01 Phy Quant 2 (length & time) (9Jan8)

Chapter 1

Chapter 1

Physical Quantities and Units Part 2 – Length & Time

Physical Quantities and Units Part 2 – Length & Time

In the quest to understand nature, scientists use physical quantities to describe the world around us.

In the quest to understand nature, scientists use physical quantities to describe the world around us.

measurement of length and time measurement of length and time

accurate measurement accurate measurement

There are two main types of errors:There are two main types of errors:

Random ErrorsRandom Errors Systematic ErrorsSystematic Errors

State • random • constant

No measurement is ever perfectly accurate. Even with high precision instruments, some error is inevitable.

State • random • constant

Occurrence

• in all measurements• observers estimate

the last figure of a reading on an instrument

• observers consistently underestimate or overestimate a reading

Remedy• reduced by

averaging a large number of readings

• minimised by method of differences

measurement of length measurement of length

length length

Length is the measurement of something from one end to the other end.Length is the measurement of something from one end to the other end.

� has a SI unit of metre (m)

� other units include centimetres (cm), millimetres (mm) and kilometres (km)

� has a SI unit of metre (m)

� other units include centimetres (cm), millimetres (mm) and kilometres (km)

One metre is the distance travelled by light in a vacuum in 1/299792458 of a second.

Q: What is the speed of light?

One metre is the distance travelled by light in a vacuum in 1/299792458 of a second.

Q: What is the speed of light?

millimetres (mm) and kilometres (km)millimetres (mm) and kilometres (km)


length length

Lengths can be measured by using the following:Lengths can be measured by using the following:

accuracy = 1 mm / 0.1 cm / 0.001 m

� metre/half-metre rule� metre/half-metre rule

� measuring tape� measuring tape

accuracy = 1 mm / 0.1 cm / 0.001 m

accuracy = 1 mm / 0.1 cm / 0.001 m


parallax error parallax error

8.2 cmwrong

8.3 cmcorrect

The eye must be positioned perpendicularly at the mark on the scale to avoid parallax error.The eye must be positioned perpendicularly at the mark on the scale to avoid parallax error.

Parallax error is due to

� incorrect positioning of the eye

� the object is not at the same level as the markings of the scale

Parallax error is due to

� incorrect positioning of the eye

� the object is not at the same level as the markings of the scale

8.5 cmwrong

wrong


zero errorzero error

Many instruments do not read zero exactly when there is nothing being measured.

Reasons include:

Many instruments do not read zero exactly when there is nothing being measured.

Reasons include:

� instruments are out of adjustment� instruments are out of adjustment

� some minor fault is present in the instrument� some minor fault is present in the instrument

Instruments are usually still accurate as long as the zero error is added or subtracted from the reading shown on the scale.

Instruments are usually still accurate as long as the zero error is added or subtracted from the reading shown on the scale.

engineer’s calipers engineer’s calipers

A pair of engineer’s calipers and ruler are used for measuring the lengths of objects without any flat sides.A pair of engineer’s calipers and ruler are used for measuring the lengths of objects without any flat sides.


the jaws are closed until the points just touch the object to be measured

remove the calipers and measure the distance between

the jaws with a ruler.

Vernier calipers measure small lengths accurately up to 0.01 cm. Vernier calipers measure small lengths accurately up to 0.01 cm.

vernier calipers vernier calipers


inside jaws tail

accuracy = 0.1 mm / 0.01 cm

outside jaws

main scalevernier scale



main scale (fixed)

A B C

reading on main scale (between A and B) = 2.4 cmreading on vernier scale (C) = 0.08 cmactual reading of object = 2.4 + 0.08

= 2.48 cm

(fixed)

vernier scale (movable)

object being measured

9 mm



When the two jaws of the vernier calipers touch each other, both zero marks on the main scale and on the vernier scale should coincide.

If not, there is a zero error in the vernier calipers.

When the two jaws of the vernier calipers touch each other, both zero marks on the main scale and on the vernier scale should coincide.

If not, there is a zero error in the vernier calipers.


main scale (fixed)

0 1

If the two jaws touch each other, but the zero marks of the main scale and vernier scale do not coincide as shown below, the zero error is positive.

If the two jaws touch each other, but the zero marks of the main scale and vernier scale do not coincide as shown below, the zero error is positive.


supposing observed reading is 3.24 cm, then corrected reading = observed reading – zero error

= 3.24 – (+0.01) = 3.23 cm

0 105

zero error = +0.01 cm

vernier scale (movable)


main scale (fixed)

0 1

If the two jaws touch each other, but the zero marks of the main scale and vernier scale do not coincide as shown below, the zero error is negative.


supposing observed reading is 4.03 cm, then corrected reading = observed reading – zero error

= 4.03 – (-0.02) = 4.05 cm

0 10

zero error = -0.02 cm

vernier scale (movable) 5

micrometer screw gaugemicrometer screw gauge


anvil spindle sleeve thimble ratchet

Micrometers measure small diameters or thicknesses.Micrometers measure small diameters or thicknesses.

accuracy = 0.01 mm / 0.001 cm

frame



thimblesleeve

reading on sleeve = 4.5 mmreading on thimble = 0.12 mmactual reading of object = 4.5 + 0.12

= 4.62 mm



When the anvil and spindle of the micrometer touch each other, the scales should read zero.

