Trend & Patterns in Experimental Data (Edexcel International A Level Physics)

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Katie M

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Katie M

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Trend & Patterns in Experimental Data

  • Graphs are used to visualise the relationship between two sets of data from two different variables
  • Trends and patterns can be identified from experimental data
  • Common trends are:
    • Linear
    • Directly proportional
    • Inversely proportional
    • Rate of change
  • A linear graph set of data is any data that creates a straight line

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An example of a linear graph

  • The rate of change of a graph is how quickly a variable is increasing or decreasing with something else
    • This can be seen from the change in gradient of the graph, an increasing gradient has an increasing rate of change and a decreasing gradient has a decreasing rate of change
  • A direct proportionality relationship is where as one amount increases, another amount increases at the same rate
    • This is represented by a straight-line graph with a positive gradient
  • For two variables, y and x this looks like:

y ∝ x

  • An inverse proportionality relationship is where as one amount increases, another amount decreases at the same rate
    • This is represented by a curved graph with a decreasing gradient
  • For two variables, y and x this looks like:

y ∝ 1 over x

Graphs of Boyle’s Law

Sketched graphs show relationships between variables

  • In the first sketch graph, above you can see that the relationship is a straight line going through the origin
    • This means as you double one variable the other variable also doubles so we say the independent variable is directly proportional to the dependent variable
  • The second sketched graph shows a shallow curve
    • This is the characteristic shape when two variables have an inversely proportional relationship
  • The third sketched graph shows a straight horizontal line,
    • This means as the independent variable (x-axis) increases the dependent variable does not change or is constant

Worked example

Comment on the trend of the graph.

Stress-Strain Worked Example

  • Stress and strain are proportional to each other, but not directly
  • The graph is linear with a positive gradient up to a strain of 1.0 × 10-3 
  • After this, the rate of change of the strain with stress decreases, as the gradient of the graph decreases up to the breaking stress at 190 MPa

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Katie M

Author: Katie M

Expertise: Physics

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.