CXC SYLLABUS SECTION A PHYSICAL MEASUREMENTS AND UNITS
W.GILL
SECTION A: PHYSICAL MEASUREMENTS AND UNITS
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What is Physics? Physics is concerned with matter in relation to energy. The study of physics may be grouped under such headings as mechanics, optics, wave motion, magnetism, electricity and nuclear physics.
Fundamental Quantities and Units Why do we need units? We need units to provide a standard when taking measurements. (Compare measuring the length of a taking using standard units (eg metre) as oppose to using nonstandard measurements (eg hand size) Fundamental Basic Quantities The value of a physical quantity is expressed as a number of units in the International System of Units (SI System). Quantity Name Mass Length Time Electric Current Absolute Temperature Temperature Amount of substance
Unit Symbol Name Symbol m kilogram kg l metre m t second s I Ampere A T Kelvin K o θ Degree Celsius C mole mol
Prefixes
Multiple
Submultiple
Name tera giga mega kilo deci centi milli micro nana pico
Derived Units These are units which are formed by multiplying or dividing one or more of the basic units. Quantity Unit Name Unit Symbol Derivation Power Watt W Joule per second (J/s) or Js1 (index Format) Pressure pascal Pa Newton per metre squared (Nm2) Force newton N kgms2 Significant Figures The first significant figure in a number is the first digit from the left other than 0, e.g in the number 0.00578 the first significant figure is 5. The number of S.F is the number of digits counting from the left from the first significant figure, e.g in the number 0.00578 there are 3 S.F but in the number 280000 there are 2. The zeroes in front of the decimal point are important to the size of the number but are not significant. Examples: 301.6 0.032 423000 NB 
4 S.F 2 S.F 3 S.F
(zero between two non zero digits is significant (1st S.F is 3) (zeroes in front of the decimal point relate to the size of the number)
When performing calculations the result should be expressed using the quantity with the least number of S.F. The number of S>F used in recording a measurement depends on the precision of the instrument. For example, a metre rule can give 6.5 cm but not 6.52 cm.
Scientific Notation or Standard Form The decimal point appears after the first significant figure. The exponent determines the number of times the number is multiplied by or divided by 10. Standard form is often used to represent very small or very large numbers. Example 1: Example 2:
30000 may be represented as 3.0 x 104 0.0003 may be represented as 3.0 x 104
Measurement Scales Types: 
Linear Scale: A scale in which the divisions are evenly spaced, e.g ruler. Nonlinear Scale: A scale in which the divisions are not evenly spaced, e.g conical flask. Analogue Scale: A scale which varies continuously with the quantity being measured. Digital Scale: A scale which represents the quantity being measured with distinct objects or digits.
SECTION A: PHYSICAL MEASUREMENTS AND UNITS
Calibration of Scales 
attach tape to the side of the test tube fill burette with water to the 0 ml mark place 1 ml of water into test tube and mark the reading on the tape repeat the above steps until 10 ml of water is in the test tube empty the test tube and recalibrate it by pouring measured volumes of water into the test tube.
Estimating Readings 1
2
3
Terms 
Range: The interval between the minimum and maximum quantity to measured, eg 0 to 100 for a laboratory thermometer but 35 to 42 for a clinical thermometer.

Sensitivity: The response of a instrument to a change in the quantity being measured. The larger the response the more sensitive the instrument.

Accuracy: This depends on the calibration of the instrument.
Errors Sources of error 
Environment o temperature and pressure conditions o magnetic effects in electrical instruments o corrosion of instructions

