Question

question 12. two cars, car a and car b, each moving at the same speed, crash head - on into identical low walls. car a has crumple zones in both the front and rear, while car b only has a rear crumple zone. which statement correctly describes the effects of the crumple zones during the collision? a. car a experiences a smaller average force than car b because its crumple zones increase the collision time, while both cars have the same change in momentum. b. car a experiences a larger average force than car b because its crumple zones increase the momentum change, while car b experiences no momentum change. c. car a and car b experience the same average force, but car a has a larger change in momentum due to the extra crumple zones. d. car a experiences a smaller change in momentum than car b, and the force on both cars is the same.

Explanation:

Step1: Analyze the change in momentum

According to the law of conservation of momentum, in a collision, the total momentum of the system is conserved. Here, the two - car system's initial momentum (since they are moving at the same speed and assume same - mass for simplicity, \(p = mv\)) and final momentum (both cars stop, \(p = 0\)) change. The change in momentum \(\Delta p\) for the two - car system is the same. For each car, the force \(F\) is related to the change in momentum \(\Delta p\) and the time of collision \(\Delta t\) by the impulse - momentum theorem \(F=\frac{\Delta p}{\Delta t}\).

Step2: Consider the effect of crumple zones

Crumple zones increase the collision time \(\Delta t\). Since \(\Delta p\) (change in momentum) is the same for both cars (because of the conservation of momentum in the collision, and they have the same initial speed and assume same - mass situation, \(\Delta p = mv - 0\) for each car in the opposite - direction collision), and \(F=\frac{\Delta p}{\Delta t}\). Car A has crumple zones (in both front and rear), which increase \(\Delta t\). Car B has no crumple zones (or less effective crumple - zone situation as it only has a front crumple zone in a head - on collision context where rear crumple zone of A may also play a role in distributing the collision time more effectively for A). A larger \(\Delta t\) (for Car A) means a smaller average force \(F\) (because \(\Delta p\) is the same for both cars, from the conservation of momentum in the collision, as the initial momentum of the two - car system and the final momentum of the two - car system are fixed, so \(\Delta p\) for each car in magnitude is the same considering the opposite - direction nature of the collision)

Answer:

A. Car A experiences a smaller average force than Car B because its crumple zones increase the collision time, while both cars have the same change in momentum.