Final answer:
The car's momentum at impact is 8.33 x 10^3 kg·m/s. The force required to stop the car hitting a concrete wall is 8.33 x 10^4 N, while hitting a padded wall requires a force of 1.67 x 10^4 N. Airbags serve to reduce force on passengers by increasing the time over which the car's momentum is brought to zero.
Step-by-step explanation:
To answer the student's question, we must apply concepts of momentum and Newton's second law. The momentum p of an object is given by the product of its mass m and its velocity v. The force F needed to stop an object is derived from the impulse-momentum theorem, which relates force, change in momentum, and the time over which the force is applied.
Questions and Answers
- a) The momentum of the car at impact is calculated as p = m × v. First, we must convert the speed from km/h to m/s: 30.0 km/h = 8.33 m/s. Therefore, p = 1.0 × 103 kg × 8.33 m/s = 8.33 × 103 kg·m/s.
- b) The force required to stop the car is given by F = Δp / Δt, where Δp is the change in momentum (which is equal to the initial momentum, since the final momentum is zero) and Δt is the time over which it changes. F = 8.33 × 103 kg·m/s / 0.10 s = 8.33 × 104 N.
- c) If the car hits a padded wall and stops in 0.50 s, the force required is F = 8.33 × 103 kg·m/s / 0.50 s = 1.67 × 104 N.
- d) The purpose of airbags is to increase the time over which the change in momentum (impulse) occurs, thereby reducing the force exerted on passengers, which can reduce injuries during a collision.