PHYSICS NOTES
CXC SYLLABUS
SECTION A
PHYSICAL MEASUREMENTS AND UNITS
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 non-standard 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 Unit
Name Symbol Name Symbol
Mass m kilogram kg
Length l metre m
Time t second s
Electric Current I Ampere A
Absolute Temperature T Kelvin K
Temperature θ Degree Celsius oC
Amount of substance mole mol
Prefixes
Multiple
Name Symbol Meaning Example
tera T 1012 terametre (Tm) giga G 109 gigawatt (GW) mega M 106 megajoule (MJ) kilo K 103 kilogram (kg) Submultiple deci d 10-1 decibel (dB) centi c 10-2 centimeter (cm)
milli m 10-3 milliampere (mA)
micro µ 10-6 microcoulomb µC
nana n 10-9 nanosecond (ns)
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 Js-1 (index Format)
Pressure pascal Pa Newton per metre squared (Nm-2)
Force newton N kgms-2
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 4 S.F (zero between two non zero digits is significant 0.032 2 S.F (1st S.F is 3)
423000 3 S.F (zeroes in front of the decimal point relate to the size of the number)
NB
- 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: 30000 may be represented as 3.0 x 104
Example 2: 0.0003 may be represented as 3.0 x 10-4
Measurement
Scales Types:
- Linear Scale: A scale in which the divisions are evenly spaced, e.g ruler.
- Non-linear 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
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
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 Instrument Measurement Instrument
1 cm to 1 m Metre rule Small accurate volumes Burette
1 mm to 1 cm Vernier calipers Mass Triple beam balance or
top pan balance
0.1 mm to 2 cm Micrometer screw gauge Weight Spring balance
Large volume Measuring cylinder Time Stop clock
Small fixed volumes Pipette Temperature Thermometer
Vernier Callipers & Micometer Screw Gauge See Transparency
Vernier Callipers
- 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.
Simple Pendulum
Terms Amplitude
- Symbol: A
- Unit: Metre (m)
Oscillation: A complete to and fro movement of the bob. Period
- Symbol: T
- Unit: Second (s)
- Definition: The time taken to make one complete oscillation.
Frequency
- Symbol: f
- Unit: Hertz (Hz)
- Definition: 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 ms-2
Area
Measuring Regular Areas
- area of a square or rectangle: length x width
- area of a triangle: ½ x base x height
- area of a circle: пr2
- surface area of a sphere: 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.
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: Using the measuring cylinder
1. Partly fill the measuring cylinder with water and note the reading.
2. Place the object in the measuring cylinder and note the reading.
3. The difference in the readings gives the volume of the object.
Method 2: Using the displacement can
1. Choose a can large enough to cover the object with water.
2. Fill the can until it overflows and collect the excess water in a measuring cylinder.
3. 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: kgm-3
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 kgm-3. What is the mass of air in grams of a room measuring 5m x
10 m x 10 m?
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)
Gradient
(x2,y2)
(use a large triangle)
(x1,y1)
Gradient (g or s) = (y2 – y1)/(x2-x1) or (y1 – y2)/(x1-x2)
Types of Graphs
Directly Proportionate Graphs
NB.
- when the x value increases the y value also increases
Inversely Proportionate Graph
NB.
- when the x value increases the y value decreases
