Estimations
Estimations Revision
Estimations
Estimations can be used to compare quantities, to check if our answers seem realistic and to help plan out experiments.
Orders of Magnitude
We can use orders of magnitude to estimate the size of an object or to compare two sizes. For example, we can estimate that the mass of the sun is about 10^{30} \text{ kg}. This represents roughly its mass to the nearest order of magnitude. However, its actual mass is slightly larger than this – approximately 1.989 \times 10^{30} \text{ kg}.
We can also compare numbers using orders of magnitude.
Experimental Design
Some of your AQA course relies on you understanding and applying experimental techniques. There are some specific key terms associated with experimental design that you should be familiar with:
- Dependent Variable – this is the variable in the experiment that is measured.
- Independent Variable – this is the variable we are changing in our experiment.
- Control Variables – these are all the other variables we need to keep the same to ensure our experiment measures what we aim for it to measure.
When we create a results table, we usually follow the guidelines below. The independent variable is put in the first column and the repeats of the dependent variable are placed in the other columns.
| Independent Variable | Dependent Variable (Repeat 1) | Dependent Variable (Repeat 2) |
Also, when drawing graphs we need to consider where we will place our variables. Usually we draw graphs in the form shown below:
Example: Orders of Magnitude
How many orders of magnitude bigger is the sun compared to Earth?
The mass of Earth is about 10 \textcolor{14cf11}{^{24}} \text{ kg}.
The mass of the Sun is about 10 \textcolor{125bc9}{^{30}} \text{ kg}.
[1 mark]
\textcolor{125bc9}{30} - \textcolor{14cf11}{24} = 6Therefore we can say that the sun is about \bold{10^6} times heavier than Earth.
This is an estimate as we have not used exact values but estimates can be useful and save time and calculations.
Estimations Example Questions
Question 1: The diameter of the Sun is 1.4 \times 10^6 \text{ km} and the diameter of the Earth is 1.2 \times 10^4 \text{ km}. Compare these two values in terms of orders of magnitude.
[1 mark]
In terms of orders of magnitude, the diameter of the Sun is 10^6 \text{ km} and the diameter of Earth is 10^4 \text{ km}.
So the Sun is approximately \bold{10^2 \text{ km}} larger in diameter than Earth.
Question 2: You are asked to conduct an experiment to determine the effect of the length of a wire on its resistance. What would your independent, dependent and control variables be?
[3 marks]
Independent Variable: length of wire \textbf{(m)}.
Dependent Variables: current \textbf{(A)} and voltage \textbf{(V)}.
Control Variables: temperature of wire, thickness of wire, material of wire, equipment.
Question 3: Design an appropriate table to collect results from the above experiment.
[3 marks]
| Length (m) | Current 1 (A) | Voltage 1 (V) | Current 2 (A) | Voltage 2 (V) | Current 3 (A) | Voltage 3 (V) | Average Current (A) | Average Voltage (V) |
1 mark for independent variable in left column.
1 mark for repeat readings of dependent variables.
1 mark for averages columns.
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