The velocity of a car as it crashes reduces abruptly; in colloquial terms this is the deceleration of the car. The following is the second law of motion found in Newton’s ‘Philosophiae Naturalis Principia,’ Net Force = mass X acceleration. The Net Force of a car is the sum of all forces acting on a car. In relation to car crashes, the Net Force is the force acting upon a car ; the force doing the damage. The mass of the car is easy to obtain, it’s the value in Kilograms the manufacture has stated and does not change. However the second component of the equation, acceleration, does vary. Acceleration in this case is deceleration because the car is stopping. However for the purposes of calculating the net force, this is irrelevant. The acceleration is defined as the rate of change of rate of change or how quickly you speed up or slow down. Two things can happen to make this value large; a) The car can slow down greatly in a period of time b) The time in which it slows can be very small. For example, a car (1500kg) that is travelling at 60 km/h that hits a wall and comes to a complete stop in a time of 5s, has a deceleration of -12km/h/s. It’s net force is therefore 18,000 Newtons. However, a car(1500kg) travelling at 40km/h that hits a wall and comes to complete rest in 1 second will be more damaged even though it’s speed was lower. The deceleration of the car will be -40km/h/s. Therefore the Net force will be a huge 60,000 Newtons! You may wonder then, why isn’t this Force applied to the wall instead of the car? The answer is in Newton’s third law. For all the force that the Car exerts on the wall, the wall exerts back on the car, hence the greater the force the car hits the wall with, the more damage it will have. This is why stopping distance is important. The greater the distance in which you stop the greater the time and hence the lower the acceleration or lower force on your vehicle. This is also the reason reaction time is important as faster reaction time means more stopping distance. The time you take to slow down your vehicle is greater hence the rate of deceleration is less making the Net Force acting on your car less. This is the reason crash helmets work. The layer of foam inside the helmet gives your head (and the brain it contains) a fraction of a second; approx 2 milliseconds, to slow down the rate of change over a crucial second rather than the virtually instantaneous change that occurs if your head hits something hard and immovable.
The momentum that a car travels with can be found by multiplying the mass by the velocity. So a car with velocity 16.67 m/s and mass 1500 kg has a momentum of approx 25000 kg m/s. When it hits another car, if it comes to complete rest upon impact, all of that momentum is transferred into the other car! The impulse is the change in momentum of an object and can be found by multiplying the Net force of an object by the amount of time that the force is applied. The impulse on a car that has been hit by a car with Momentum 25000 kg m/s is therefore 25000 N s and the result is a car moving in the same direction the original car was with the same momentum!
Inertia is the tendency of an object to remain in its state of motion. This is the reason we use seatbelts and head rests. As a vehicle decelerates or accelerates, the passenger will remain at the speed the vehicle was previously travelling at. So if this is an abrupt deceleration like in a crash, without seatbelts the passenger would continue to move at the rate of change as what the vehicle was previously doing and because the vehicle isn’t so far forward as what it would have been without the crash, our passenger finds himself through the glass of a windshield.
The kinetic energy of an object can be found by multiplying half the mass by the Velocity2
The kinetic energy is measured in joules just as all energy is and the work done to stop the car must be absorbed by the car somehow. For a car of mass 1500kg and velocity 60 km/h about
2.7 x 103kJ of work must be done to stop the vehicle from moving. This is why a 100 percent increase in speed means a 400 percent increase in the work required to stop the car. Work is the amount of energy needed and can be found by multiplying the force by the distance it which it exerts this force. To stop a car, the work must be equal and in the opposite direction to the car. The work exerted on the car must be absorbed by the car. Therefore to reduce the instantaneous rate of change in a collision, some of the energy is absorbed into the ‘crumple zone’ of a car. The zone that ‘crumples’ to slow down the rate of change therefore reduces the inertia on your body and the crumpling of the component of the car you are in.
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