PHYSICS HIGH SCHOOL NOTES FOR KCSE PREPARATIONS
MEASUREMENT I
In order to measure we need to know or define the quantity to be measured and the units for measuring it. In 1971 a system known as the International System of Units (Systeme’ Internationale) and seven basic units were agreed upon as follows.
Other quantities can be obtained from these basic quantities and are referred to as derived quantities. LengthThis is the measure of distance between two points in space. The SI unit for length is the metre (m).Therefore 1 km = 1000 m
1 Hm = 100 m Length is measured using a metre rule (100 cm), tape measure (100 m, 300 m, 500 m)1 Dm= 10 m 1 mm = 0.001 m AreaThis is the measure of the extent of a surface. It is a derived quantity of length. Its SI units are square metres (m^{2}). Other units are cm^{2}, km^{2}, etc. Formulas are used to determine areas of regular bodies while for irregular bodies an approximation of area is used.VolumeThis is the amount of space occupied by matter. The SI units for volume is cubic metre (m^{3}). Other submultiples are cm^{3}, mm^{3} and l. Hence 1 m^{3} = 1,000,000 cm^{3} and 1litre = 1,000 cm^{3}. Volume can be measured using a measuring cylinder, eureka can, pipette, burette, volumetric flask, beaker, etc.MassThis is the quantity of matter contained in a substance. Matter is anything that occupies space and has weight. The SI unit for mass is the Kilogram (kg). Other submultiples used are grams (g), milligrams (mg) and tonnes (t). 1 kg = 1,000 g = 1,000,000 mg=100 tonnes. A beam balance is used to measure mass.DensityThis is mass per unit volume of a substance. It is symbolized by rho (ρ) and its SI units are kg/m^{3}. Density = mass / volume.Examples
Example
The mass of an empty density bottle is 20 g. Its mass when filled with water is 40.0 g and 50.0 g when filled with liquid X. Calculate the density of liquid X if the density of water is 1,000 kgm^{3}. Solution
Mass of water = 40 – 20 = 20 g = 0.02 kg. Volume of water = 0.02 / 1,000 = 0.00002 m^{3}. Volume of liquid = volume of bottle Mass of liquid = 50 – 20 = 30 g = 0.03 kg Therefore density of liquid = 0.03 / 0.00002 = 1,500 kgm^{3} Relative densityThis is the density of a substance compared to the density of water.It is symbolized by (d) and has no units since it’s a ratio. Relative density (d) = density of substance / density of water. It is measured using a relative density bottle ExampleThe relative density of some type of wood is 0.8. Find the density of the wood in kg/m^{3}.Solution
Density of substance = d × density of water
Density of substance = 0.8 × 1,000 = 800 kgm^{3} Densities of mixtures
We use the following formula to calculate densities of mixtures Density of the mixture = mass of the mixture / volume of the mixture Example100 cm^{3} of fresh water of density 1,000 kgm^{3} is mixed with 100 cm^{3} of sea water of density 1030 kgm^{3}. Calculate the density of the mixture.Solution
Mass = density × volume Mass of fresh water = 1,000 × 0.0001 = 0.1 kg Mass of sea water = 1030 × 0.0001 = 0.103 kg Mass of mixture = 0.1 + 0.103 = 0.203 kg Volume of mixture = 100 + 100 = 200 cm^{3} = 0.0002 m^{3} Therefore density = mass / volume = 0.203 / 0.0002 =1,015 kg/m^{3}. TimeThis is a measure of duration of an event. The SI unit for time is the second (s). Submultiples of the second are milliseconds, microseconds, minute, hour, day, week and year. It is measured using clocks, stop watches, wrist watches, and digital watches.Accuracy and errorsAccuracy is the closeness of a measurement to the correct value of the quantity being measured. It is expressed as an error. An error is therefore the deviation of measurement to the correct value being measured. The smaller the error the accurate the measurement.% error = (sensitivity / size measured) × 100.
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