Units and Dimensions Flashcards
Name all the base units and their quantities
Length - m ‘the metre’
Second - s ‘the second’
Amount of substance - mol ‘The mole’
Electric current - A ‘The ampere’
Temperature - K ‘The kelvin’
Mass - Kg ‘The kilogram’
Example: What is the SI derived unit for speed?
- Definition: Speed is the measure of distance travelled over a period of time
Speed = Distance/time
IDENTIFY THE BASE UNITS
- Distance has the SI base unit of the metre/m.
Time has SI base unit of the second, s.
Speed = m/s Substitute base units into definition (equation)
- The SI derived unit for speed is therefore metres per second ms^-1.
Acceleration derived unit and name
ms^-2 don’t have one
Force derived unit and name
kgms^-2 Newton(N)
Pressure derived unit and name
kgm^-1s^-2 Pascal (Pa)
Energy derived unit and name
kgm^2s^-2 Joule (J)
Charge derived unit and name
A s Coulomb (C)
Potential difference derived unit and name
kgm^2A^-1s^-3 Volt (V)
Resistance derived unit and name
kgm^2A^-2s^-3 Ohm (Ω)
femto (f)
x10^-15
pico (p)
x10^-12
nano (n)
x10^-9
micro (μ)
x10^-6
milli (m)
x10^-3
centi (c)
x10^-2
deci (d)
x10^-1
kilo (k)
x10^3
mega (M)
x10^6
giga (G)
x10^9
tera (T)
x10^12
peta (P)
x10^15
How to convert from cm^2 to m^2
- Think about a simple example e.g. the area of a square with sides 1 cm (i.e. 0.01 m). 1 cm x 1 cm = 1 cm2; 0.01 m x 0.01 m = 0.0001 m2. Therefore 1 cm2= 0.0001 m2or 1x10-4 m2.
*Again think about a simple example e.g. the volume of a square with sides 1 mm (i.e. 0.001 m). 1 mm x 1 mm x 1 mm = 1 mm3; 0.001 m x 0.001 m x 0.001 m = 0.000000001 m3. Therefore 1 mm3= 0.000000001 m3or 1 x 10-9 m3.
How to convert from kmh^-1 to ms^-1
Yet again think about a simple example e.g. 1 kmh-1is 1000 m in 3600 s (i.e. 60 min x 60s). Therefore 1 kmh-1= 1000 / 3600 ms-1= 0.28 ms-1
How to convert from kWh to J
Joules are standard units of energy. However, electricity bills are given in kWh which are also units of energy. So 1 kWh is 1000 W for an hour. Using E = P x t gives E = 1000 x 3600 = 3600000 = 3.6 x 106 J. Therefore 1 kWh = 3.6 x 106 J.
How to convert from eV to J
Electron volts (eV) is a measure of energy typically used for very small energies. Think of it as raising one electron through a potential of one Volt. You should be comfortable that P = IV and hence E=IVt. I = Q / t so E = (Q / t) x Vt and therefore E = QV. In this case we’re considering an electron so the charge (Q) is 1.60 x 10-19Coulombs. Therefore 1 eV = 1.60 x 10-19x 1 = 1.60 x 10-19 J.
What does a base unit do?
The base units lets everyone know how to give the dimensions a number (how big or small). i.e. units are a human invention, the universe doesn’t care what we use.
Important rule for equations and dimensions
Any equation must have the same dimensions on either side of an equation!
What is a dimensionless quantity?
If you have a quantity which does not relate to a physical quantity, it will not have any dimensions.
Definition of accuracy
A measurement is accurate if it close to the true value for that physical quantity
Definition of Precision
Precision is a measure of spread from the mean. A precise measurement is one which is close to the mean of all the measurements you have taken.
*It does not tell you if you are close to the true value!
Random errors influence
These influence precision
Systematic errors influence
These influence the accuracy of a result.
Mistakes lead to
These lead to ‘bad’ data points
How do random errors occur?
Random errors occur because of uncontrollable aspects of an experiment.*
Variations in environmental conditions (e.g. temperature or light fluctuations which cause differences in the measured values).
*Variations due to manufacture. For example, say you use lots of different pieces of wire, how do you know if they are identical (have the same resistivity) etc.
*Limitation of the equipment itself. Maybe the equipment is not sensitive enough to measure the physical quantity well enough
How do you minimise random errors?
How to minimise random errors?
*Some can be minimised, for example, using a temperature-controlled room. Fluctuations will still occur, but they should be smaller in magnitude.
*Good experimental practice, for example using a fiducial mark (a reference point) to read an instrument from the same place each time.
*Plot a graph to establish any patterns and use a line of best fit. This is essentially taking a mean.
*Take more repeat measurements!
Why should you take mean averages?
Random errors are…random! They will sometimes be bigger or smaller than the mean. Averaging together means some of these errors cancel out, and the mean is a better measure of the true value!
*More measurements, the better measure the mean is for the true value.
*The standard deviation around the mean is a measure of spread (and thus precision
What are Systematic errors?
Systematic errors cause the value of the measured physical quantity to be shifted away from its ‘true’ value.
*This could be caused by parallax errors (viewing consistently from the wrong angle for all measurements)
*Environmental conditions –for example a consistent amount of background radiation.
*Zero error (voltmeter, ammeter, micrometre etc) where zero is not actually zero.
*Calibration error (zero error is an example of this) where an instrument should give a reading under a particular condition, but doesn’t
How to minimise Systematic errors?
These can be minimised through designing a better experiment, and using calibrated equipment!
*For example, thinking about how you will observe the measurement consistently.
*Checking your voltmeter reads zero when you expect it to.
*Taking a background reading, and subtracting this from your measured value (very common in science) –this is essentially a calibration.
What is resolution?
Resolution is the minimum precision you can measure your physical quantity with.
