Course: Combined Science + Separate Physics | Tier: Foundation + Higher | Equation sheet: given in the exam
The equation
force applied to a spring = spring constant × extension F = k e
| Quantity | Symbol | Unit |
|---|---|---|
| force | F | newtons (N) |
| spring constant | k | newtons per metre (N/m) |
| extension | e | metres (m) |
Rearranged: k = F ÷ e | e = F ÷ k | Only works up to the limit of proportionality.
Use FIFA for every answer
- F – Formula: write the equation as it appears on the sheet.
- I – Insert: put in the numbers (convert to standard units first).
- F – Fix: rearrange to make the unknown the subject.
- A – Answer: calculate and always give the unit.
Foundation: aim for Q1–8. Higher: aim for Q4–10. Most questions need rearranging.
Questions
Q1 (F) The spring in a clicky pen has a spring constant of 200 N/m. It is compressed by 0.02 m. Calculate the force applied.
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F: F = k e
I: F = 200 × 0.02
F: F is already the subject – no rearranging needed
A: 4 N
Q2 (F) In a bungee cord safety test, a force of 50 N stretches a short cord by 0.25 m. Calculate the spring constant.
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F: F = k e
I: 50 = k × 0.25
F: k = 50 ÷ 0.25
A: 200 N/m
Q3 (F) A car suspension spring has a spring constant of 30 000 N/m. A force of 6000 N acts on it. Calculate the compression.
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F: F = k e
I: 6000 = 30 000 × e
F: e = 6000 ÷ 30 000
A: 0.2 m
Q4 (F) The spring in a kitchen scale extends by 4.0 cm when a force of 2.0 N is applied. Calculate the spring constant.
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Convert first: 4.0 cm = 0.040 m
F: F = k e
I: 2.0 = k × 0.040
F: k = 2.0 ÷ 0.040
A: 50 N/m
Q5 (F) A trampoline spring has a spring constant of 5000 N/m. A force of 150 N stretches it. Calculate the extension in cm.
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F: F = k e
I: 150 = 5000 × e
F: e = 150 ÷ 5000 = 0.03 m
A: 0.03 × 100 = 3 cm
Q6 (F/H) A gym resistance band is 50 cm long and has a spring constant of 400 N/m. It is pulled with a force of 120 N. Calculate its new length in cm.
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F: F = k e
I: 120 = 400 × e
F: e = 120 ÷ 400 = 0.30 m = 30 cm
A: new length = 50 + 30 = 80 cm
Watch out: extension is the increase in length, not the total length.
Q7 (F/H) A spring in a mattress compresses by 15 mm when a force of 45 N acts on it. Calculate the spring constant.
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Convert first: 15 mm = 0.015 m
F: F = k e
I: 45 = k × 0.015
F: k = 45 ÷ 0.015
A: 3000 N/m
Q8 (F/H) A crane’s steel cable behaves like a spring with k = 2.4 × 106 N/m. It lifts a load of 6.0 × 104 N. Calculate the extension of the cable in mm.
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F: F = k e
I: 6.0 × 104 = 2.4 × 106 × e
F: e = 6.0 × 104 ÷ 2.4 × 106 = 0.025 m
A: 0.025 × 1000 = 25 mm
Q9 (H) An angler’s spring balance has a spring constant of 490 N/m. When a fish is hung from it, the spring stretches by 6.0 cm. Calculate the mass of the fish. (g = 9.8 N/kg)
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Step 1 – force on the spring
F: F = k e
I: F = 490 × 0.060
A: F = 29.4 N (this is the fish’s weight)
Step 2 – mass of the fish
F: W = m g
I: 29.4 = m × 9.8
F: m = 29.4 ÷ 9.8
A: 3.0 kg
Q10 (H) A door-closer spring is 12.0 cm long with a spring constant of 35 N/m. A force of 2.4 N stretches it. Calculate its new length in cm, to 3 significant figures.
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F: F = k e
I: 2.4 = 35 × e
F: e = 2.4 ÷ 35 = 0.06857… m = 6.857… cm
A: new length = 12.0 + 6.857… = 18.857… = 18.9 cm (3 s.f.)