Instrument o calibration of the instrument o zero error in the instrument

Experimenter o poor vision o slow response time
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Ways to Reduce Error 
take a reading several times and use the average reading avoid parallax errors (do not take reading at an angle) look for a pattern in measurements to identify incorrect readings (e.g all values increasing or decreasing)
Types of Instruments Measurement 1 cm to 1 m 1 mm to 1 cm
Instrument Metre rule Vernier calipers
Measurement Small accurate volumes Mass
0.1 mm to 2 cm Large volume Small fixed volumes
Micrometer screw gauge Weight Measuring cylinder Time Pipette Temperature
Instrument Burette Triple beam balance or top pan balance Spring balance Stop clock Thermometer
the main scale is measured in cm but has mm divisions read the main scale up to the 0 mark on the vernier scale. the vernier scale has 10 divisions each 0.9 mm to read the vernier scale look for the mark on the scale that lines up with a mark on the main scale. Micrometer Screw Gauge 
the ratchet slips when the object is held tight enough the sleeve scale is marked in mm and has 0.5 mm marks each revolution of the ratchet opens or closes the jaws by 0.5 mm. the timble has 50 divisions therefore, each division of the timble is 0.5/50 = 0.01 mm.
A Metre (m) The maximum displacement of the bob from its rest position.
SECTION A: PHYSICAL MEASUREMENTS AND UNITS Oscillation:
A complete to and fro movement of the bob.
Period 
Symbol: Unit: Definition:
T Second (s) The time taken to make one complete oscillation.
Frequency 
Symbol: Unit: Definition:
f Hertz (Hz) The number of complete oscillations made in one second.
The relationship Between the Period and the Frequency T = 1/f Factors Affecting the Period of a Pendulum 
the length of the pendulum is proportional to the period changing the mass of the bob has no affect on the period changing the angle of the swing has no affect on the period the acceleration due to gravity affects the period
NB T = 2п Sqrt(l/g) where l is the length of the pendulum and g = 10 ms2
Area Measuring Regular Areas 
area of a square or rectangle: area of a triangle: area of a circle: surface area of a sphere:
length x width ½ x base x height пr2 4 пr2
Measuring Irregular Areas
Divide the shape into squares of known area and add up all squares. Squares which are partly filled will be added together to make a whole square.
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Measuring Regular Volumes NB. 
The instrument must be vertical. Take the reading at the bottom of the meniscus. Your eye should be level with the meniscus.
Measuring Irregular Volumes Method 1: 1. 2. 3.
Using the measuring cylinder Partly fill the measuring cylinder with water and note the reading. Place the object in the measuring cylinder and note the reading. The difference in the readings gives the volume of the object.
Method 2: 1. 2. 3.
Using the displacement can Choose a can large enough to cover the object with water. Fill the can until it overflows and collect the excess water in a measuring cylinder. Place the empty measuring cylinder under the spout and lower the object into the water. The water that flows into the measuring cylinder is the volume of the object.
Measuring Volumes of Objects that Float A metal object of known volume may be used as a sinker. One of the methods above may be used to determine the volume of the object plus the sinker. The difference in volumes between the sinker alone and the sinker plus the object gives the volume of the floating object.
Density Definition:
The density of a substance is its mass per unit volume.
Unit: kgm3 Equation:
Density = mass/volume
Symbols:
ρ = m/v
Example 1:
A block has a mass of 40g and a volume of 5 cm3 . What is the block’s density?
Example 2:
The density of air is 1.3 kgm3. What is the mass of air in grams of a room measuring 5m x 10 m x 10 m?
Example 3:
The density of petrol is 0.8 gcm3. What is the volume of 24000g of petrol.
SECTION A: PHYSICAL MEASUREMENTS AND UNITS
Relative Density Definition:
The relative density of a substance is the number of times it is more dense than water.
Equation 1:
Relative Density = density of substance/density of water
Equation 2:
Relative Density = mass of a given volume of substance / mass of same volume of water
NB. 
Relative density has no unit, it is a dimensionless quantity. For example, the density of Al is 2.7 g/cm3 and its relative density is 2.7.
Graphs NB 
use x or o for coordinates use a suitable scale to ensure that the graph takers up most of the page Draw Line of Best Fit
x x x x x
Intercepts
Y intercept (point where the line cuts the y axis) X intercept (point where the line cuts the x axis)
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SECTION A: PHYSICAL MEASUREMENTS AND UNITS
Gradient
(x2,y2)
(use a large triangle)
(x1,y1)
Gradient (g or s) = (y2 – y1)/(x2x1) or
(y1 – y2)/(x1x2)
Types of Graphs Directly Proportionate Graphs
NB. 
when the x value increases the y value also increases when the x value decreases the y value also decreases
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SECTION A: PHYSICAL MEASUREMENTS AND UNITS
Inversely Proportionate Graph
NB. 
when the x value increases the y value decreases when the x value decreases the y value increases
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