Mechanics Measurement A physical quantity is a quantity that can be measured.   Examples of physical quantities are Length Mass   Temperature Time and Energy  . Every physical quantity has a numerical size and a unit. All units must be written, even in intermediate working. Example: 15 m + 12 m = 27 m.                (Not: 15 + 12 = 27 m)

Mechanics Measurement SI Units Scientists around the world agree to use the SI units for measuring physical quantities. The SI units for all other physical quantities can be expressed in terms of these base quantities.   Fundamental Quantity SI Unit Symbol Length Metre m Mass Kilogram kg Time Second s Temperature Kelvin K

Mechanics Measurement Examples: Volume of a cube = length x length x length Hence, SI unit of volume = SI unit of length x SI unit of length x SI unit of length                                           = m x m x m                                          = m3.   Density = Mass / Volume Hence, SI unit of density = SI unit for mass / SI unit for volume                                         = kg m -3

Mechanics Measurement Prefixes Prefixes allow scientists to write the size of very large or very small physical quantities easily. Example   15 km = 15 × 1 000 m = 15 000 m Prefix Symbol Meaning Mega- M 1 000 000 Kilo- k 1 000 Milli- m 1 / 1 000 Micro 1 / 1 000 000

Mechanics Measurement Scientific Notation – Standard Form The velocity of light in a vacuum is 300 000 000 ms-1 = 3.00 x 108 ms-1 The wave length of violet light is 0.000 000 42 m = 4.2 x 10-7 m Standard form is used to abbreviate numbers with a large number of digits To do quick comparisons of value by comparing their powers of 10 Eg The mass of the sun is 1.99 x 1030 kg The mass of Jupiter is 1.90 x 1027 kg The mass of the sun is approximately 1030 -27 = 103 = 1000 times that of Jupiter

Mechanics Measurement To see how to do the previous calculation of a scientific calculator, click here

Mechanics Measurement Systematic Errors All Experiments contain errors. Some of these errors are related directly to the instruments used. Here are some examples, Parallax error when using a ruler.

Mechanics Measurement Parallax error when using a measuring cylinder Parallax error occurs when you place your eye at the wrong position and end up reading at an angle.

Mechanics Measurement Other systematic errors that can occur in experiments are: Friction Reaction Time Error Zero Error (instruments not being set to zero correctly) These errors are fixed and can be allowed for Instruments used to measure length Instrument Used to measure Precision Tape Measure > 1 m 1 mm Metre Rule 10 cm to 1 m Vernier Caliper 20 mm to 100 mm 0.1 mm Micrometer 0 mm to 25mm 0.01 mm

Mechanics Measurement Calculating with Measured Values: Rule 1: When ADDING or SUBTRACTING measurements, round the answer to the smallest number of decimal places Rule 2: When MULTIPLYING or DIVIDING measurements, round the answer to the smallest number of significant figures. 4.7 m + 12.354 m + 3.86 m 75.648 kg - 36.81 kg 18.24 m x 6.43 m 73.612 m / 7.02 s = 20.9 m = 38.84 kg = 117 m2 = 10.5 ms-1

Mechanics Measurement There is also uncertainty in measurements because of the accuracy of the device you are using. Measurements on a metre rule would be to ± 1mm

Mechanics Measurement Watch a video on how to use Vernier Callipers https://www.youtube.com/watch?v=FNdkYIVJ3Vc

Mechanics Measurement

Mechanics Measurement Watch a video on how to use https://www.youtube.com/watch?v=W6qEKBA2zCE

Mechanics Measurement

Mechanics Measurement Triple Beam Balance Watch a video on how to use a triple beam balance https://www.youtube.com/watch?v=FfuBO3-K8AQ#t=79

Mechanics Measurement Example: Find the volume of a microscope slide by using suitable equipment to measure its length, width and thickness

Mechanics Measurement Example: Find the density of a marble Use suitable equipment to find the diameter and the mass of the marble. Density = Mass/Volume Volume of the marble = 𝟒𝝅 𝒓 𝟑 𝟑 where r is the radius and is half of the diameter

Mechanics Measurement