Transcript Measurement – length

Measurement
Measurement
 All measurements cannot be 100% accurate!!
 But accuracy is important in Science.
 How can we increase accuracy?
 Using suitable tools and equipment
 Using the correct techniques
 Taking several readings. The average of the readings is
determined and taken as the measurement.
Accuracy and Precision are different!!
Precision
 The precision of a measurement can be shown by
how the figures are written
 A length written as 100 metres, means the length is
measured to the nearest metre.
 What if the length is written as 100.0 metres or 100.00
metres?
 Answer = nearest tenth or hundredth of a metre
Uncertainty
 There is always uncertainty with measurement
 E.g. a stopwatch used in a 100m race gives a reading
of 10.1 seconds.
 But it is only accurate to 0.1 seconds, The reading may
be 10.1 s but this means the actual reading is between
10.05s and 10.15s.
 The reading is therefore written 10.1 ± 0.05s
 The reading may be improved to the nearest 1/100th of
a second using an electronic timer. If the reading is
10.12s, what is the actual reading between?
Error
 Errors are different
 They arise from poor equipment or poor use of
equipment
 Many times it is human error
 An example is the parallax error when looking to take
a reading from a rule, which we will see later
Measuring length
 Length is the distance between two points
 The SI unit for length is the metre (m)
 Short lengths measured in centimetres (cm) or
millimetres (mm)
 Longer lengths are measured in kilometres (km)
 Measuring straight lines with tape or ruler
 Careful : Parallax error
Measurement – length - Parallax
error
Measurement – length of curve
Measurement diameter with Calipers
Measuring Area
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An area is the extent of a surface or plane figure.
The SI unit for area is square metre (m2)
Larger areas (km2). Smaller areas (mm2)
The area of regular shaped objects such as a
rectangle, triangle or circle can be measured using
mathematical formulae.
Measuring Irregular Areas
Measuring Volume
 Volume is the amount of space occupied by a three
dimensional object.
 The SI unit is cubic metre (m3). Other units of volumes
include cubic centimetre (cm3) and cubic millimetre
(mm3).
 Volume of solids usually measured in cm3 and mm3.
 Volumes of liquids are usually measured in millilitres
(ml) or litres (l)
 1 cm3 = 1 ml
Measuring volume of solid (length x
width x height)
Measuring the volume of liquids
 Measured using a measuring cylinder
 The level of any liquid in a measuring cool is curved.
This is called the Meniscus
 When taking a reading, ensure that the position of
the eye is at the same level as the bottom of the
meniscus. (except mercury)
 When taking a measurement from a measuring
cylinder, make sure it is placed on a flat surface.
Measuring Volume - Meniscus
Measuring volume of irregular shape
solid
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The water displacement method
Record intial volume of water
Lower in the object to the water
Record final volume of water
Volume = Final Volume - initial volume
Measuring volume of irregular solid
Pipette and Burette also used for
measuring volumes of liquids
Time Measurement
 How do we measure time?
 With a stopwatch or clock, depending on accuracy
required
 A clock is generally used to tell the time of day
 Stopwatch generally to one tenth of a second, a digital
clock to one hundredth.
 But what is the problem here if you or I are operating the
stop watch?
 Human reaction time !!
 Hence we usually use electronic devices to measure more
accurately than humans
The Simple Pendulum
 Clocks must have a device that repeats at regular intervals –
early clocks used a pendulum.
 A simple pendulum consists of a light string, clamped at the top
with a mass at the bottom.
 The time it takes for the pendulum to make one swing back and
forth is called the period.
 The mass at the bottom and the length of the string can be
varied to alter the period
 What do you think will happen if you string longer / shorter?
 What do you think will happen if the weight is heavier / lighter
Simple pendulum – How do we
measure the period accurately?
How should we measure the Period
accurately?
 To measure the time for a single period period or
oscillation accurately is difficult with a handheld stop
watch is 0.1s.
 To find the period accurately, we time at least 10
oscillations and then divide the reading by the
number of swings.
 This reduces the uncertainty for one oscillation by a
factor of 10 from 0.1s to 0.01s.