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

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Chapter 1 Physical Quantities and Units Part 2 – Length & Time In the quest to understand nature, scientists use physical quantities to describe the world around us.

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measurement of length and time accurate measurement There are two main types of errors: Random Errors Systematic Errors 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 No measurement is ever perfectly accurate. Even with high precision 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? measurement of length length 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)

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measurement of length length measuring tape accuracy = 1 mm / 0.1 cm / 0.001 m Lengths can be measured by using the following: accuracy = 1 mm / 0.1 cm / 0.001 m metre/half-metre rule

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measurement of length 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 8.5 cm wrong 8.2 cm wrong 8.3 cm correct The eye must be positioned perpendicularly at the mark on the scale to avoid parallax error.

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measurement of length zero error Many instruments do not read zero exactly when there is nothing being measured. Reasons include: 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 the reading shown on the scale.

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

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Vernier calipers measure small lengths accurately up to 0.01 cm. vernier calipers measurement of length accuracy = 0.1 mm / 0.01 cm inside jaws outside jaws main scale vernier scale tail

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reading on main scale (between A and B) = 2.4 cm reading on vernier scale (C) = 0.08 cm actual reading of object = 2.4 + 0.08 = 2.48 cm vernier calipers measurement of length main scale (fixed) vernier scale (movable) object being measured A B C 9 mm

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vernier calipers measurement of length 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.

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supposing observed reading is 3.24 cm, then corrected reading = observed reading – zero error = 3.24 – (+0.01) = 3.23 cm measurement of length 0 10 5 zero error = +0.01 cm main scale (fixed) vernier scale (movable) 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 . vernier calipers

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supposing observed reading is 4.03 cm, then corrected reading = observed reading – zero error = 4.03 – (-0.02) = 4.05 cm measurement of length 0 10 zero error = -0.02 cm main scale (fixed) vernier scale (movable) 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 . 5 vernier calipers

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micrometer screw gauge measurement of length accuracy = 0.01 mm / 0.001 cm anvil spindle sleeve thimble ratchet frame Micrometers measure small diameters or thicknesses.

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micrometer screw gauge measurement of length reading on sleeve = 4.5 mm reading on thimble = 0.12 mm actual reading of object = 4.5 + 0.12 = 4.62 mm thimble sleeve

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measurement of length micrometer screw gauge 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.

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measurement of length micrometer screw gauge 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 divisions

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measurement of length micrometer screw gauge If the anvil and spindle touch each other, but the scales do not read zero as shown below, the zero error is negative . supposing observed reading is 2.87 mm, then corrected reading = observed reading – zero error = 2.87 – (-0.03) = 2.90 mm } 3 divisions

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measurement of time time has a SI unit of second (s) other units include years, months, days, hours, minutes and seconds

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measurement of time Time can be measured by using the following: analogue stopwatch digital stopwatch clocks All timing devices make use of some regular process. time

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measurement of time Time can also be measured by using the following simple pendulum. oscillations are regularly repeating motions the period is time in which 1 oscillation occurs the period of a simple pendulum pendulum bob tied to one end of a thread B A O

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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 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 measurement of time pendulum clock (cuckoo clock) pendulum clock

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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 crystals vibrating comes from a small battery many watches still make use of coiled springs to supply the needed energy watch measurement of time wrist watch

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A stopwatch is used to measure short intervals of time. stopwatch accuracy = 0.1 s accuracy = 0.01 s measurement of time stopwatches (analogue and digital) When using a digital stopwatch to time a race, the time to the nearest 0.1 s should be given.

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ticker-tape timer measurement of time An electrical device that makes use of the oscillations of a steel strip to mark short intervals of time. steel strip magnet coil ticker-tape drawing pin carbon paper disc 6 ~ 12 V a.c.

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ticker-tape timer measurement of time 10-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 dots are made in a second on the paper tape

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e.g. metre rule half-metre rule measuring tape vernier calipers micrometer screw gauge pendulum clock watch stopwatch ticker-tape timer length (m) mass (kg) time(s) electric current (A) temperature (K) amount of substance (mol) luminous intensity (cd) Prefixes Measurement Physical quantities are made up of can be measured with e.g. of Numerical values and suitable units Vector Scalar Base quantities Base SI units Time Length micro (  ) 10 -6 milli (m) 10 -3 centi (c) 10 -2 deci (d) 10 -1 kilo (k) 10 3 mega (M) 10 6 may be include use such as for can be measured with