Investigate force and spring extension, then determine work done stretching a spring. Use a securely clamped spring, mass hanger, known masses, vertical ruler and a pointer.Original labelled apparatus schematic; not to scale. Follow the stated measurements and safety instructions.
Clamp the stand securely or weight its base and keep falling masses away from feet. Use eye protection and avoid stretching the spring beyond a safe manufacturer/teacher limit.
Fix the ruler parallel to the spring and read the pointer at eye level. A pointer makes a clear reference; the ruler zero does not need to coincide with the spring end if differences are measured.
Measure the unloaded reference length or pointer position before adding load. Extension x = loaded length minus original length; it is not the total loaded length.
Loading method and graph
Add known masses in suitable equal steps, including the hanger's mass where it contributes load. Allow the spring to settle before reading; stop oscillations without forcing the final position.
Convert total hanging mass to force using F = mg. Record mass, force, loaded reading and extension with units; convert extension to metres for SI calculations.
Repeat readings at each load and, within the safe range, unload in steps to check return towards the original length. Permanent extension indicates the elastic limit has been exceeded.
Plot force vertically against extension horizontally. In the proportional region, F = kx and gradient k is spring constant in N/m.Qualitative force–extension graph: the straight part follows Hooke’s law, and area under the graph gives work. Curvature beyond the proportional limit need not imply permanent deformation.
The limit of proportionality is where force ceases to be proportional to extension. It is not automatically identical to the elastic limit, which concerns return to original length after unloading.
Draw a best-fit straight line for the proportional part of the graph. Do not force all points onto it or assume the spring obeys Hooke’s law at every load.
For a linear spring starting with zero extension, work done = ½Fx = ½kx². Work is the triangular area under a force–extension graph, not F times x for the final force throughout.
For a non-linear force–extension relationship, work is still the area under the graph, but the triangular formula may not apply. An exam may ask for a graph-area estimate.
For an ideal elastic spring with negligible losses, the work done becomes stored elastic potential energy and can be recovered. Permanent deformation or different loading and unloading curves (hysteresis) can mean some energy heats the surroundings instead, so less is recovered.
Precision and evaluation
Read the same pointer reference each time and avoid parallax. A fixed ruler and pointer improve repeatability; a slipping clamp creates a changing reference.
Small extensions have larger relative uncertainty. Use a safe useful load range and suitable ruler resolution, rather than overloading the spring merely to make readings larger.
Extension is a difference between loaded and unloaded readings, so both readings contribute uncertainty. Check the unloaded position again after the experiment: a changed position may show a slipping reference or permanent extension.
A large triangle on the straight best-fit line estimates k more reliably than a ratio from one noisy point. Remember that swapping graph axes changes the meaning of the gradient.
Control spring identity and temperature and use the same settling rule. Different springs can legitimately have different spring constants; this is not necessarily an anomaly.
Quote graph evidence for proportionality and any departure. Distinguish a measurement improvement from altering the scientific question, and explain the physical error addressed.
Exam skills: planning, precision and evaluation
State what you change (the independent variable), what you measure (the dependent variable) and what you keep the same (control variables). Explain how you keep each control variable constant, rather than just saying “make it fair”.
Accuracy means how close a result is to the true value. Precision means how close repeated measurements are to each other. Resolution is the smallest change an instrument can show. More digits on a display do not automatically mean a more accurate result.
Repeat measurements for each condition, calculate a mean and describe how spread out the results are. This helps assess and reduce the effect of random errors. Repeating cannot fix an error that pushes results consistently in one direction (a systematic error), such as a slipping clamp changing the reference position.
Repeatability means getting similar results when the same person repeats the same method with the same equipment. Reproducibility means getting similar results when someone else, or different suitable equipment, repeats the experiment. Results can be consistent but still inaccurate.
Check that instruments read zero correctly and are calibrated where needed. Read scales at eye level: looking from an angle can give a wrong reading (parallax error). Choose suitable ranges, measurement intervals and scale divisions (resolution).
Write down the original readings straight away in a table, with units in the headings. Use decimal places that match the instrument’s resolution. Keep the original data and round only when needed. Do not discard a result just because it differs from your prediction.
An anomalous result does not fit the pattern of the other results. Repeat that measurement and check the method. Only leave it out of a mean if you have a clear reason; state which result you excluded and why.
For continuous variables, plot the independent variable on the horizontal axis and the dependent variable vertically. Use sensible scales, units and a best-fit line or curve; do not automatically join every point or force the graph through zero.
Find the gradient of a straight best-fit line using a large triangle: vertical change ÷ horizontal change. For a curve, draw a tangent to estimate the gradient at one point. Explain what the gradient shows in this experiment, include its units and use measured values to support your conclusion.
Uncertainty describes the possible range around a measurement. For one reading on a scale, half the smallest division is a useful classroom estimate unless the question says otherwise. If you subtract two readings, both have uncertainty. Percentage uncertainty = absolute uncertainty ÷ measured value × 100. Follow the method specified in the question.
Use results as evidence and then explain what they mean. A pattern linking variables (a correlation) does not prove that one causes the other. If the ranges of repeat results overlap, a claimed difference may be less convincing. Keep conclusions within the range tested and suggest an improvement that tackles a specific error.
Mr Kidman's Classroom