Impact Force (helmets) Safety Devices

[Shane-O]

I'm doing a physics assignment on safety devices such as helmets and i need help with a question.

Why is the Impact force reduced for a helmet with a soft interior VS a hard interior?

I know it is because the soft padding on the inside of soft the helmet will reduce the time taken for your head to stop therefore decreasing the force inflicted on your head but I cannot find a real solid answer about how this can relate to the Hard interior helmet.
Any Help?

 

[JHamm]

Want you want to consider is the impulse of the collision, since we know that $F = \frac{\Delta P}{\Delta T}$ then rearranging we obtain $F \Delta T = \Delta P$ and this is what we call the impulse. So from this we can see that since, when something hits you, that object will have the same change in momentum regardless of what type of hat you are wearing (from its velocity to 0) the $\Delta P$ stays constant; what the padding does is increase the time the impact takes (think of punching a pillow where your hand sinks in verses a wall where your hand bounces off in much less time), and since $\Delta P$ is constant an increase in $\Delta T$ will cause a decrease in $F$. This $F$ is the average force felt so the soft padding will lead to a lower average force but over a longer time.