If not, there is a zero error in the micrometer.

When the anvil and spindle of the micrometer touch each other, the scales should read zero.

If not, there is a zero error in the micrometer.



If the anvil and spindle touch each other, but the scales do not read zero as shown below, the zero error is positive.If the anvil and spindle touch each other, but the scales do not read zero as shown below, the zero error is positive.

supposing observed reading is 2.37 mm, then corrected reading = observed reading – zero error

= 2.37 – (+0.02) = 2.35 mm


= 2.37 – (+0.02) = 2.35 mm

} 2 divisions



If the anvil and spindle touch each other, but the scales do not read zero as shown below, the zero error is negative.If the anvil and spindle touch each other, but the scales do not read zero as shown below, the zero error is negative.


= 2.87 – (-0.03) = 2.90 mm


= 2.87 – (-0.03) = 2.90 mm

} 3 divisions

measurement of timemeasurement of time

timetime

� has a SI unit of second (s)

� other units include years, months, days, hours, minutes and seconds

� has a SI unit of second (s)

� other units include years, months, days, hours, minutes and seconds


Time can be measured by using the following:Time can be measured by using the following:

� analogue stopwatch

� analogue stopwatch

� clocks� clocks

timetime

� digital stopwatch

� digital stopwatch

All timing devices make use of some regular process.All timing devices make use of some regular process.


Time can also be measured by using the following simple pendulum.

Time can also be measured by using the following simple pendulum.

� oscillations are regularly repeating motions

� the period is time in

� oscillations are regularly repeating motions

� the period is time in

the period of a simple pendulumthe period of a simple pendulum

pendulum bob tied to one end of a thread

� the period is time in which 1 oscillation occurs

� the period is time in which 1 oscillation occurs

BA O

� clocks make use of a process which is a regularly repeating motion (oscillations), such as the swing of a pendulum

� such oscillations are very regular so period is regular

� clocks make use of a process which is a regularly repeating motion (oscillations), such as the swing of a pendulum

� such oscillations are very regular so period is regular


pendulum clockpendulum clock

� most modern clocks depend on the vibration of quartz crystals to keep time accurately

� in clocks that are wound up, elastic potential energy is stored in coiled springs

� most modern clocks depend on the vibration of quartz crystals to keep time accurately

� in clocks that are wound up, elastic potential energy is stored in coiled springs

pendulum clock

(cuckoo clock)

� used for measuring long intervals of time

� most modern watches depend on the vibration of quartz crystals to keep time accurately

� the energy that keeps these

� used for measuring long intervals of time

� most modern watches depend on the vibration of quartz crystals to keep time accurately

� the energy that keeps these

watchwatch


� the energy that keeps these crystals vibrating comes from a small battery

� many watches still make use of coiled springs to supply the needed energy

� the energy that keeps these crystals vibrating comes from a small battery

� many watches still make use of coiled springs to supply the needed energy

wrist watch

A stopwatch is used to measure short intervals of time.A stopwatch is used to measure short intervals of time.

stopwatchstopwatch


� stopwatches (analogue and digital)� stopwatches (analogue and digital)

accuracy = 0.1 s accuracy = 0.01 s

When using a digital stopwatch to time a race, the time to the nearest 0.1 s should be given.

When using a digital stopwatch to time a race, the time to the nearest 0.1 s should be given.

ticker-tape timerticker-tape timer


An electrical device that makes use of the oscillations of a steel strip to mark short intervals of time.An electrical device that makes use of the oscillations of a steel strip to mark short intervals of time.

steel strip carbon paper disc6 ~ 12 V a.c.

magnetcoil ticker-tape drawing pin

ticker-tape timerticker-tape timer


� steel strip vibrates 50 times a second; therefore 50 dots are made in a second on the paper tape

� steel strip vibrates 50 times a second; therefore 50 dots are made in a second on the paper tape

10-dot tape10-dot tape

as there are 10 spaces on a piece of tape,

time taken for the tape to pass through the timer

= 10 x 0.02 s

= 0.20 s

between 2 consecutive dots, time interval = 1 s / 50 dots

= (1/50) s or 0.02 s

e.g.

length (m)length (m)mass (kg)mass (kg)time(s)time(s)

electric current (A)electric current (A)

PrefixesPrefixesMeasurementMeasurement

Physical quantitiesPhysical quantitiesare made up of

Numerical values Numerical values and suitable unitsand suitable units

VectorVectorScalarScalar

Base quantitiesBase quantitiesBase SI unitsBase SI units

may be

include

usesuch as for

metre rulemetre rulehalfhalf--metre rulemetre rulemeasuring tapemeasuring tapevernier calipersvernier calipers


pendulum clockpendulum clockwatchwatch

stopwatchstopwatchtickerticker--tape timertape timer

electric current (A)electric current (A)temperature (K)temperature (K)

amount of substance (mol)amount of substance (mol)luminous intensity (cd)luminous intensity (cd)

can be measured with

e.g. of

TimeTimeLengthLength

micro (micro (µµ)) 1010--66

milli (m) milli (m) 1010--33

centi (c) centi (c) 1010--22

deci (d)deci (d) 1010--11

kilo (k)kilo (k) 101033

mega (M)mega (M) 101066

can be measured with

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01 Phy Quant 2 (length & time) (9Jan8)