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

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

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

measurement of length parallax error The eye must be positioned perpendicularly at the mark on the scale to avoid parallax error. 8.3 cm correct 8.2 cm wrong 8.5 cm wrong Parallax error is due to incorrect positioning of the eye the object is not at the same level as the markings of the scale

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.

measurement of length engineer’s calipers 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.

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

vernier scale (movable) measurement of length vernier calipers A B C main scale (fixed) vernier scale (movable) object being measured 9 mm 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

measurement of length 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.

vernier scale (movable) measurement of length vernier calipers 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. 1 main scale (fixed) vernier scale (movable) 5 10 zero error = +0.01 cm supposing observed reading is 3.24 cm, then corrected reading = observed reading – zero error = 3.24 – (+0.01) = 3.23 cm

vernier scale (movable) measurement of length vernier calipers 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. 1 main scale (fixed) vernier scale (movable) 5 10 zero error = -0.02 cm supposing observed reading is 4.03 cm, then corrected reading = observed reading – zero error = 4.03 – (-0.02) = 4.05 cm

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

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

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.

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. } 2 divisions supposing observed reading is 2.37 mm, then corrected reading = observed reading – zero error = 2.37 – (+0.02) = 2.35 mm

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. } 3 divisions supposing observed reading is 2.87 mm, then corrected reading = observed reading – zero error = 2.87 – (-0.03) = 2.90 mm

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

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

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

measurement of time pendulum clock 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 pendulum clock (cuckoo clock)

measurement of time watch 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 wrist watch

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

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

measurement of time ticker-tape timer steel strip vibrates 50 times a second; therefore 50 dots are made in a second on the paper tape 10-dot tape between 2 consecutive dots, time interval = 1 s / 50 dots = (1/50) s or 0.02 s 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

Numerical values and suitable units Base quantities Base SI units Physical quantities are made up of may be include Numerical values and suitable units Base quantities Base SI units Vector Scalar such as for use length (m) mass (kg) time(s) electric current (A) temperature (K) amount of substance (mol) luminous intensity (cd) Measurement Prefixes e.g. e.g. of micro () 10-6 milli (m) 10-3 centi (c) 10-2 deci (d) 10-1 kilo (k) 103 mega (M) 106 Length Time can be measured with can be measured with metre rule half-metre rule measuring tape vernier calipers micrometer screw gauge pendulum clock watch stopwatch ticker-tape timer