# 6.7 Data Collection

## Data Collection

• After an experiment has been carried out, sometimes the raw results will need to be processed before they are in a useful or meaningful format
• Sometimes, various calculations will need to be carried out in order to get the data in the form of a straight line
• This is normally done by comparing the equation to that of a straight line: y = mx + c A straight life graph showing the y-intercept and gradient, m

• The mathematical skills required for the analysis of quantitative data include:
• Using standard form
• Quoting an appropriate number of significant figures
• Calculating mean values

#### Using Standard Form

• Often, physical quantities will be presented in standard form
• For example, the speed of light in a vacuum equal to 3.00 × 108 m s−1This makes it easier to present numbers that are very large or very small without having to repeat many zeros
• It will also be necessary to know the prefixes for the numbers of ten

Prefixes Table #### Using Significant Figures

• Calculations must be reported to an appropriate number of signiﬁcant ﬁgures
• Also, all the data in a column should be quoted to the same number of signiﬁcant ﬁgures It is important that the significant figures are consistent in data

#### Calculating Mean Values

• When several repeat readings are made, it will be necessary to calculate a mean value
• When calculating the mean value of measurements, it is acceptable to increase the number of significant figures by 1 #### Graph Skills

• In several experiments during A-Level Physics, the aim is generally to find if there is a relationship between two variables
• This can be done by translating information between graphical, numerical, and algebraic forms
• For example, plotting a graph from data of displacement and time, and calculating the rate of change (instantaneous velocity) from the tangent to the curve at any point

• Graph skills that will be expected during A-Level include:
• Understanding that if a relationship obeys the equation of a straight-line y = mx + c then the gradient and the y-intercept will provide values that can be analysed to draw conclusions
• Finding the area under a graph, including estimating the area under graphs that are not linear
• Using and interpreting logarithmic plots
• Drawing tangents and calculating the gradient of these
• Calculating the gradient of a straight-line graph
• Understanding where asymptotes may be required

#### Worked example

A student measures the background radiation count in a laboratory and obtains the following readings: The student is trying to verify the inverse square law of gamma radiation on a sample of Radium-226. He collects the following data: Use this data to determine if the student’s data follows an inverse square law. Step 1: Determine a mean value of background radiation • The background radiation must be subtracted from each count rate reading to determine the corrected count rate, C

Step 2: Compare the inverse square law to the equation of a straight line

• According to the inverse square law, the intensity, I, of the γ radiation from a point source depends on the distance, x, from the source • Intensity is proportional to the corrected count rate, C, so • The graph provided is of the form 1/C1/2 against x
• Comparing this to the equation of a straight line, y = mx
• y = 1/C1/2 (counts min–1/2)
• x = x (m)

• If it is a straight-line graph through the origin, this shows they are directly proportional, and the inverse square relationship is confirmed

Step 3: Calculate C (corrected average count rate) and C–1/2 Step 4: Plot a graph of C–1/2 against x and draw a line of best fit • The graph shows C–1/2 is directly proportional to x, therefore, the data follows an inverse square law ### Get unlimited access

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