Springs — OCR A-Level Physics
Test yourself on Springs with OCR A-Level practice questions.
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Springs explained
When a material is subjected to opposing forces, it can deform.
Read the full explanation
Tensile deformation occurs when forces stretch the material, producing an extension (increase in length). Compressive deformation occurs when forces squash the material, producing a compression (decrease in length). For example, a spring pulled at both ends experiences tensile deformation and its extension is the increase from its natural length. A spring pushed at both ends experiences compressive deformation and its compression is the decrease from its natural length. Extension and compression are both measured in metres and are vector quantities in the sense that they have direction along the line of the force, but in this course they are usually treated as magnitudes with a sign convention. The deformation is elastic if the material returns to its original shape when the forces are removed, and plastic if it does not.
(b) Hooke’s law
Hooke’s law states that the extension of a spring or wire is directly proportional to the force applied, provided the limit of proportionality is not exceeded. Mathematically, F = kx, where F is the applied force in newtons, x is the extension in metres, and k is the spring constant in newtons per metre (N m⁻¹). The law also applies to compression, where x is the compression. For example, if a spring extends by 0.05 m when a force of 10 N is applied, then k = F/x = 10 / 0.05 = 200 N m⁻¹. A force–extension graph is a straight line through the origin up to the limit of proportionality; beyond that, the graph curves and Hooke’s law no longer applies. The spring constant is a measure of stiffness: a larger k means a stiffer spring.
(c) force constant k of a spring or wire; F = kx
The force constant k measures stiffness: the force needed per unit extension. For a spring or wire obeying Hooke's law, F = kx, where F is the applied force in newtons, x is the extension (or compression) in metres and k is in N m⁻¹. A stiff spring has a large k, so a given force produces only a small extension. Example: a spring with k = 200 N m⁻¹ extends 0.05 m under F = kx = 200 × 0.05 = 10 N. Rearranged, k = F ÷ x. The relationship is linear only up to the limit of proportionality; beyond it the graph curves and F = kx no longer holds. Extension is the change in length, not the total length, so always subtract the original length.
(d)
This row is a specification sub-heading marker rather than a taught statement, so treat it as a signpost to the material that follows in section 3.4.1. When reading the specification, use such markers to organise your notes: the content under (d) continues the study of springs and wires, building on the force constant and Hooke's law from earlier clauses. Your task is to locate the sub-clauses that sit beneath this heading, read each one carefully, and map how they connect: definitions, graphs, and practical techniques. Do not invent examinable facts from the heading itself; instead, use it to structure revision and to check that every following sub-clause has been covered.
(i) force–extension (or compression) graphs for springs and wires
A force–extension graph plots applied force F on the y-axis against extension x on the x-axis. For a spring or wire obeying Hooke's law, the initial region is a straight line through the origin; its gradient equals the force constant k, since F = kx. The straight region ends at the limit of proportionality. Beyond it the line curves, and eventually the elastic limit is passed so the material no longer returns to its original length. For a wire, the same shape appears but the gradient is much steeper because a wire is stiffer. Compression graphs for springs show the same linear behaviour for small compressions. The area under the graph represents the work done in stretching the spring.
(ii) techniques and procedures used to investigate force–extension characteristics for arrangements which may include springs, rubber bands, polythene strips.
To investigate force–extension characteristics, clamp the support and hang the sample vertically. Measure the original length with a ruler, then add masses one at a time, recording the new length and calculating extension as new length minus original length. Use a fiducial marker and read at eye level to reduce parallax. For a spring, add masses up to and beyond the limit of proportionality; for a rubber band or polythene strip, the graph is non-linear and shows hysteresis, so load and unload to compare. Plot force (mg) against extension. Repeat readings and take a mean, and check the zero by noting the reading with no added mass. Safety: place a cushion below in case the sample snaps.
Your focus
- Define tensile and compressive deformation and distinguish between extension and compression.
- Identify whether a given deformation is tensile or compressive from a description or diagram.
- Measure extension or compression from the natural length of a material.
Show all 18 objectives
- State Hooke’s law and identify the conditions under which it applies.
- Use the equation F = kx to calculate force, extension, or spring constant.
- Interpret a force–extension graph to determine the spring constant and the limit of proportionality.
- Define the force constant k and give its unit.
- Use F = kx to calculate force, extension or force constant.
- Explain why F = kx fails beyond the limit of proportionality.
- Identify the sub-clauses that follow this heading in section 3.4.1.
- Explain how each sub-clause connects to the force constant and Hooke's law.
- Use the heading to audit revision coverage of the springs topic.
- Sketch and interpret force–extension graphs for springs and wires.
- Determine the force constant from the gradient of the linear region.
- Explain the significance of the point where the graph stops being straight.
- Describe a safe procedure to obtain force–extension data for a spring, rubber band or polythene strip.
- Process the data into a force–extension graph and interpret its shape.
- Evaluate the reliability of the measurements and suggest improvements.
Springs exam tips
Marking Points
- Tensile deformation is caused by forces that stretch a material, producing an extension.
- Compressive deformation is caused by forces that squash a material, producing a compression.
- Extension is the increase in length from the natural length; compression is the decrease in length from the natural length.
- Both extension and compression are measured in metres (m).
- Elastic deformation is reversible; plastic deformation is permanent.
- The direction of the deforming force determines whether deformation is tensile or compressive.
