Physics Principles Used in the Analysis of Accidents and Collisions When accidents occur, it is essential to reconstruct the accident to figure out what exactly transpired.

This is necessary as law enforcement agencies, personal injury attorneys, insurance companies, and many other people need to determine the actual cause of the accident. Accidents & Collisions This science of investigating and analyzing vehicle collisions is known as vehicular accident reconstruction.

Its purpose is to determine what caused or contributed to an accident, including the role of the drivers, the vehicle, the roadway, and weather conditions.

Vehicular accident reconstruction uses the principles of engineering as well as the laws of math and physics when analyzing a collision.

In this presentation, we will discuss the key role that physics plays in analyzing accidents. Accident Reconstruction Collisions are interactions resulting from the close approach of two or more bodies, particles, or systems of particles, and confined to a relatively short time interval during which the motion of at least one of the particles or systems changes abruptly.

Collision are happening every second of our lives from when we step on the floor, drive our cars, and brush our teeth. Collisions People and Textbooks usually talk about 3 different types of collisions but in reality, it is more true to say there are two ends of a spectrum (range) of collision types. Types of Collisions An elastic collision occurs when the two objects "bounce" apart when they collide. Two rubber balls are a good example.

In an elastic collision, both momentum and kinetic energy are conserved. No energy is lost to sound, heat, or deformation.

In the rubber ball example, the first rubber ball deforms, but then quickly bounces back to its former shape, and transfers almost all the kinetic energy to the second ball. Elastic Collisions We will now show a video of someone performing Newton’s Cradle Experiment. This experiment will show what happens during an elastic collision. Please watch this video with your full attention. Newton’s Cradle Experiment An inelastic collisions occurs when two objects collide and do not bounce away from each other.

Momentum is conserved, but kinetic energy is not.

Some of the kinetic energy is converted into sound, heat, and deformation of the objects. A high speed car collision is an inelastic collision. Inelastic Collisions When investigating an accident, it is crucial that investigators find every bit of information possible.

For example, prediction of what happened in a collision by examination of what remains in the form of residual damage can be used to calculate speed change or Delta Velocity (∆v) experienced by the vehicles in the collision.

Sometimes re constructionists will make assumptions like “had the driver been travelling at the speed limit….”

And then they will make another assumption such as “ had the driver been traveling passed the speed limit…”

These are basic information that reconstructionists use in more complex physics equations to analyze an accident. Finding out Important Information Momentum plays an important role in collisions and therefore it is essential for re constructionists to have a depth of knowledge on momentum.

Momentum is the product of the mass of an object and its velocity. It is also referred to as “mass in motion”.

Momentum is why the driver of a car applies the brakes to stop the car rather than just taking his foot off the accelerator. The car has gathered momentum and will continue to move forward after the driver stops accelerating it. Momentum The formula used to calculate the momentum of an object is

p = momentum (kgm/s), m = mass (kg), v = velocity (m/s)

The greater the mass of the object the more momentum it possesses. Objects at rest have no momentum either. An object in motion possesses momentum as it has both mass and motion.

Momentum is a vector quantity and the SI unit for momentum is kg × m/s

The mass of a car is 2000kg and it travels at a velocity of 30m/s east. Calculate its momentum

Solution:

= 2000 kg x 30 m/s [E]

= 60000 kg x m/s [E] Example If there are no external forces, the momentum of an isolated system is constant.

The total momentum energy before the collision and after the collision in an isolated system is the same, thus the term conservation of momentum energy is used.

The investigator can use the conservation of energy and momentum theories to try to establish facts such as initial velocity of the vehicles and so build a detailed picture of the collision. Conservation of Momentum A school bus is on a highway and strikes a stationary cop car. This impact causes the cop car to travel in the same direction the bus was headed.

After the collision the school bus slows down and loses its momentum and the cop car gains the momentum of the bus. This represents the conservation of momentum energy during a collision. Example The simple definition for impulse is that it is a change in momentum. We can write that as

If an object’s velocity changes, there is a change in momentum, so there must be an impulse.

In this presentation, we will assume that the mass of objects remain the same. Impulse The formula for impulse is : Δp = m Δv

Example: A box of tic tacs (15g) is sliding along the table at 5.0m/s. I try to stop it, but only slow it down to 1.6 m/s. Determine the impulse I impart to the box.

Solution : Δp = m Δv

Δp = m (vf – vi)

Δp = 0.015kg (1.6m/s – 5.0m/s)

Δp = -0.051 kg m/s

The negative sign means momentum was taken away from the object. Sir Isaac Newton developed three mathematical laws of motion which provide the foundation for traffic accident reconstruction. NEWTON’S LAWS OF MOTION Newton’s first law can be stated as the following: A body at rest remains at rest, and a body in motion remains in motion with constant velocity along the same straight line unless acted upon by some outside force.

In Newton’s first law of motion an important property of matter appears. It is known as inertia, that property of matter by which an object maintains a constant velocity in the absence of an unbalanced external force.

When an automobile is suddenly stopped, the passengers obey Newton’s first law and continue in their motion with constant velocity until some external force changes their state of motion. Newton’s first law of motion: Inertia of rest and motion Newton’s second law states that if a body is acted upon by an unbalanced force F, its center of mass will accelerate in the direction of the force.

The acceleration of a body is directly proportional to the net force upon the body and acceleration is inversely proportional to the mass of the body.

