PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
During safety testing, identical 4.5kg instrumented headforms are dropped from rest from the same height onto a rigid surface while fitted with two different bicycle helmets. Helmet A brings the headform to rest in 6.0ms, whereas Helmet B, equipped with an improved crushable liner, brings it to rest in 12ms. The decelerating force exerted by each helmet on the headform is approximately constant during impact, and the headform’s mass remains constant. The speed of the headform just before impact is the same in both tests.
(a) In terms of the stopping time Δt and any necessary physical constants, derive a general expression for the magnitude of the average impact force exerted on the headform.
(b) Using the expression from part (a), derive an algebraic expression for the percent reduction in the magnitude of the average impact force when the stopping time increases from Δt1 to Δt2.
(c) Apply your expression to calculate the percent reduction in average impact force achieved by Helmet B compared with Helmet A.
(d) Discuss qualitatively why increasing the stopping time is an effective strategy for reducing the risk of head injury, citing the relationship you derived and the typical biomechanical response of the human brain.