A 4.0 kg instrumented headform moving at 6.0 m/s stops in a crash test. Liner P stops it in 0.012 s and is reusable after small impacts; liner Q stops it in 0.030 s but must be replaced after one severe impact. P costs $18, Q costs $29. (a) Calculate the momentum change and average force magnitude for each liner. [5] (b) Explain why the calculations do not prove either helmet prevents injury. [3] (c) Evaluate the physical, economic, environmental and user-access implications. [6] (d) Make a conditional recommendation and identify further evidence needed. [2]

Question

Accepted Answer

The momentum change magnitude is 24 kg m/s. Average force is 2000 N for P and 800 N for Q. Q reduces average force in this test, but a recommendation also needs peak-force, fit, certification, replacement and user-context evidence. (a) Initial momentum is mv = 4.0 × 6.0 = 24 kg m/s and final momentum is zero, so the change has magnitude 24 kg m/s opposite the original motion. (a) Average force magnitude for P is Δp/Δt = 24/0.012 = 2000 N. For Q it is 24/0.030 = 800 N, so the longer stopping time lowers the average force in this test. (b) Injury can depend on peak rather than average force, rotational acceleration, impact direction, fit and biological variation. One headform speed is not a complete safety test or a guarantee for a rider. (c) Q offers the lower calculated average force in the stated severe impact, while P's reuse after minor impacts may reduce replacement cost and material waste. A damaged liner that looks unchanged also creates a behaviour and inspection risk. (c) Higher purchase and replacement costs can reduce access, especially for families or shared-cycle schemes. Manufacturers, users, emergency clinicians, waste services and regulators value different outcomes, so price alone is not the decision rule. (d) Prefer a certified design that keeps both peak linear and rotational acceleration within accepted limits and fits the user. If Q meets those tests materially better, recommend Q for severe-impact protection while making replacement guidance and support affordable. (d) Seek repeated impacts at several speeds and angles, peak-force and rotational data, fit testing, certification results, material life-cycle evidence and real replacement compliance before a final procurement decision.

Choose a safer helmet liner using impulse evidence

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