- Hooke’s law: the extension of a material is directly proportional to the applied force, provided the limit of proportionality is not exceeded.
- The equation is F = kx, where F is force in newtons, x is extension in metres, and k is the spring constant in N m⁻¹.
- The law applies to both extension and compression, with x representing the change in length from the natural length.
- A force–extension graph is a straight line through the origin for a material obeying Hooke’s law.
- The spring constant k is a measure of stiffness; a steeper graph indicates a larger k.
- The limit of proportionality is the point beyond which extension is no longer directly proportional to force.
- States that k is the force per unit extension and has units N m⁻¹.
- Applies F = kx correctly, including rearrangement to k = F ÷ x or x = F ÷ k.
- Uses extension (change in length), not total length, in the calculation.
- Recognises that F = kx applies only within the limit of proportionality for the spring or wire.
- Plots force on the y-axis and extension (or compression) on the x-axis.
- Identifies the straight-line region through the origin as Hooke's law behaviour.
- Relates the gradient of the linear region to the force constant k.
- Describes the curve beyond the limit of proportionality and the loss of elastic behaviour.
- Measures original length and each new length with a ruler, calculating extension as the difference.
- Uses a fiducial marker and reads at eye level to reduce parallax error.
- Adds masses in equal steps and records force as weight, F = mg, using g = 9.81 N kg⁻¹.
- Plots force against extension and identifies the linear region and any non-linear behaviour.
- Repeats readings and takes a mean to improve reliability.
- Describes the different behaviour of rubber bands or polythene strips, including non-linearity and hysteresis on loading and unloading.
Examiner Tips
- 💡Read the question carefully to identify whether the material is being stretched or squashed.
- 💡Use the terms extension and compression correctly in your answers.
- 💡If a graph of force against extension is given, note that the gradient gives the spring constant for a spring obeying Hooke’s law.
- 💡Remember that extension and compression are measured in metres, and convert from cm or mm if necessary.
- 💡Always identify the extension from the natural length before substituting into F = kx.
- 💡If a graph is given, calculate the gradient to find k, and check that the line passes through the origin.
- 💡Remember that Hooke’s law applies to both stretching and compressing, but the sign of x may need a convention.
- 💡In multiple-choice questions, look for the statement that extension is proportional to force, not to total length.
- 💡Write the equation, substitute values with units, then rearrange only after listing known quantities.
- 💡Check that x is in metres before dividing; convert centimetres by dividing by 100.
- 💡Sanity-check the size of k: a very small k means a very stretchy spring.
- 💡Highlight each sub-clause under this heading and tick it off once you can explain it without notes.
- 💡Link the sub-clauses to earlier work on the force constant so your revision forms one connected topic.
- 💡Use the heading as a checklist item, not as a fact to memorise.
- 💡Label both axes with quantity and unit before plotting any points.
- 💡Draw a straight line of best fit through the origin for the linear region and read the gradient from it.
- 💡State clearly where the straight region ends when describing the graph.
- 💡State the independent variable (force), dependent variable (extension) and control variables such as the same sample and support.
- 💡Describe how you would improve reliability: repeat readings, take a mean, and use a fiducial marker.
- 💡When comparing materials, keep the method identical and comment on the shape of each graph.
Common Mistakes
- Confusing extension with compression: extension is an increase in length, compression is a decrease. Correct by checking whether the material is stretched or squashed.
- Thinking that compression always means the material gets shorter than its natural length: compression is a decrease relative to the natural length, but the material may still be under compression while shorter than its original length.
- Assuming all deformation is elastic: some materials deform plastically beyond their elastic limit. Correct by distinguishing between elastic and plastic behaviour.
- Forgetting to measure extension from the natural length, not from an arbitrary starting point. Correct by always using the unstretched length as the reference.
- Thinking Hooke’s law applies to all extensions: it only applies up to the limit of proportionality. Correct by checking whether the graph is linear through the origin.
- Confusing the spring constant k with the force constant of a different spring or with the elastic limit. Correct by using k only as the gradient of the force–extension graph in the linear region.
- Using the total length instead of the extension in F = kx. Correct by calculating extension as the increase from the natural length.
- Forgetting that k has units N m⁻¹, not N m. Correct by remembering that k = F/x, so units are N divided by m.
- Using the total length of the spring instead of the extension; the correction is to subtract the original length to find x.
- Treating k as a force rather than force per unit extension; the correction is to quote k in N m⁻¹ and remember it describes stiffness.
- Assuming F = kx holds for any force; the correction is that the linear relationship fails beyond the limit of proportionality.
- Treating the heading as a standalone fact to be learned; the correction is to read it as a signpost to the sub-clauses beneath it.
- Skipping the sub-clauses because the heading looks empty; the correction is to work through each following statement in turn.
- Revising the sub-clauses in isolation; the correction is to connect them to Hooke's law and the force constant already studied.
- Plotting total length on the x-axis instead of extension; the correction is to plot the change in length so the line passes through the origin.
- Reading the gradient as the reciprocal of k; the correction is that gradient = k because F = kx.
- Assuming the graph stays straight for all forces; the correction is that it curves beyond the limit of proportionality.
- Recording total length as extension; the correction is to subtract the original length from each reading.
- Ignoring the weight of the mass hanger; the correction is to include it in the total force or to zero the scale before adding masses.
- Assuming rubber bands obey Hooke's law; the correction is that their force–extension graph is curved and shows hysteresis.