OCR · GCSE · Physics
Course version: J249 · Version from Sept 2018
Forces in action: calculate a spring constant in linear cases
In linear cases a spring stretches in proportion to the force applied, so a graph of force against extension is a straight line through the origin.
Checked against the OCR J249 specification (opens in a new tab) on .
- Point 11 of 21
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
In linear cases a spring stretches in proportion to the force applied, so a graph of force against extension is a straight line through the origin. The spring constant k measures stiffness and is found by rearranging F = kx to give k = F ÷ x, where F is the applied force in newtons and x is the extension in metres (final length minus original length). A spring needing 6 N to stretch 0.03 m has k = 6 ÷ 0.03 = 200 N/m. A stiffer spring needs more force for the same extension, so it has a larger k. Convert centimetres to metres before dividing, and remember that extension is the change in length, not the total length. The gradient of the force–extension line also equals k.
What earns the marks
- Rearranges F = kx correctly to k = F ÷ x before substituting values.
- Uses extension rather than total length, subtracting the original length from the stretched length.
- Converts extension from centimetres to metres so that k is expressed in N/m.
- Divides force in newtons by extension in metres and states the unit N/m with the answer.
- Recognises that a larger spring constant corresponds to a stiffer spring for the same extension.
Common mistakes and how to put them right
Uses the total stretched length as the extension.
Put it right: Subtract the original length first.
Leaves the extension in centimetres and reports k in N/cm.
Put it right: Convert to metres so the unit is N/m.
Multiplies force by extension instead of dividing.
Put it right: Apply k = F ÷ x.
Exam tips
- Write the equation, then the rearranged form, then substitute numbers so the method is visible.
- Convert every length to metres before dividing, and check the unit of the answer is N/m.
- Sanity-check the size of k: a stiff spring gives a large value, a soft spring a small one.
Try the lesson
The start of the Forces in action: calculate a spring constant in linear cases lesson, made from checked teaching notes for this specification point.
Have a go first
A 6 N force produces an extension of 0.03 m in a spring that obeys a linear relationship. What is the spring constant?
Listen
In linear cases a spring stretches in proportion to the force applied, so a graph of force against extension is a straight line through the origin. The spring constant k measures stiffness and is found by rearranging F = kx to give k = F ÷ x, where F is the applied force in newtons and x is the extension in metres (final length minus original length). A spring needing 6 N to stretch 0.03 m has k = 6 ÷ 0.03 = 200 N/m. A stiffer spring needs more force for the same extension, so it has a larger k. Convert centimetres to metres before dividing, and remember that extension is the change in length, not the total length. The gradient of the force–extension line also equals k. A strong answer earns marks for these points. Rearranges F = kx correctly to k = F ÷ x before substituting values. Uses extension rather than total length, subtracting the original length from the stretched length. Converts extension from centimetres to metres so that k is expressed in N/m. Divides force in newtons by extension in metres and states the unit N/m with the answer. Exam tip: Write the equation, then the rearranged form, then substitute numbers so the method is visible.
See it
Put it in order
Put these steps in the order they happen.
- 1. Rearrange F = kx to k = F ÷ x
- 2. Larger k means stiffer spring
- 3. Divide force in newtons by extension in metres
- 4. Force F applied to spring
- 5. Spring stretches
- 6. Spring constant k in N/m
- 7. Extension x = final length minus original length
- 8. Convert x from centimetres to metres
Key words
Say what each word means before you turn the card.
spring constant
Try answering aloud or in your head before turning the card.
extension
Try answering aloud or in your head before turning the card.
stiffness
Try answering aloud or in your head before turning the card.
force–extension line
Try answering aloud or in your head before turning the card.
See every definition
- spring constant
- A measure of stiffness, found by rearranging F = kx to give k = F ÷ x, where F is the applied force in newtons and x is the extension in metres.
- extension
- The change in length, calculated as the final length minus the original length, rather than the total length.
- stiffness
- A property measured by the spring constant, where a stiffer spring needs more force for the same extension and so has a larger k.
- force–extension line
- A straight line through the origin in linear cases, whose gradient also equals k.
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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