Units and Dimensions

Question 1

Name all the base units and their quantities

Answer 1

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’

Question 2

Example: What is the SI derived unit for speed?

Answer 2

1. Definition: Speed is the measure of distance travelled over a period of time

Speed = Distance/time

IDENTIFY THE BASE UNITS

2. 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)

3. The SI derived unit for speed is therefore metres per second ms^-1.

Question 3

Acceleration derived unit and name

Answer 3

ms^-2 don’t have one

Question 4

Force derived unit and name

Answer 4

kgms^-2 Newton(N)

Question 5

Pressure derived unit and name

Answer 5

kgm^-1s^-2 Pascal (Pa)

Question 6

Energy derived unit and name

Answer 6

kgm^2s^-2 Joule (J)

Question 7

Charge derived unit and name

Answer 7

A s Coulomb (C)

Question 8

Potential difference derived unit and name

Answer 8

kgm^2A^-1s^-3 Volt (V)

Question 9

Resistance derived unit and name

Answer 9

kgm^2A^-2s^-3 Ohm (Ω)

Question 10

femto (f)

Answer 10

x10^-15

Question 11

pico (p)

Answer 11

x10^-12

Question 12

nano (n)

Answer 12

x10^-9

Question 13

micro (μ)

Answer 13

x10^-6

Question 14

milli (m)

Answer 14

x10^-3

Question 15

centi (c)

Answer 15

x10^-2

Question 16

deci (d)

Answer 16

x10^-1

Question 17

kilo (k)

Answer 17

x10^3

Question 18

mega (M)

Answer 18

x10^6

Question 19

giga (G)

Answer 19

x10^9

Question 20

tera (T)

Answer 20

x10^12

Question 21

peta (P)

Answer 21

x10^15

Question 22

How to convert from cm^2 to m^2

Answer 22

• 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.

Question 23

How to convert from kmh^-1 to ms^-1

Answer 23

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

Question 24

How to convert from kWh to J

Answer 24

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.

Question 25

How to convert from eV to J

Answer 25

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.

Question 26

What does a base unit do?

Answer 26

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.

Question 27

Important rule for equations and dimensions

Answer 27

Any equation must have the same dimensions on either side of an equation!

Question 28

What is a dimensionless quantity?

Answer 28

If you have a quantity which does not relate to a physical quantity, it will not have any dimensions.

Question 29

Definition of accuracy

Answer 29

A measurement is accurate if it close to the true value for that physical quantity

Question 30

Definition of Precision

Answer 30

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!

Question 31

Random errors influence

Answer 31

These influence precision

Question 32

Systematic errors influence

Answer 32

These influence the accuracy of a result.

Question 33

Mistakes lead to

Answer 33

These lead to ‘bad’ data points

Question 34

How do random errors occur?

Answer 34

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

Question 35

How do you minimise random errors?

Answer 35

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!

Question 36

Why should you take mean averages?

Answer 36

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

Question 37

What are Systematic errors?

Answer 37

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

Question 38

How to minimise Systematic errors?

Answer 38

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.

Question 39

What is resolution?

Answer 39

Resolution is the minimum precision you can measure your physical quantity with.