3.8 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

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/C^–1/2 against x
  • Comparing this to the equation of a straight line, y = mx
    • y = 1/C^–1/2 (counts min^–1/2)
    • x = x (m)
    • Gradient = constant, k

  • 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