero (0) so the reading you will get with this micrometer will be short by 0.01 mm. To correct the reading you must add 0.01 to it. e.g the reading you get is 3.67 mm correct reading will be 3.67 + 0.01 mm = 3.68 mm


POSITIVE ZERO ERROR

0’ is BELOW the datum line when fully closed, the 0 does not coincide with the datum line so there is a ZERO ERROR. 0

Each line on the thimble scale represents 0.01 mm so the zero error is 0.02 (there are two lines above 0). Do not look at the number shown in the thimble scale just count the no. of lines.

Correction of zero error. As the scale is starting two lines below zero (0) so the reading you will get with this micrometer will be more by 0.02 mm. To correct the reading you must subtract 0.02 from it. e.g the reading you get is 3.67 mm correct reading will be 3.67 - 0.02 mm = 3.65 mm 2. Stopwatch 00:00:00 h

min

NO ZERO ERROR! s

00:00:05

The stopwatch does not start from zero (0) so there is a zero error. It starts 5 seconds ahead.

Correction of zero error. Subtract 5 s from your reading. For example if you get 55 s with this stopwatch you must subtract 5 s from it i.e. 55 – 5 = 50 s. The correct time is 50 s.

OTHER MEASUREMENT TECHNIQUES 1. Measuring the diameter of a lead ball with a ruler. Line up ten similar balls as shown. Use the wooden supports to push the balls together so that there are no air gaps in between the balls.

L metre rule

wooden support

wooden support

Place a metre rule as shown and take the length of ten balls. Divide the length of ten balls by 10 to obtain the length of one ball i.e. the diameter of the lead ball. Formula:

diameter of one ball,

=


2. Measuring the diameter of a wire with a ruler. Wind the wire on top of a pencil as shown.

L metre rule

Measure the length of 10 turns. Divide the length of 10 turns by 10 to obtain the diameter of the wire. Formula:

diameter of wire,

=

Time We use a stop watch to record time. Experiment:

Using a stopwatch to measure the time period of a simple pendulum.

Diagram:

Method:

take time for 20 oscillations and divide it by 20 to obtain the time for 1 oscillation. Then use the formula

=

where t is the time for 20 oscillations.

NOTE: we take twenty oscillations because this way the human reaction time error is reduced.

Definitions: Time period, T: it is the time taken for one complete oscillation. Frequency, f:

it is the number of oscillations in one second.

=

unit of frequency: Hertz (Hz)


MEASUREMENTS AND UNITS