OCR · GCSE · Physics
Course version: J249 · Version from Sept 2018
Recall and apply: force exerted by a spring (N) = spring constant (N/m) ×…
Full specification wording
Forces in action: recall and apply: force exerted by a spring (N) = spring constant (N/m) × extension (m)
Hooke's law links the force a stretched spring exerts to how far it is stretched.
Checked against the OCR J249 specification (opens in a new tab) on .
- Point 1 of 21
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Hooke's law links the force a stretched spring exerts to how far it is stretched. The equation is F = k × e, where F is the force in newtons (N), k is the spring constant in newtons per metre (N/m) and e is the extension in metres (m). Extension means the change in length from the natural length, not the total length, so subtract the original length first. A spring with k = 200 N/m stretched by 0.05 m gives F = 200 × 0.05 = 10 N. Rearranged, k = F ÷ e and e = F ÷ k. Keep units consistent: convert centimetres to metres by dividing by 100, so 5 cm becomes 0.05 m. The relationship holds within the elastic limit, where the spring returns to its original length when the force is removed.
What earns the marks
- Selects the equation F = k × e and substitutes the spring constant in N/m and the extension in m.
- Converts an extension given in centimetres to metres by dividing by 100 before substituting.
- Calculates extension as the change in length from the natural length rather than the total stretched length.
- Rearranges the equation correctly to find k = F ÷ e or e = F ÷ k when force is the known quantity.
- States the force in newtons and the spring constant in N/m with correct unit labels.
Common mistakes and how to put them right
Uses the total stretched length as the extension.
Put it right: Subtract the natural length to find the change in length.
Substitutes centimetres directly into the equation.
Put it right: Convert to metres first by dividing by 100.
Inverts the relationship and multiplies force by extension.
Put it right: Divide force by extension to find the spring constant.
Omits units or mixes N and N/m.
Put it right: Label force in N and spring constant in N/m.
Exam tips
- Write the equation, then list the known values with their units before substituting.
- Check whether the length given is total length or extension, and convert cm to m if needed.
- Sanity-check the answer: a stiffer spring (larger k) needs a larger force for the same extension.
Try the lesson
The start of the Forces in action: recall and apply: force exerted by a spring (N) = spring constant (N/m) × extension (m) lesson, made from checked teaching notes for this specification point.
Have a go first
A spring has a spring constant of 40 N/m. It is stretched by 0.20 m. What force does the spring exert?
Listen
Hooke's law links the force a stretched spring exerts to how far it is stretched. The equation is F = k × e, where F is the force in newtons (N), k is the spring constant in newtons per metre (N/m) and e is the extension in metres (m). Extension means the change in length from the natural length, not the total length, so subtract the original length first. A spring with k = 200 N/m stretched by 0.05 m gives F = 200 × 0.05 = 10 N. Rearranged, k = F ÷ e and e = F ÷ k. Keep units consistent: convert centimetres to metres by dividing by 100, so 5 cm becomes 0.05 m. The relationship holds within the elastic limit, where the spring returns to its original length when the force is removed. A strong answer earns marks for these points. Selects the equation F = k × e and substitutes the spring constant in N/m and the extension in m. Converts an extension given in centimetres to metres by dividing by 100 before substituting. Calculates extension as the change in length from the natural length rather than the total stretched length. Rearranges the equation correctly to find k = F ÷ e or e = F ÷ k when force is the known quantity. Exam tip: Write the equation, then list the known values with their units before substituting.
See it
Key words
Say what each word means before you turn the card.
Unit consistency and conversion between cm and m
Try answering aloud or in your head before turning the card.
Distinguishing extension from total length
Try answering aloud or in your head before turning the card.
Rearranging equations to solve for any variable
Try answering aloud or in your head before turning the card.
See every definition
- Unit consistency and conversion between cm and m
- Keep units consistent by converting centimetres to metres, dividing by 100, so 5 cm becomes 0.05 m.
- Distinguishing extension from total length
- The change in length from the natural length, not the total length, so subtract the original length first.
- Rearranging equations to solve for any variable
- Rearranged, the spring constant equals force divided by extension, and extension equals force divided by spring constant.
Label the diagram
Some boxes have lost their names. Pick the right name for each number.
1Box 1
2Box 2
3Box 3
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