Required practical

Investigate the relationship between force, extension and work done extending a spring

There are different ways to investigate the relationship between force and extension for a spring. In this required practical activity, it is important to:

  • make and record length accurately
  • measure and observe the effect of force on the extension of springs
  • collect the data required to plot a force-extension graph

Aim of the experiment

A clamp stand holds both a spring and a ruler. The spring has a weight hooked onto the bottom. The clamp is attached to a bench.

To investigate the relationships between force and extension for a spring, and the work done in extending the spring.


  1. Secure a clamp stand to the bench using a G-clamp or a large mass on the base.
  2. Use bosses to attach two clamps to the clamp stand.
  3. Attach the spring to the top clamp and a ruler to the bottom clamp.
  4. Adjust the ruler so that it is vertical and with its zero level with the top of the spring.
  5. Measure and record the unloaded length of the spring.
  6. Hang a 100 g slotted mass carrier - weight 0.98 newtons (N) - from the spring. Measure and record the new length of the spring.
  7. Add a 100 g slotted mass to the carrier. Measure and record the new length of the spring.
  8. Repeat step 7 until you have added a total of 1,000 g.


Record your results in a suitable table.

Force (N)Length (mm)Extension (mm)
0 (unloaded)220


Force extension graph. Linear section drawn from origin to occupy two-thirds of graph area. Non linear section has an increasing gradient.

  1. For each result, calculate the extension:
    • extension = length - unloaded length
  2. Plot a line graph with extension on the vertical axis, and force on the horizontal axis. Draw a suitable line or curve of best fit.
  3. Identify the range of force over which the extension of the spring is directly proportional to the weight hanging from it.
  4. For the region where extension is proportional to force, find the gradient of the line. The spring constant, k, is the reciprocal of this gradient.
  5. Work done = force × distance moved. Here, the work done in extending the spring is given by the area under the line on the graph.
  6. The energy transferred to a spring's elastic store is given by the equation: Ee = \frac{1}{2} \: k \: x^{2} Compare the area under the line, from the origin up to a point, with the calculation of the energy stored in the spring for that extension.


It is important to keep the ruler vertical. Suggest another way to improve the accuracy of the length measurements.

Hazards and control measures

HazardConsequenceControl measures
Equipment falling off tableHeavy objects falling on feet - bruise/fractureUse a G-clamp to secure the stand
Sharp end of spring recoiling if the spring breaksDamage to eyes and cuts to skinWear eye protection and support and gently lower masses whilst loading the spring
Masses falling to floor if the spring failsHeavy objects falling on feet - bruise/fractureGently lower load onto spring and step back
Move on to Test