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 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 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.