Question detail
A student records the following data for a spring: force (N) 10, 20, 30, 40 and corresponding extensions (m) 0.02, 0.04, 0.06, 0.08. Using the straight‑line section of the force‑extension graph, explain how the student can determine whether the spring is behaving proportionally.
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At a glance
Question
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Style
Topic
Forces and elasticity
Question
A student records the following data for a spring: force (N) 10, 20, 30, 40 and corresponding extensions (m) 0.02, 0.04, 0.06, 0.08. Using the straight‑line section of the force‑extension graph, explain how the student can determine whether the spring is behaving proportionally.
Answer
The student should plot the data with force on the vertical axis and extension on the horizontal axis. If the points lie on a straight line through the origin, the relationship is proportional, indicating Hooke’s law applies. The slope of this line gives the spring constant. Any deviation from a straight line would show the spring has entered the non‑linear region.
Explanation
This answer shows the student understands how to use a force‑extension graph to test proportionality, recognising the straight‑line criterion and the significance of the slope as the spring constant. It tests application of graph interpretation skills and knowledge of Hooke’s law.
Common mistake
Identifying Proportionality
Students often confuse the straight-line section of a force-extension graph with non-linear sections, leading to incorrect conclusions about proportional behaviour.
To fix this, students should focus on identifying the straight-line section clearly and understand that it indicates a direct proportionality between force and extension, ensuring they differentiate it from any curves present in the graph.
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