Question

1. engineers are designing a car bumper that crumples upon impact. this crumple zone increases the time it takes for the car to come to a stop during a collision. which statement best describes the purpose of this design?

the crumple zone increases the collision time, increasing the force and impulse experienced by the vehicle
the crumple zone increases the collision time, decreasing the speed of the collision and reducing the momentum change.
the crumple zone increases the collision time, decreasing the force experienced by the car and its occupants.
the crumple zone decreases the collision time, increasing the impact force by changing the vehicle’s inertia.
clear all

Explanation:

To solve this, we use the concept of impulse (\(J = F\Delta t=\Delta p\), where \(J\) is impulse, \(F\) is force, \(\Delta t\) is time, and \(\Delta p\) is change in momentum). In a collision, the change in momentum (\(\Delta p\)) of the car is fixed (since initial and final momenta are determined by speed and mass). The crumple zone increases \(\Delta t\) (collision time). From \(F=\frac{\Delta p}{\Delta t}\), if \(\Delta t\) increases, \(F\) (force) decreases.

• First option: Wrong, because increasing \(\Delta t\) should decrease force (not increase), and impulse (\(J = \Delta p\)) is constant (since \(\Delta p\) is fixed), so impulse doesn't increase.
• Second option: Wrong, because the speed change (and thus \(\Delta p\)) is fixed by the collision (e.g., from moving to stopping), so momentum change isn't reduced. The crumple zone affects time, not the momentum change itself.
• Third option: Correct. Increasing \(\Delta t\) (collision time) while \(\Delta p\) is constant means \(F=\frac{\Delta p}{\Delta t}\) decreases, so the force on the car and occupants is reduced.
• Fourth option: Wrong, the crumple zone increases (not decreases) collision time, and increasing time decreases (not increases) force.

Answer:

The crumple zone increases the collision time, decreasing the force experienced by the car and its occupants.