Engineering Essay

By Author: Anthony W Bills
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Engineering Essay
Task 1
a) Deceleration of a car on a crash
A car with no air bags moving at 30km/h crashes into a wall. Front deforms by 200mm.
We can solve the problem using Newton’s laws of linear motion. Newton’s first equation of linear motion relates the initial velocity and the final velocity of a body with the distance traveled within the time period of the acceleration/deceleration.
Initial velocity of the car u = 30 km/h
30*1000/60*60m/s
8.33ms-1
Distance traveled during the collision, s = 200mm = 0.2m
Final velocity v = 0 m/s
i) Using Newton’s first equation of motion,
v2-u2=2as
a = (v2-u2)/2s
a= 250000/2*0.2
=250000/0.4
= 6,250,000 ms-2
i) Time taken for the collision
t= (v-u)/a
=(0-500)/-6250000
=0.00008s.
b) Deceleration of an unbelted driver in a crash
distance steering wheel deflects = 50mm= 0.05m
final velocity v = 0 m/s
initial velocity u = 30*1000/60*60
= 3.3333ms-1
Distance moved upon collision = 50 mm = 0.05m
V2-u2=2as => a = ...
... (v2-u2)2s
a = (3.3333*3.3333-0)/2*0.75
= 0.074 ms-1
ii) How long after impact the driver hits the wheel
This is a case is linear motion of a body moving with uniform velocity 500ms-1
time = distance / speed
v = 30000/60*60
8.333 ms-1
t = Distance/ speed
= 0.75/8.333
= 0.09 s.
Initial velocity u = 30km/h = 30*1000/60*60
8.333m/s
Distance traveled, s = 50 mm = 0.05m
Initial velocity = 8.33m/s
Final velocity = 0 m /s
a = (v –u)/t
=8.33/0.09
92.5m/s2
Initial velocity = 8.33m/s
Final velocity = 0
Distance traveled upon impact = 50mm = 0.05m
Acceleration = 8.33/0.05
time = 166
Time = distance/velocity
=0.2/8.33
0.024 seconds distance = 200mm = 0.2m
Initial velocity u = 8.33ms
Final velocity v = 0ms-1
Time taken for the second impact to occur
Time = distance/speed
= 0.75/0.833
0.9 s
Time taken for the impact to occur
t = distance / velocity
=0.75/0.83
= 6.225 s
Task 2
In the calculations made above, the assumption has been made that that the motion of the driver is linear. This is not always the case because sometimes the during a collision, the vehicle deflects and does not move in a straight line. In most crash cases the car skids and swerves to one side.
In the calculations I have also made the assumptions that there is no friction between the driver and the seat of the car. The assumption has been made that the driver moves straight forwards towards the steering wheel after the collision.
It has futher been assumed that the driver does not support himself with his hands on the wheel during the collision.
The distance traveled by the driver in the collision = 200mm = 0.2m
The final velocity was 0 meters per second
Initial velocity = 8.33m per second
V2-u2=2as
a= (v2-u2)/2s
(0-8.33*8.33)/2*0.2
= -578 ms-2
Therefore the deceleration is 578 m per second squared.
Initial velocity = 8.33ms-1
Final velocity = 0
Time taken for the acceleration =
6.225s from the previous question.
Acceleration = 8.33/6.225
=1.33s
F=2N
M=70kg
F= 2000N
In the calculations made above, I have made the following assumptions:
- That the motion of the driver is linear
- That the motion of the car is linear
- That the driver moves forward towards the steering wheel without any friction.
Air Bags
In the event of a collision, when the driver hits the wheel, the bag deflates. The driver then hits the bag and the bag absorbs the kinetic energy of the driver. The bag reduces the deceleration of the driver so by absorbing the mechanical energy of the driver to and converting it to internal energy of the gas (air) of the gas in the bag. This becomes thermodynamic energy of the air in the gas. in the absence of the air bag, the driver moves forward at the initial speed and hits the steering wheel. The steering wheel then stops the driver and all the energy used in deforming the body of the driver which causes death. Air bags have been used to save many lives which would have been lost in car crashes. In case of a a collision they inflate in less than a tenth of a second protecting people from the force of collision.
In a head on collision an air bag reduces the chances of dying by approximately 30%. In most countries nowadays, new cars are required to have driver and passenger side air bags.
When the driver wears a seat belt, it protects him in case of a collision by reducing the deceleration. The rate at which the speed of the driver is brought to zero is reduced within the distance the seat belt stretches, thereby reducing the deceleration. Initially. The driver is traveling at the speed at which the car is traveling. When the collision occurs, the driver continues to move at the same speed. In the absence of the airbag and seatbelt, all the kinetic energy possesses due to the mass of the driver is expended at the steering wheel. This is what causes the fatality of the drivers.
Task 3
The calculations above show that the impact of a crash is greatly reduced by an airbag and a seatbelt. Injury is caused by immediate deceleration and therefore the way to avoid fatality is by reducing deceleration during a collision. if a driver wears a seatbelt, in case of a collision, the seat belt stretches within which time the deceleration occurs. This reduces the impact of the driver on the wheel and therefore statistically reduces the number of fatalities during car collisions.
The purpose of the seatbelt is to prevent the driver with the car so that the stopping distance is about 5 times greater than if he had no seatbelt. A crash which stops the car and driver must take away all its kinetic energy, and the work-energy principle then implies that the longer the stopping distance, the les the stopping force. For the car crash above, the stopping distance is 0.2m, the force on a 70kg driver is about 2000N. The stretch in the seatbelt can extend the stopping distance and reduce the average impact force on the driver..
If the driver has no seatbelt and a the collision occurs, then he/she flies free until stopped by collision with the steering wheel and the the windscreen.. The work done to stop the driver is equal to the average impact force on the driver times the distance traveled in stopping. In this crash which stops the driver and the car took away the kinetic energy of the driver. The work energy principle dictates that the less the stopping distance.
When a body is in motion, it possesses kinetic energy due to its motion. When the body is brought to rest, this energy must be expended. In the case of the car in the case above, the driver in the car has kinetic eherty due to the fact that he is in motion together with the car. When the car crashes, the driver continues in the initial state of motion according to Newton’s laws of motion, until he crashes on the wheel.

