A large truck and a car, both moving with a velocity of magnitude v, have a head-on collision and both of them come to a halt after that. If the collision lasts for 1 s:
a. Which vehicle experiences greater force of impact?
b. Which vehicle experiences greater change in momentum?
c. Which vehicle experiences greater acceleration?
d. Which vehicle is likely to suffer more damage?
Let the mass of the truck be M and that of the car be m and their initial velocity be v.
→ M > m
Let the final velocity of both vehicles be v′.
Given that both vehicles come to rest after collision, i.e. v’ = 0
Time of impact, t = 10 s
a. From Newton's second law of motion, the net force experienced by each vehicle is given by the relation:
Fcar = m (v′ − v)/t = mv/10
Ftrack = M (v′ − v)/t = −Mv/10
since the mass of the truck is greater than that of the car, it will experience a greater force of impact.
b. Initial momentum of the car = mv
Final momentum of the car = 0
Change in momentum = mv
Initial momentum of the truck = Mv
Final momentum of the truck = 0
Change in momentum = Mv
Mass of the truck is greater than that of the car. Thus, the truck will experience a greater change in momentum as compared to the car.
c. According to the ﬁrst equation of motion, acceleration produced in a system is independent of the mass of the system. The initial velocity, final velocity and time of impact remain the same in both cases. Hence, the car and truck experience the same amount of acceleration.
d. According to Newton's third law of motion, for every action, there is an equal and opposite reaction which acts on different bodies. Since the truck experiences a greater force of impact (the action force), this large impact force is also experienced by the car as a reaction force. Thus, the car is likely to suffer more damage than the truck.
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