Ciaran Carroll – Demonstrate understanding of physics relevant to a selected context
Seatbelts are fundamental safety devices in almost all of today’s vehicles. It is estimated that they have saved over 250,000 lives since their introduction in the United States alone. It is without a doubt that seatbelts are essential in making transportation safer globally. But why do we need them? And how do they help us? The functionality of seatbelts is heavily reliant physics principles, specifically mechanics. It is thanks to these principles, inertia, energy and pressure, that seatbelts continue to do the great life saving work that they do.
The everyday seatbelt is a strip of fabric that is stretched over the wearer’s shoulder, and lap. Normally, the belt will extend and retract at ease. When you put it on, it seems to move easily enough from the wall of the car, there is almost no resistance. However, when the car crashes, it tightens and keeps you firmly in place, and is able to keep the wearer in place in a collision.
The need for seatbelts in motor vehicles is due to a concept called inertia. Inertia is an object’s ability to resist a change in motion, whether that be in speed or direction. Sir Isaac Newton referred to this in the first of his three laws of motion: An object maintains constant velocity unless acted upon by an external unbalanced force. If a car is traveling at 100 kilometres per hour due north, it will want to keep going at that velocity. Although a human inside the car and the car itself are obviously different bodies, the car will push the person up to speed with it, and they both travel at 100 kilometres per hour. But when they stop it’s a different story. If the car were to crash into a solid tree, the car would most definitely stop. Without a seatbelt, however, the driver would keep going. The tree that stopped the car doesn’t stop the person, as it doesn’t touch the person at all. Without a seatbelt, there is nothing anchoring the person to the car, and they will maintain their velocity: 100 kilometres per hour north, straight into the steering column and windshield. (Fig 1)
A seatbelt stops the person from smashing forward into the windshield, and holds them back in their chair. The seatbelt keeps the driver firmly attached to the car, so that the stopping force that the tree applied to the car is also applied to them.
It doesn’t matter how the crash occurs; inertia must be overcome to stop the person whether it’s through collision with the windshield, or from the help of a seatbelt. The latter does this job particularly well, inertia is overcome and the person is stopped in a more controlled manner. However, it is vitally important that the seatbelt is able to exert the stopping force on the person in a safe way, otherwise we might as well not wear them.
One way that seatbelts stop us in a safe way is their lengthening function. A seatbelt can extend about 15 cm in a collision, lengthening the person’s stopping distance by 50%. The reason the stopping distance is so critical is due the change in energy experienced in the collision. When a car is moving forward, it and the person inside have kinetic energy, which is calculated using the formula EKinetic= 12mv2, where m is mass and v is velocity. In the collision, the driver must lose all of the kinetic energy, as they stop moving.
Assuming a car travelling at 100 km/h (28m/s) and a driver with a mass of 80kg:
EKinetic = 12mv2
EKinetic =12x 80kg x (28m/s)2
EKinetic= 31360 Joules
Work is a change in energy, and is often expressed as Energy. Work is done to stop the person’s movement forwards, as the kinetic energy of the person changes. Mechanical work, as in a case like this, can also be calculated using W = Fd, where W is work, F is force and d is the distance. Therefore Fd =12mv2, as energy is always conserved.
W = Fd = EKinetic
If the kinetic energy of the person and the stopping distance of the person is known, the force on the driver can be calculated. A driver not wearing a seatbelt travels about 6 cm into the steering column in the collision:
Fd = 31360 J
F x 0.06m = 31360 J
F = 521700 N
A driver wearing a non-stretching seatbelt will travel 30 cm, which is the distance that a modern day car will crumple on impact:
Fd = 31360 J
F x 0.3m = 31360 J
F = 104500 N
This is very nearly a fifth of the force experienced without a seatbelt.
But the 30 cm crumpling of the car along with the 15 cm of seatbelt extension, a total stopping distance of 45 cm, gives:
Fd = 31360
F x 0.45m = 31360 J
F = 69690 N
This is less than a seventh of the force experienced without a seatbelt.
The extending function is quite important to the seatbelt, as the stopping distance is inversely proportional to the force applied to the driver. With the extra distance that the extended seatbelt provides to the driver, the force is lessened, and the driver has a much greater chance of escaping death and serious injury.
There are is another principle that needs to be taken into account so that the person’s forward movement is stopped in a safe way: pressure. Pressure is a force applied over a certain area, and is given in the formula P =FA, where P is pressure, F is the force applied and A is the area over which the force is applied. The the greater the force, or the smaller the area, the greater the pressure will be. For example, not much pressure is applied when cutting an object with a knife. However, the surface area of the blade is so small that the pressure applied to the object will be very great, as the pressure is the force applied divided by the area it is applied to.
This principle is quite important in relation to seatbelts. A seatbelt has a relatively large surface area in contact with the body, of around 600cm2. If a seatbelt had less surface area, in a crash it could cut straight through your body. For example, in the car crash scenario above, wearing a seatbelt put 69690 Newtons of force on the driver. Pressure is force divided by surface area. For a seatbelt with less surface area, through a single strap or a thinner belt will have a much smaller area in contact with the body. For example, a seatbelt with a surface area of 50cm2:
P =FA
P =69690N0.005m2
P = 13,938,000 Pa
By having the stopping force applied to a larger area, the pressure is much less, and therefore the person is stopped in a safer way, as less pressure means that there is less stress put on the body, and there is less chance that a serious injury will be endured.
P =FA
P =69690N0.06m2
P = 1161500 Pa
The seatbelt is also designed so that the stopping force is applied to stronger parts of the body: the pelvis and the chest. An impact on these areas are much likely to be endured than on a weaker, more fragile one. Without a seatbelt, the person will feel the force of the impact on the head, which is very weak, and is likely to kill the person, even with a relatively weak impact force. Instead, the pelvis and the ribs are very very strong parts of the body, and are able to take much larger forces than other body parts.
Seatbelts are an amazing example of the integration of mechanics into the real world. By acknowledging and utilising the principles of inertia, energy and pressure, seatbelts are able to do their job effectively and saves the many hundreds of thousands of lives that they do. It is thanks to physics that these rather simple devices are able to reduce death and serious injuries in road accidents by an amazing 50%, without which, the world would be left in a much more vulnerable place.
Sources:
http://hyperphysics.phy-astr.gsu.edu/hbase/seatb.html#cc4
http://hyperphysics.phy-astr.gsu.edu/hbase/carcr2.html#cc1
https://www.cdc.gov/motorvehiclesafety/seatbelts/facts.html
http://www.youthforroadsafety.org/news-blog/news-blog-item/t/seatbelts_saving_thousands_of_lives_around_the_world_everyday
https://auto.howstuffworks.com/car-driving-safety/safety-regulatory-devices/seatbelt.htm
Fig 1 attained from http://hyperphysics.phy-astr.gsu.edu/hbase/carcr2.html#cc1
Figs 2, 3 and 4 attained from http://hyperphysics.phy-astr.gsu.edu/hbase/seatb.html#cc4
All other images from google.