For a 1.00 m (100 cm) crumple zone, how much deformation do you think is needed in order
to keep the passenger the safest?
In order to determine the deformation needed in the crumple zone to keep the passenger safest, we can consider the concept of impulse. Impulse is equal to the change in momentum, which can be calculated by multiplying the force applied and the time over which it is applied.
When a vehicle collides, the crumple zone is designed to absorb the energy of the impact by deforming, lengthening the impact time, and reducing the force experienced by the passengers. This increased impact time reduces the rate at which the passengers' momentum changes during the collision. According to the law of conservation of momentum, the change in momentum of the vehicle is equal and opposite to the change in momentum of the passengers.
To maximize safety, we want to reduce the force experienced by the passengers. This can be achieved by increasing the time interval required to stop the passengers during the collision. The length of the crumple zone plays a crucial role in increasing the time interval.
So, to keep the passenger safest, a longer crumple zone with greater deformation is generally desirable. However, the exact amount of deformation needed would depend on various factors such as the speed of the collision, the weight and position of the passengers, and the design and performance characteristics of the vehicle's safety features.