a large bus and a van, both moving with a velocity of magnitude v, have a head-on-collision and both the vehicles stop after the collision. if the time of the collision is 1 sec then, a) which vehicle experiences smaller force of impact? b) which vehicle experiences the smaller momentum change? c) which vehicle experiences the greater acceleration? d) why is it that the truck suffers less damage than the car?
a) action is equal in magnitude and opposite in direction to reaction, Newton 3
b) total momentum is conserved
Initial momentum = Mv - m v
final momentum = 0 if both stopped
so I claim that the mass of the bus equals the mass of the van if they both stop. If not they would continue in the direction the more massive vehicle was traveling. I suspect a typo and both did not stop. Anyway if both stopped, their momentum change was equal in magnitude and opposite in sign.
b) since mass and initial speeds the same, same acceleration.
c) It must be stronger.
I think this question is a typo and in fact the vehicles did not stop but continued on in the direction of the truck but I answered what you asked.
c) acceleration is
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In order to answer these questions, we need to understand some concepts in physics - specifically, momentum, force, and acceleration.
a) The force of impact can be calculated using the concept of impulse, which is the product of force and the time duration of the collision. The impulse experienced by each vehicle will be the change in momentum. Since both vehicles come to a stop, it implies that the impulse on each vehicle is the same. However, we can compare the force of impact using the equation F = ΔP/Δt, where F represents force, ΔP represents change in momentum, and Δt represents the time of the collision. As the time duration of the collision is the same for both vehicles (1 second), the force experienced by each vehicle will depend on their respective changes in momentum.
b) The momentum change can be calculated using the equation ΔP = m * Δv, where ΔP represents the change in momentum, m represents the mass of the vehicle, and Δv represents the change in velocity. Since both vehicles come to a stop, their respective change in velocity will be the same (equal to magnitude v). Comparing the momentum change, the larger the mass (m), the smaller the change in momentum. Therefore, the vehicle with a smaller mass will experience a smaller momentum change.
c) Acceleration can be calculated using the equation a = Δv/Δt, where a represents acceleration, Δv represents change in velocity, and Δt represents the time taken for that change. From the given scenario, we know that both vehicles stop after the collision in the same amount of time (1 second). However, since the van has a smaller mass compared to the bus, it will experience a larger acceleration. This can be understood by considering Newton's second law, F = m * a, which implies that the acceleration is inversely proportional to mass (for a constant force).
d) The fact that the truck suffers less damage than the car can be attributed to the concept of inertia. Inertia is the resistance of an object to changes in its state of motion. The larger mass of the truck leads to a higher inertia compared to the smaller mass of the car. It means that the truck is more resistant to changes in motion and thus suffers less damage during the collision. The car, having less mass, experiences a greater change in momentum, resulting in more damage.
To summarize:
a) The vehicle experiencing a smaller force of impact will depend on their respective changes in momentum and the time duration of the collision.
b) The vehicle with smaller mass will experience a smaller momentum change.
c) The vehicle with smaller mass will experience a greater acceleration.
d) The truck suffers less damage due to its higher inertia resulting from its larger mass.