Momentum and

Impulse of Your

Helmet The Law of Conservation of Momentum The law of conservation of momentum states that the momentum a system has before a collision, will equal the momentum the system

has after the collision.

This law can be illustrated in the formula p before = p after, where "p" represents momentum.

The law of conservation of momentum can only be accurately observed in an isolated system on which no external forces, such as friction, are present. What is Momentum? Momentum is the quantity of motion all objects possess. This is the product of the mass of the object, and its velocity.

Theoretically, this quantity of motion of a system stays constant before and after the objects collide. What is Impulse? When an object's velocity changes, its momentum will change as seen in the relationship between the two quantities in the momentum formula. Impulse can be defined as this change in momentum. We are able to predict the momentum an object or system will have using the formula p=mv

"p" represents the momentum of the object in N.s

"m" represents the mass of the object in kg

"v" represents the velocity of the object in m/s Impulse can be represented by the formula ∆p = m∆v

"∆p" represents the change in momentum (impulse) in N.s

"m" represents the mass of the object in kg

"∆v" represents the change in velocity in m/s Impulse can also be represented by the equation ∆p = Fnet . t

Therefore the relationship between impulse and momentum can be expressed as Fnet . t = m∆v How do Helmets Protect Your Head? As seen in the formula Fnet . t = m∆v as we increase the time (t) of the impulse we decrease the intensity of the net force exerted.

When you fall off your bike and hit your head not protected by a helmet, the collision of your head with the concrete is very quick and it is your head that deforms to abosorb the force exerted by the concrete.

However by wearing a helmet, when your head hits the concrete the deformation or collision time is longer. The force from the concrete is exerted over a longer period of time due to the thickness of the helmet. As well, it will be the helmet that deforms to absorb the force rather than your skull!

The helmet also increases surface area therefore the force exerted by the concrete is distributed over a larger area. This decreases the intensity of the blow to your head. How Does This Relate to the Law of Conservation of Momentum? Hitting your head with as much force as would be exerted by falling off your bike, is enough to cause serious damage to your brain.

The momentum your head has before you fall, will be equivalent to the momentum your head will have after it bounces off the pavement. However Some of this kinetic energy is converted to thermal energy through deformation.

The purpose of a helmet is to minimize the force exerted on the head by maximizing the absorption of energy by the helmet.

When the helmet absorbs most of the energy, the impulse is carried out over a longer period of time thus reducing the force exerted on the head Material Components of Bicycle Helmets I'm sure most people would agree that your brain is a very important part of your body. It is also very sensitive to injury. The rapid acceleration of your brain alone, when falling off your bike can cause tissue damage. Using the law of conservation of momentum we are able to manufacture helmets to reduce the effect of force on the head during a collision or tumble off a bike. Bicycle helmets are usually composed of a solid outer layer, a 20mm foam middle layer, and sometimes a cushioned inner layer as well.

The middle foam layer must absorb the most energy per unit volume of force, limiting the damage to the skull. Materials often used include balsa, cork and polystyrene. http://www.grantadesign.com/resources/materials/casestudies/helmet.htm

http://www.motorcycle-usa.com/378/746/Motorcycle-Article/Motorcycle-Helmets-Product-Guide.aspx

http://www.bikeradar.com/news/article/new-helmet-could-protect-against-rotational-injuries-25081

http://www.youtube.com/watch?v=Fyvpvcs-ixI The outer layer is a hard shell designed to prevent objects from penetrating. The innermost layer is cushioning to provide comfort as well as creating a longer time of the impulse as your head compresses the cushioning. Example calculations: Suzy is riding her bike down her street at a velocity of 1.40 m/s. She decided, against her mothers wishes, to not wear her bike helmet. Suzy hits a large rock in the road and she is sent flying over her handle bars head first. If suzy has a total weight of 45.0 kg, and as she was not wearing a helmet her head was in contact with the ground for 0.150 s, what was the average force exerted on her head during the collision? ∆v = 1.40 m/s

m = 45.0 kg

∆t = 0.150 s F∆t = m∆v

F = m∆v / ∆t F = (45.0 kg)(1.40 m/s) / (0.150 s)

F = 420 N Suzy had a realy tough week because a few days later she fell off her bike once again. However this time she listened to her mother and was wearing her helmet. Suzy was riding the same speed and was the same weight as she was when she first fell. However with her helmet, her head was in contact with the ground for 0.750 s. What was the average force exerted on her head while wearing the helmet? ∆v = 1.40 m/s

m = 45.0 kg

∆t = 0.750 s F∆t = m∆v

F = m∆v / ∆t F = (45.0 kg)(1.40 m/s) / (0.750 s)

F = 84 N Wearing her helmet reduced the force exerted on Suzy's head by a significant amount. This is due to the fact that the helmet deforms during the collision, increasing the time of the impulse. The helmet absorbs the force that would otherwise have been exerted on Suzy's head. Theoretically what will be Suzy's velocity after the collision? Theoretically her velocity should be the same after the collision as her mass didn't change. However as this is an inelastic collision, much of the kinetic energy present in the system before the collision was converted into thermal energy after the collision. This thermal energy is present due to the deformation of the helmet, friction etc. The following video briefly explains what basically happens to a hemlet during a collision. The man in this video describes how a professional motorcyclist survived a crash because of the protection he had on his head. Resources Momentum Before

Momentum After =

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# The Law of Conservation of Momentum ProtectsYour Head

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