A.2 · IB Physics
Springs in series and parallel
Hang a load from two springs joined end to end or side by side, and compare how each spring stretches, the total extension and the effective spring constant on a force–extension graph.
F = mg = k x
Series: 1/k = 1/k₁ + 1/k₂, x = x₁ + x₂
Parallel: k = k₁ + k₂, F = F₁ + F₂
Load weight F
Extension of spring 1, x₁
Extension of spring 2, x₂
Total extension x
Effective k
Tension F₁ / F₂
Try this
- Set k₁ = k₂ = 100 N m⁻¹. Check that the series effective constant is half of one spring and the parallel one is double.
- In series, set k₁ = 200 N m⁻¹ and k₂ = 50 N m⁻¹. Which spring stretches more, and what is x₁ : x₂? Then switch to parallel and compare F₁ : F₂.
- Double the load in each arrangement. Does the gradient of the graph line change, or only the position of the dot?
Common error: adding spring constants for springs in series — in series each spring carries the full load and the extensions add, so the combination is softer than either spring alone.