Interpret data from an investigation of the relationship between force and…

The idea

In this investigation, a spring or wire is stretched by adding masses or weights, and the total length is measured for each force. Extension is the increase in length, found by subtracting the original length from each measured length. Plotting force on the y-axis against extension on the x-axis gives a straight line through the origin while the spring obeys Hooke's law, showing that force and extension are directly proportional. The gradient of this linear section equals the spring constant k. Beyond the limit of proportionality the line curves, so equal increases in force produce larger increases in extension. Anomalous points that do not fit the pattern should be identified and either rechecked or ignored when drawing the line of best fit.

What earns the marks

• Calculate extension for each reading by subtracting the original length from the measured total length.
• Plot force on the y-axis against extension on the x-axis and draw a line of best fit through the linear points.
• Describe the straight line through the origin as showing that force and extension are directly proportional in that region.
• Use the gradient of the linear section to obtain the spring constant, including its unit N/m.
• Identify the point at which the graph starts to curve as the limit of proportionality.
• Recognise anomalous results as points that do not follow the overall pattern and explain that they should be rechecked or excluded from the line of best fit.

Common mistakes and how to put them right

• Plotting total length instead of extension.

  Put it right by subtracting the original length from every reading.

• Joining every point with straight segments instead of drawing a single line of best fit.

  Put it right by drawing one smooth or straight line that follows the pattern.

• Treating the first curved point as part of the linear region.

  Put it right by using only points on the straight section to find k.

Exam tips

• Label both axes with the quantity and unit, and choose a scale that uses most of the grid so the gradient can be read accurately.
• When describing the relationship, refer to the graph rather than repeating the table, and state the range of forces over which the line is straight.
• If asked to improve the investigation, suggest repeating measurements, using smaller force intervals near the limit of proportionality, or checking anomalous points.