Using momentum and force principles, explain why an air bag reduces injury in an automobile collision.

Momentum is the product of an object's mass and velocity (p = mv), which is a measure of the object's motion. Force (F) acting on an object is related to the rate of change of its momentum with respect to time, as given by Newton's second law of motion: F = dp/dt. In a car collision, the car and its passengers experience a sudden change in velocity. Their momentum changes rapidly, which results in a large force acting on the passengers.

During a collision, the passengers' momentum changes from an initial value to zero, as the vehicle comes to a sudden stop. This change in momentum occurs over a short period of time. The force on the passengers can be calculated as the rate of change in momentum over this short time span. Without any safety measures, the force experienced by the passengers would be extremely high due to the quick change of momentum. The passengers' bodies would experience strong impact forces, leading to a higher risk of injury.

The main function of an air bag is to slow down the change in momentum of the passengers, thereby reducing the force experienced by them. When a collision occurs, the air bag inflates rapidly, providing a cushion between the passenger and the vehicle's hard surfaces. As the passengers come in contact with the air bag, their body will be decelerated over a longer length of time as they are pushed against the air bag. The extended duration of deceleration will reduce the overall force experienced by the passengers, minimizing the risk of injury.

By slowing down the rate of change of momentum, the air bag effectively reduces the force acting on the passengers. Using Newton's second law (F = dp/dt), we can see that, by increasing the time it takes for the passengers' momentum to change, the force experienced by them is decreased. Hence, the air bag acts as a force-distributing mechanism, spreading the force experienced by the passengers over a larger area and time, which lessens the impact of the collision and reduces the likelihood of injury. In conclusion, the air bag works on the principles of momentum and force to protect passengers during automobile collisions. By slowing down the rate of change of momentum and distributing the force experienced by the passengers, it effectively reduces the risk of severe injuries.