WHY DOES SPEED KILL? – A SAFETY MOMENT




I have heard people say that speeding is not wrong. Many people claim that speeding is safe. On an empty road if you speed, probably you won’t run into many concerns. The problem occurs in a collision. The fatality of a collision is proportional to speed.
We have all studied the momentum equation in high school. We have studied the different types of collisions and have calculated the force generated during a collision.  Let us take a look at the following to see the effect of speeding. (It has been many years since I worked out these problems. Please feel free to let me know if you find any errors). This is mainly for youngsters who argue against speed limits.
Please refer to basic physics to refresh your memory on vector and scalar quantities.


The direction of travel to the east is taken as a positive quantity and West as a negative quantity.


In a collision, a force acts upon an object for a given amount of time to change the object's velocity. The product of force and time is known as impulse. In a collision, the impulse encountered by an object is equal to the change in momentum.


Impulse = Momentum Change


F • t = mass • Delta v


In a collision between object 1 and object 2, the force exerted on object 1 (F1) is equal in magnitude and opposite in direction to the force exerted on object 2 (F2). In equation form:


F1 = - F2


The time during which the force acts upon object 1 (t1) is equal to the time during which the force acts upon object 2 (t2). In equation form:


t1 = t2


then F1 • t1 = - F2 • t2


Since Force is equal to mass. acceleration,  we arrive at the equation,
m1 • Delta v1 = - m2 • Delta v2
According to this equation, after a collision, one object gains momentum while the other object loses momentum. The amount of momentum gained by one object is equal to the amount of momentum lost by the other object. The total amount of momentum of the two objects does not change.


m1 • v1 + m2 • v2 = m1 • v1' + m2 • v2'


v1 is the initial velocity of object 1, m1 is the mass of object 1. v1' is the final velocity of object 1.
v2 is the initial velocity of object 2, m2 is the mass of object 2. v2' is the final velocity of object 2.
 

The average force exerted by object 2 on object 1 is m1 v1' – m1v1 from the impulse-momentum theorem.

The average force of object 1 on object 2 is m2 v2' – m2v2

Let us see why speed kills.
A car of mass 1000 kg travels east at 30 m/s and collides with a 3000 kg truck travelling west at 20 m/s.

m1 = 1000 kg , v1 = 30 m/s

m2 = 3000 kg, v2 = 20 m/s


Car crashes are a completely inelastic form of collision. The kinetic energy generated by the collision deforms the cars. As this is an inelastic collision, m1v1+m2v2 = (m1+m2)vf

Velocity is a vector quantity. If we take east as the positive direction, then the truck's velocity has a negative sign since the truck was travelling West.

 vf = [ (1000) (30) + (3000) (-20) ] / (1000 + 3000) = -7.5 m/s, which is 7.5 m/s west

The change in kinetic energy can be found by adding up the kinetic energy before and after the collision:

KE lost in collision = (0.5m1v1v1 + 0.5m2v2v2) – (0.5m1vfvf+0.5m2vfvf); 1050000-112500 =              -937500 J
Percentage of KE lost = 100% x 937500 / 1050000 = 89.3%


So, a great deal of the kinetic energy is lost in the collision. This kinetic energy is directed towards deforming the car.


In the case of the completely inelastic collision, your momentum would change from 1000 kg x 30 m/s east = 30000 kg m/s east to 1000 kg x 7.5 m/s west = -7500 kg m/s east, which is a net change of 22500 kg m/s. Assuming change in time is 0.1 sec

Deceleration  = 7.5-30/0.1sec = -225 m/s2

Force = ma = 1000 X 225 = 225000 N

This change in momentum is produced by an average force acting for the 0.1 s of the collision, so the force works out to 225,000 N.
If the initial velocity had been 100 m/s east for the car, vf = {(1000)(100) + (3000)(-20)]/(1000+3000) = -10m/s

Deceleration = 10-100/0.1 =  -900 m/s2

And since force = ma, 900 X 1000 = 900,000N

the momentum would be 1000 kg X 100m/s = 100,000 the net change in momentum is 90000 kg m/s. This net change acting for 0.1 sec produces a force of 900,000 N.
The force generated when travelling at 100 m/s is four times more than the force generated while travelling at 30m/s. This force acts upon the vehicle to cause deformation and also acts upon the passengers.

This is why speed kills.

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