Unification of these concepts reveals that force is equal to the mass of an object multiplied by its acceleration or F = m.a

One Newton produces an acceleration of one meter per second, per second, in a mass of one kilogram. Newton’s second law of motion Newton’s third law is also known as the action-reaction law. It is equally valid when dealing with bodies in rest or motion.

It can be stated as: Whenever one body exerts a force upon a second body, the second body exerts an equal and opposite force on the first.

For example, the wheels of an automobile in motion push backward on the road, but the road pushes forward on the wheels with an equal force during acceleration. Newton’s third law of motion: Reaction Newton’s first law of motion tells us that if you’re moving at a particular speed, you will continue moving at that speed indefinitely unless an external force acts on you to stop you.

Think about this in the context of sitting in a moving car. You are moving at the same speed as the car that you’re in.

If the car comes to a sudden stop, you will continue to move forward at the speed your car was travelling in.

This is why you always slow down before stopping the car, so that your body slows down too and comes to rest with the car.

But if the car stops suddenly, such as when it hits a pole, your body has not had time to slow down and keeps moving at the same speed the car was moving at before the collision. Newton’s Laws and Car Accidents

Newton’s second law of motion tells us that the force that acts on you or that you exert on another object depends on your mass and how fast you’re moving, and your acceleration.

So you are in your car which is building up speed, accelerating, and then it hits an object, say another vehicle, or a pole.

If you were not wearing a seat belt, you continue to obey Newton’s first law and you continue moving, and hit something, the dashboard, or the windscreen.

You will hit that object with a force that is the product of your mass and the acceleration of the vehicle that you were in. Newton’s Laws and Car Accidents Continued Sir Isaac Newton actually did some work with momentum as well.

When he was developing his laws on motion, he was actually playing around with some new ideas.

When he stated his second law he actually said that force is proportional to the rate of change in momentum.

F = ∆p/∆t Newton and Momentum We can solve this formula to get our present day formula of F = m.a:

F = ∆p/∆t but we know ∆p = m. ∆v

F = (m ∆v)/ ∆t and we know a = ∆v/ ∆t

So F = m.a

There is a more versatile form of the impulse formula.

Δp = m Δv

F = ∆p/∆t

Δp = F Δt

Sticking the two, we get :F Δt = m Δv This equation explains why you would want to come to a stop by hitting a haystack instead of a brick wall with your car.

In each case the impulse is the same (your mass stays the same, your Δv stays the same).

When you hit the brick wall…

F Δt = Δp

All that force on your body is going to hurt! The impulse happened in a very short time period.

When you hit the haystack… F Δt = Δp

Not much force at all, since the impulse is spread out over a long time period!

It’s the force that “hurts”, so you want it to be as small as possible. Explanation of F Δt = m Δv What is the area under the graph?

Area = base X height

= F Δt

Area = Impulse At times it can be useful to graph Force vs. Time to determine impulse. Graphing Friction is a key concept when you are attempting to understand car accidents. The force of friction is a force that resists motion when two objects are in contact. If you look at the surfaces of all objects, there are tiny bumps and ridges.

Those microscopic peaks and valleys catch on one another when two objects are moving past each other. Friction There are two forms of friction, kinetic and static. If you try to slide two objects past each other, a small amount of force will result in no motion. The force of friction is greater than the applied force.

This is static friction. Static Friction If you apply a little more force, the object "breaks free" and slides, although you still need to apply force to keep the object sliding. This is kinetic friction. You do not need to apply quite as much force to keep the object sliding as you needed to originally break free of static friction. Kinetic friction Buckle up! It's the law.

Buckle up with a properly fastened seat belt no matter how short the journey.

Protect children travelling in your vehicle. Use child safety seats according to manufacturer's instructions.

Make sure teenagers buckle up.

Keep your hands on the wheel

Keep your mind on the task at hand. Pull over to talk if you are using a cellular phone. Driving isn't the time to be shaving, putting on make-up, or eating your lunch. Keeping Safe Stay alert

Check traffic in all directions before entering an intersection.

Watch for pedestrians, bicyclists, motorcyclists and children playing.

Obey the speed limit

Slow down when road and weather conditions are poor.

Give yourself a space cushion

Leave space around your vehicle so you have room to stop or manoeuvre in an emergency.

Always check your blind spot

Look in your mirrors and shoulder check before you change lanes.

Be aware of other driver’s blind spots. Can they see you?

Make the smart choice -- Drive alert

Alcohol, medication, fatigue or stress affects your driving. Drive only when you are fully alert.

Have your vehicle serviced regularly

A well-maintained vehicle is a safe vehicle.

Yield the right-of-way

If in doubt, let the other driver go first. http://regentsprep.org/Regents/physics/phys01/colitype/default.htm

http://hyperphysics.phy-astr.gsu.edu/hbase/elacol.html

http://encyclopedia2.thefreedictionary.com/collision

http://www.youtube.com/watch?v=mFNe_pFZrsA

http://theory.uwinnipeg.ca/physics/mom/node3.html

http://www.enotes.com/accident-reconstruction-reference/accident-reconstruction

http://static.slidesharecdn.com/swf/doc_player.swf?doc=biomechalphysics-090903134632-phpapp02&stripped_title=n-motor-vehicle-accident-reconstruciton-and-biomechanical-physics

http://maryspad.com/on-newtons-laws-of-motion-and-the-person-in-a-motor-vehicle-accident/

http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/ben_townsend/TypesofCollisions.htm Bibliography Thank you for paying attention

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