01 Phy Quant 2 (Length & Time) (9Jan8)

8/3/2019 01 Phy Quant 2 (Length & Time) (9Jan8)

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Chapter1

Chapter1

Physical Quantities and UnitsPart 2 Length & Time

Physical Quantities and UnitsPart 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.


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measurement of length and timemeasurement of length and time

accurate measurementaccurate measurement

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

Random ErrorsRandom Errors Systematic ErrorsSystematic Errors

State random constant

Occurrence in all measurements observers estimate the

last figure of a readingon an instrument

observers consistentlyunderestimate oroverestimate a reading

Remedy reduced by averaginga large number ofreadings

minimised by methodof differences

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


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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?

measurement of lengthmeasurement of length

lengthlength

Length is the measurement of something fromone end to the other end.Length is the measurement of something fromone 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)


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lengthlength

measuring tape measuring tape

accuracy = 1 mm / 0.1 cm / 0.001 m

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


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Parallax error is due to

incorrect positioning of the eye

the object is not at the same level as the markings of thescale

Parallax error is due to

incorrect positioning of the eye

the object is not at the same level as the markings of thescale

parallax errorparallax error

8.5 cmwrong

8.2 cmwrong

8.3 cmcorrect

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


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zero errorzero error

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

Reasons include:

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

Reasons include:

instruments are out of adjustment

some minor fault is present in the instrument

instruments are out of adjustment

some minor fault is present in the instrument

Instruments are usually still accurate as long as

the zero error is added or subtracted from thereading shown on the scale.

Instruments are usually still accurate as long as

the zero error is added or subtracted from thereading shown on the scale.


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engineers calipersengineers calipers

A pair of engineers calipers and ruler are used for measuringthe lengths of objects without any flat sides.A pair of engineers calipers and ruler are used for measuringthe lengths of objects without any flat sides.


the jaws are closed untilthe points just touch theobject to be measured

remove the calipers andmeasure the distance between

the jaws with a ruler.


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Vernier calipers measure small lengths accurately up to0.01 cm.

Vernier calipers measure small lengths accurately up to0.01 cm.

vernier calipersvernier calipers


accuracy = 0.1 mm / 0.01 cm

inside jaws

outside jaws

main scalevernier scale

tail


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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



main scale(fixed)

vernier scale(movable)

object being

measured

A B C

9 mm


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

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


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supposing observed reading is 3.24 cm, thencorrected reading = observed reading zero error

= 3.24 (+0.01)

= 3.23 cm


0 105

zero error = +0.01 cm

main scale

(fixed)


0 1

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

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



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supposing observed reading is 4.03 cm, thencorrected reading = observed reading zero error

= 4.03 (-0.02)

= 4.05 cm


0 10

zero error = -0.02 cm

main scale

(fixed)


0 1

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

5



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micrometer screw gaugemicrometer screw gauge


accuracy = 0.01 mm / 0.001 cm

anvil spindle sleeve thimble ratchet

frame

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


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

= 4.62 mm

thimblesleeve


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

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

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

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


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If the anvil and spindle touch each other, but the scales donot read zero as shown below, the zero error is positive.If the anvil and spindle touch each other, but the scales donot read zero as shown below, the zero error is positive.

supposing observed reading is 2.37 mm, thencorrected reading = observed reading zero error

= 2.37 (+0.02)

= 2.35 mm


= 2.37 (+0.02)

= 2.35 mm

} 2 divisions


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If the anvil and spindle touch each other, but the scales donot read zero as shown below, the zero error is negative.If the anvil and spindle touch each other, but the scales donot 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


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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


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

analoguestopwatch

analoguestopwatch

digitalstopwatch

digitalstopwatch

clocks clocks

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

timetime


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Time can also bemeasured by using thefollowing simple pendulum.

Time can also bemeasured by using thefollowing simple pendulum.

oscillations are regularly

repeating motions the period is time in

which 1 oscillation occurs

oscillations are regularly

repeating motions the period is time inwhich 1 oscillation occurs

the period of a simple pendulumthe period of a simple pendulum

pendulum bobtied to one end

of a thread

BAO


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clocks make use of a processwhich is a regularly repeatingmotion (oscillations), such asthe swing of a pendulum

such oscillations are very

regular so period is regular

most modern clocks depend onthe vibration of quartz crystalsto keep time accurately

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

clocks make use of a processwhich is a regularly repeatingmotion (oscillations), such asthe swing of a pendulum

such oscillations are very

regular so period is regular most modern clocks depend on

the vibration of quartz crystalsto keep time accurately

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


pendulum clock

(cuckoo clock)

pendulum clockpendulum clock


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used for measuring long intervalsof time

most modern watches depend onthe vibration of quartz crystals tokeep time accurately

the energy that keeps thesecrystals vibrating comes from asmall battery

many watches still make use of

coiled springs to supply the neededenergy

used for measuring long intervalsof time

most modern watches depend onthe vibration of quartz crystals tokeep time accurately

the energy that keeps thesecrystals vibrating comes from asmall battery

many watches still make use of

coiled springs to supply the neededenergy

watchwatch


wrist watch


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

stopwatchstopwatch

accuracy = 0.1 s accuracy = 0.01 s


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

When using a digital stopwatch totime a race, the time to the nearest0.1 s should be given.

When using a digital stopwatch totime a race, the time to the nearest0.1 s should be given.


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ticker-tape timerticker-tape timer


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

steel strip

magnetcoil ticker-tape drawing pin

carbon paper disc6 ~ 12 V a.c.


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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

steel strip vibrates 50 times a second; therefore 50 dotsare made in a second on the paper tape

steel strip vibrates 50 times a second; therefore 50 dotsare made in a second on the paper tape
http://www.glenbrook.k12.il.us/gbssci/phys/Class/1DKin/U1L2b.html


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e.g.

metre rulemetre rule

half-metre rulehalf-metre rule

measuring tapemeasuring tape



pendulum clockpendulum clock

watchwatch

stopwatchstopwatch


length (m)length (m)

mass (kg)mass (kg)

time(s)time(s)electric current (A)electric current (A)

temperature (K)temperature (K)

amount of substance (mol)amount of substance (mol)

luminous intensity (cd)luminous intensity (cd)

PrefixesPrefixesMeasurementMeasurement

Physical quantitiesPhysical quantitiesare made upof

can bemeasured with

e.g. of

Numerical valuesNumerical valuesand suitable unitsand suitable units

VectorVector

ScalarScalarBase quantitiesBase quantitiesBase SI unitsBase SI units

TimeTimeLengthLength

micro (micro ()) 1010-6-6

milli (m)milli (m) 1010-3-3

centi (c)centi (c) 1010-2-2

deci (d)deci (d) 1010-1-1

kilo (k)kilo (k) 101033

mega (M)mega (M) 101066

maybe

include

usesuch as for

can bemeasured with

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01 Phy Quant 2 (Length & Time) (9Jan8)