Introduction to Physics

Introduction to Physics
Standards of Measurement

The value of a physical quantity is shown with:

A number where the significant figures and error reflects how accurately the quantity is known
Units showing the type of quantity.
Direction if it is a vector quantity

Physical quantities can be measured directly or calculated from measured data.

Examples

The length of the desk is 70.00 cm. The true length of the desk lies between 69.995 and 70.005 cm

The mass of the glider is 78.0 +/- 0.2 g. The true mass of the glider lies between 77.8 and 78.2 g

The velocity of the car is 60 kph North. We don’t know if the 0 is significant or not.

Standard Form

Number in standard form are written as a number between 1 and 10 times a power of ten
Example
1. 625 = 6.25 x 10²2. 10 342 = 1.0342 x 10⁴
3. 0.37 = 3.7 x 10^-14. 0.00045601 = 4.5601 x 10^-4

Number are written in standard form so the number of significant figures is clear

Fundamental and derived units

Fundamental Units

In Physics Systeme Internationale or SI units are usually used.

There are seven fundamental SI units -

The meter (m) to measure length
The kilogram (kg) to measure mass
The second (s) to measure time
The ampere (A) to measure current
The kelvin (K) to measure temperature
The mole (mol) to measure the amount of a substance where 1 mol contains 6.023 x 10²³ molecules.
The candela (cd) to measure luminous intensity

Derived Units

All other units can be derived from the seven fundamental units

Example

Velocity is rate of change of displacement with respect to time
rate of change of displacement = displacement divided by time = m/s = m.s^-1

Acceleration is rate of change of velocity with respect to time
rate of change of velocity = velocity divided by time = (m/s)/s = m.s^-2

Force is measured in Newton (N)
Force = mass x acceleration
1 N = 1 kg.m.s^-2

Energy is measured in Joules (J)
Kinetic energy = ¹/₂ mass x velocity squared
1 J = 1 kg.(m/s)² = 1 kg.m².s^-2

Changing Units

Common prefixes used with SI units

Prefix	pico	nano	micro	milli		kilo	mega	giga
Factor	x 10^-12	x 10^-9	x 10^-6	x 10^-3	x 1	x 10³	x 10⁶	x 10⁹
Symbol	p	n	m	m		k	M	G
Example	2.0 pF = 2.0 x 10^-12 F	500 nm = 500 x 10^-9 m	2.003 m m = 2.003 x 10^-6 m	25 mV = 25 x 10^-3 mV		50 kW = 50 x 10³ W

Quantities must be converted to SI units before being used in calculations

Example

Convert mm³ to m³
mm³ = (10^-3 m)³ = 10^-9 m³
The conversion factor is x 10^-9

What is the area of a rectangle 2.005 mm X 46.1 m m in SI units?
Area = 2.005 x 10^-3 m X 46.1 x 10 ^-6m
= 2.005 x 46.1 x 10^-9 m²
= 92.4305 x 10^-9 m²
= 9.24305 x 10^-8 m²

Convert 36 kph to m/s
36 kph = (36 km/1hr)(1000 m/1 km)(1 hr/3600 s)
= (36 x 1000 / 3600) x (km x m x hr) /( hr x km x s)
= (36 / 3.6) m/s
= 10 m/s
(Note the number should be treated first and then the units can be treated like algebraic symbols)
Uncertainties and Errors
Sources of Errors

Limitations in the measuring device

The error allowed is half the smallest division

This reading error must be recorded when making measurements
eg a ruler marked in millimeters has a reading error of +/- 0.5 mm

Lack of precision in making the measurement

Readings must be repeated to increase accuracy
eg a length is measured three times and the readings are 0.565 m, 0.560 m and 0.570 m

Mistakes

Random Uncertainties and Systematic Errors

Random Uncertainties

Repeated measurements of the same quantity vary

The best estimate of the value is the mean

The uncertainty is half the difference between the maximum and minimum reading, ignoring mistakes

Example: Five reading of the thickness (t) of a wire are made with a micrometer and the following value are obtained - 0.501 mm, 0.497 mm, 0.498 mm, 0.447 mm and 0.504 mm.
The micrometer can be read to the nearest 0.001 mm so the reading error is +/- 0.0005 mm
Clearly the 0.447 mm reading is a mistake and should be ignored
t = (0.501 +0.497+, 0.498 + 0.504 mm)/4 = 0.500 mm
D t = (0.504 - 0.497)/2 = 0.0035 mm (If all the measurements were the same then D t = 0.0005 mm)
Thickness = 0.500 +/- 0.004 mm

If the measurements are graphed the line of best fit has points scattered equally above and below it

To find the gradient (m) draw two lines of best fit with realistic maximum m₁and minimum m₂ gradients

m = (m₁ + m₂)/2, D m = (m₁ - m₂)/2

Systematic Errors

The apparatus may have an inbuilt error
eg zero errors

When a systematic error is recognised all measurements should be adjusted accordingly