Question

part i
to ensure that a vehicle crash is inelastic, vehicle safety designers add crumple zones to vehicles. a crumple zone is a part of a vehicle designed to crumple easily in a crash. use newtons second law to explain why crumple zones reduce the force in a collision.
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Explanation:

Step1: State Newton's second - law

Newton's second law is $F = ma$, where $F$ is force, $m$ is mass and $a$ is acceleration.

Step2: Relate acceleration to time - change in velocity

Acceleration $a=\frac{\Delta v}{\Delta t}$, where $\Delta v$ is the change in velocity and $\Delta t$ is the time interval. So $F = m\frac{\Delta v}{\Delta t}$.

Step3: Analyze the effect of crumple zones

In a crash, the change in velocity $\Delta v$ of the vehicle is fixed (from its initial velocity to zero). Crumple zones increase the time $\Delta t$ of the collision. Since $F = m\frac{\Delta v}{\Delta t}$ and $m$ and $\Delta v$ are constant, when $\Delta t$ increases, the force $F$ decreases.

Answer:

Crumple zones increase the time of the collision. According to Newton's second - law $F = m\frac{\Delta v}{\Delta t}$, with the mass $m$ of the vehicle and the change in velocity $\Delta v$ during the crash being constant, an increase in the time $\Delta t$ of the collision leads to a decrease in the force $F$ experienced during the collision.