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Extension is final length minus original length. Within the linear elastic range, F = ke, where k is spring constant and e extension in metres. A force–extension graph has gradient k in that region. Beyond the limit of proportionality the relationship is no longer linear; beyond the elastic limit permanent deformation can occur. These limits describe different ideas, even when they occur close together in a particular material.
Video by Cognito. The video’s own board label is retained; follow the specification reference and scope notes on this lesson for assessed content.
Viewing focus: Use Hooke’s law within its limits
After watching, attempt these questions before opening the answers. You can also use the written lesson below.
After watching 1: What is extension?
Increase from original length. Subtract the starting length.
After watching 2: Which distance belongs in a moment?
Perpendicular distance to the force’s line of action. The lever arm must be perpendicular.
What you'll be able to do
Extension is final length minus original length. Within the linear elastic range, F = ke, where k is spring constant and e extension in metres. A force–extension graph has gradient k in that region. Beyond the limit of proportionality the relationship is no longer linear; beyond the elastic limit permanent deformation can occur. These limits describe different ideas, even when they occur close together in a particular material.
For a linear spring, stored energy is Ee = ½ke². It is also the triangular area under the force–extension graph. If the graph is not linear, use an appropriate area method rather than applying the triangle formula automatically. Add masses gradually, measure extensions carefully and keep a ruler aligned to reduce parallax. A safety precaution should address the actual hazard, such as a falling mass or snapping spring.
A moment is force times perpendicular distance from pivot to the force’s line of action. A longer lever can produce the same moment with less force. For rotational equilibrium, total clockwise and anticlockwise moments balance; translational equilibrium also requires balanced forces. A force acting through the pivot has zero moment even if it is large. Identify the line of action before choosing the distance from a diagram.
Attempt these problems on paper before opening the worked reasoning. Explain your steps as well as giving a final answer.
Common mistakes to avoid
Key takeaways
Question 1: A 10 N force acts 0.30 m from a pivot. What force at 0.50 m balances it?
6.0 N in the opposite turning direction.
Check the assessed scope and practical or mathematical requirements.
An external explanation or interactive activity to use alongside the lesson. It may include extension material.
Close the notes and answer from memory. Revisit any explanation you cannot yet reconstruct.
Test yourself
Answer a few questions, then review anything you missed.
Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.