Physics

Problem

A bicycle helmet manufacturer claims that the foam liner can limit the average force on a rider’s head to

4.0\times10^{3}\,\text{N}

in a vertical fall from rest at a height of

1.5\,\text{m}

. The mass of the rider’s head is approximately

5.0\,\text{kg}

. Tests show that the liner extends the collision time in proportion to its thickness according to

\Delta t = (2.0\times10^{-4}\,\text{s/mm})\,d

, where

d

is the thickness of the foam that actually compresses during impact. Which of the following thicknesses

d

is the minimum that meets the manufacturer’s force claim for the described fall? a)

20\,\text{mm}

35\,\text{mm}

30\,\text{mm}

40\,\text{mm}