Required practical activity 18: investigate the relationship between force…

The idea

This required practical explores how a spring stretches when a force is applied. You hang a spring from a clamp and add masses one at a time, recording the total weight as the force and the extension as the increase in length from the original. Plot force on the y-axis against extension on the x-axis. The graph is a straight line through the origin while the spring obeys Hooke's law, so force is directly proportional to extension. Beyond the limit of proportionality the line curves and the spring may not return to its original length. The gradient of the straight section equals the spring constant k, measured in N/m. Use F = kx to calculate k, and take repeat readings to reduce random error.

What earns the marks

• Measure the natural length of the spring before adding any masses, using a ruler with the eye level aligned to avoid parallax error.
• Add masses one at a time and record the total weight as the force, using W = mg with g taken as 9.8 N/kg unless told otherwise.
• Calculate extension as stretched length minus natural length, not the total length, and record it in metres or convert from cm.
• Plot a graph of force against extension, draw a line of best fit and identify where the straight line through the origin ends.
• Determine the spring constant from the gradient of the straight section, using k = F ÷ x, and state the unit N/m.
• Repeat each measurement and calculate a mean to reduce the effect of random errors, and check that the spring returns to its original length.
• Identify the limit of proportionality as the point where the graph stops being a straight line through the origin.

Common mistakes and how to put them right

• Using the total stretched length instead of the extension.

  Put it right: Subtract the natural length from each stretched length.

• Plotting extension on the y-axis and force on the x-axis.

  Put it right: Plot force on the y-axis and extension on the x-axis so the gradient gives the spring constant.

• Assuming the graph stays straight for all masses.

  Put it right: Check for curvature and only use the straight section to find the spring constant.

Exam tips

• State clearly that the spring constant is the gradient of the straight-line section and give its unit as N/m.
• Describe how you ensured the spring did not exceed its elastic limit, for example by stopping when the graph began to curve.
• When comparing springs, link a steeper gradient to a larger spring constant and therefore a stiffer spring.