Course: Combined Science + Separate Physics | Tier: Foundation + Higher | Linked equations: F = ke, Eₑ = ½ke² | Linked practical: RP 6: Force and Extension
Notes
To stretch, bend or compress an object, you need more than one force. For example, stretching a spring needs one force pulling at each end (or the spring is fixed at one end).
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- Elastic deformation: the object returns to its original shape and size when the forces are removed.
- Inelastic deformation: the object does not return to its original shape and size.
- The extension of an elastic object is directly proportional to the force applied, up to the limit of proportionality. This gives F = k × e.
- The spring constant (k) tells you how stiff a spring is. Unit: N/m.
- Work done stretching or compressing a spring is stored as elastic potential energy, as long as it isn’t inelastically deformed.
Force–extension graphs
- The straight (linear) part shows extension is proportional to force.
- The graph starts to curve (non-linear) after the limit of proportionality.
- On a force (y) against extension (x) graph, the gradient = spring constant.
- Extension = new length − original length. Always use extension, not total length!
Questions
Q1 (F) What is the difference between elastic and inelastic deformation?
Show answer
After elastic deformation, the object returns to its original shape when the forces are removed. After inelastic deformation, it doesn’t.
Q2 (F) Why do you need more than one force to stretch an object?
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With only one force, the object would just move (accelerate) instead of changing shape.
Q3 (F) A spring is 12 cm long. When a weight is added, it is 18 cm long. What is the extension?
Show answer
18 − 12 = 6 cm (0.06 m)
Q4 (F) A spring has a spring constant of 40 N/m and is stretched by 0.15 m. Calculate the force.
Show answer
F: F = k e
I: F = 40 × 0.15
A: 6.0 N
Q5 (F/H) Calculate the elastic potential energy stored in the spring in Q4.
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F: Eₑ = ½ k e²
I: Eₑ = 0.5 × 40 × 0.15²
A: 0.45 J
Q6 (F/H) What is the limit of proportionality, and how can you spot it on a force–extension graph?
Show answer
The point beyond which extension is no longer directly proportional to force. It’s where the straight line starts to curve.
Q7 (H) A 5.0 N force stretches spring A by 0.10 m and spring B by 0.25 m. Which spring is stiffer? Show your working.
Show answer
k = F ÷ e
Spring A: 5.0 ÷ 0.10 = 50 N/m
Spring B: 5.0 ÷ 0.25 = 20 N/m
Spring A is stiffer (larger spring constant).