In a case where the driver has no seatbelt, he flies free until stopped abruptly by collision on the steering wheel.
The logic behind the working of a seatbelt is that it prevents the driver from flying into the steering wheel and the windshield. The reason why this happens is that the car and the driver has inertia due to his/her state of motion. This is an object's tendency to keep moving until an external force acts on the body to stop this motion or it may be put that it is a body’s resistance to changing its speed and direction of travel. Things naturally want to keep going. In the case above, the car and the driver would continue to move in a straight line until when it collides with the wall which exerts a force on the car. The driver the moves forward and hits the steering wheel, he impacts on the steering wheel the kinetic energy which he/she possessed due to the state of motion. On collision with the wheel. All this energy is expended in injuring the driver.
When a car is in motion, everything in the car, including the driver, has its own inertia, which is separate from the car's inertia. The car accelerates everything in it to its velocity. Imagine that you're coasting at a steady 50 miles per hour. Your speed and the car's speed are pretty much equal, so you feel like you and the car are moving as a single unit.
On collision, the inertia of the driver is independent from that of the car. The force of the wall on the car brings the car to an immediate stop, but your speed of the driver remains the same until he/she hits the steering wheel. In the absence of the seatbelt, the driver would either hit the steering wheel at 8.33meters per second or go flying through the windshield at the same speed. Just as the wall brought the car to a stop, the steering wheel and the dashboard, exerted the force required to bring the driver so a halt. The fact is that a force must be provided to stop the motion. If the driver hits the windshield with his/her head, the stopping power is concentrated on the head. This can easily cause a fatality or severely injure the driver.
A seatbelt transfers the stopping force to more durable sections of the body over a longer period of time. The shoulders and the abdomen are more durable than the head and therefore serve to save the driver or passenger.
While moving, the car and rider have momentum, defined as product of mass and while moving, the car and rider have momentum, defined as product of mass and velocity. A force is needed whenever a moving mass is to be stopped, or decelerated. In situations involving collision, it is more convenient to think of impulse: that which changes the momentum of an object. Impulse is defined as product of average force and elapsed time.
When a heavy car is stopped, an impulse acts on it to bring its momentum to zero value. The amount of impulse needed is exactly equal to the amount of momentum the car had originally; the impulse amount is independent of the manner in which the car is stopped. However, if the car is stopped suddenly in a collision (rather than gradually with the brakes), the elapsed time is small resulting in a large average force.
The crushable front end of the car serves to extend the time duration of the collision so as to lessen the force. But the rider has inertia and will keep moving once the car is stopped, until he/she strikes something that can deliver an impulse on him/her.
If a rider is not wearing a harness, he/she would likely be stopped suddenly by the steering wheel, dashboard and windshield. These are not crushable (the person more-likely is) so the impulse would be a combination of a short time and a very large force; injury or even death is the result.
A force is needed whenever a moving mass is to be stopped, or decelerated. In situations involving collision, it is more convenient to think of impulse: that which changes the momentum of an object. Impulse is defined as product of average force and elapsed time.
When a heavy car is stopped, an impulse acts on it to bring its momentum to zero value. The amount of impulse needed is exactly equal to the amount of momentum the car had originally; the impulse amount is independent of the manner in which the car is stopped. However, if the car is stopped suddenly in a collision (rather than gradually with the brakes), the elapsed time is small resulting in a large average force.
The crushable front end of the car serves to extend the time duration of the collision so as to lessen the force. But the rider has inertia and will keep moving once the car is stopped, until he/she strikes something that can deliver an impulse on him/her.
If a rider is not wearing a harness, he/she would likely be stopped suddenly by the steering wheel, dashboard and windshield. These are not crushable (the person more-likely is) so the impulse would be a combination of a short time and a very large force; injury or even death is the result.

Bibliography
Andrews, P.& Roy, P(1999;102) Linear Motion. London, Macmillan
Roy and Andrews (1991) Calistas Roy Function Adaptive Model.
Andrews and Roy 1991a p. 17). Linear Collisions Model, London, Macmillan.

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