2.3.5Forces, Space and Radioactivity
Investigating the Force-Extension Graph for a Spring
5 min read 7 parts Lesson 17 of 41 Unit quiz
Section 1 of 7Aim and variables
The aim
- The aim To find out how the extension of a spring depends on the stretching force and to test whether the spring obeys Hooke's law, F = k × x.
- Here k is the spring constant in N/m, F is the force in newtons and x is the extension in metres.
Variables
- Variables Independent variable: the stretching force, which you change by adding masses.
- Dependent variable the extension of the spring, which you measure with a ruler.
- Control variables the same spring throughout, the same ruler and pointer, and readings taken from the same point on the spring each time.
Equipment
- Equipment Clamp stand, boss and clamp to hold the spring;
- a metre ruler fixed beside it;
- a pointer attached to the bottom of the spring to make the reading precise.
- A 100 g mass hanger plus six or seven 100 g slotted masses to provide the force.
Section 2 of 7Method
1
Fix the ruler firmly to the clamp stand so that it cannot move, hang the spring from the clamp and attach the pointer to the lower end.
2
Measure the original length of the spring with nothing hanging from it, reading the ruler at eye level.
3
Hang the 100 g mass hanger on the spring, wait until it is stationary and record the new length.
4
Add one 100 g mass at a time, waiting for the spring to settle and recording the length after every addition.
5
Repeat each reading a few times, or repeat the whole experiment, and calculate an average length for each load.
6
Calculate the force and the extension for every load (see the next part) and record everything in a results table.
Section 3 of 7Processing the results
| Quantity | How to find it | Unit |
|---|---|---|
| Force, F | Weight of the load, W = m × g, using g = 10 N/kg (or 9.8 N/kg) | newtons, N |
| Mass, m | Total mass hanging on the spring, converted from grams to kilograms | kilograms, kg |
| Extension, x | Current length minus the ORIGINAL length (not minus the previous length) | metres, m |
| Spring constant, k | Gradient of the force-extension graph, or F ÷ x in the straight section | N/m |
Section 4 of 7Drawing and reading the graph
1Plot the points
- Plot the points Plot force on the vertical axis against extension on the horizontal axis, with sensible scales that use most of the paper.
2Draw a line of best fit
- Draw a line of best fit Draw a smooth line through the trend of the points rather than joining the dots, ignoring any clear anomalies.
3Look for a straight line through the origin
- Look for a straight line through the origin A straight line through (0, 0) shows that force is directly proportional to extension,
- so the spring obeys Hooke's law.
4Find the limit of proportionality
- Find the limit of proportionality If the line starts to curve, the spring has been stretched beyond its limit of proportionality and F = k × x no longer applies.
Section 5 of 7Evaluation and safety
Reducing systematic error
- Reducing systematic error Read the ruler at eye level to avoid parallax error.
- Check the ruler is vertical and has not slipped, and measure the original length carefully because every extension depends on it.
Reducing random error
- Reducing random error Wait for the masses to stop bouncing before taking a reading.
- Use the pointer, always read from the same point on the spring, and repeat readings to take averages.
Safety
- Safety Wear eye protection in case the spring snaps or a mass is released.
- Clamp the stand to the bench, put a soft mat or tray under the masses, keep feet clear and do not exceed the maximum load of the spring.
Section 6 of 7Key terms
| Term | Meaning |
|---|---|
| Hooke's law | The extension of a spring is directly proportional to the force applied, provided the limit of proportionality is not exceeded. |
| Extension | The increase in length of a spring compared with its original, unstretched length. |
| Spring constant | The force needed to produce one metre of extension, measured in N/m; it is the gradient of the straight part of the graph. |
| Limit of proportionality | The point beyond which a spring no longer obeys Hooke's law and the force-extension graph curves. |
| Parallax error | A reading error caused by looking at a scale from an angle instead of straight on. |
| Directly proportional | Two quantities whose graph is a straight line through the origin, so doubling one doubles the other. |
Section 7 of 7Exam technique
1
Working out the increase in length between each pair of readings instead of the total extension from the original length. If your extensions all look about the same, you have made this mistake.
2
Forgetting to convert masses from grams to kilograms (or lengths from centimetres to metres) before using W = m × g or F = k × x.
3
Plotting extension on the vertical axis. For this practical force goes on the y-axis, so that the gradient equals the spring constant.
4
Saying a curved line shows the spring is 'broken'. It shows only that the limit of proportionality has been passed, so the spring no longer obeys Hooke's law.
5
Joining the plotted points with a zigzag line instead of drawing a single line of best fit.