Introduction To Momentum & Energy Applications In Crash Reconstruction
4th Malaysian Workshop on CrashInvestigation & Injury AnalysisIntroduction toMomentum & EnergyApplications inCrash ReconstructionEngr. Iskandar Abdul Hamid(IEM Reg. 22253), M.Sc (Mech)(Manchester UK), B.Eng (Mech)(UNITEN)1Research OfficerCrash Reconstruction UnitMIROS
Presentation Outline Objectives Momentum applications in crash reconstruction Conservation of momentum Coefficient of restitution Impulse Example Work, energy and speed from damage in crash Work Conservation of Energy Example2
Background knowledgerequired Understanding of algebra A grasp of trigonometrywill make it easier4
Quick survey Any engineers in the room? Any mathematicians? Any physicists? Any lawyers? Any ‘non-technical background’ personnel? So I can suit my presentations accordingly Any politician?5
Momentumapplications in crashreconstruction6
Why momentum? To determine the velocities of vehicleswhen they first come into contact with eachother. To do this, it is necessary to understandhow the vehicles moved from first contactto maximum engagement to separation andfinally to their rest positions.7
Definition Newton first expressed the notion of abody’s quantity of motion by multiplyingthe body’s mass by its velocity. Momentum is a vector quantity. So it hasmagnitude and direction International standard symbol is P8
Definition Thus, the momentum of an object (or vehicle) isexpressed byP mvwhere P momentum in N-secm mass in kgv velocity in m/sec9
Conservation of momentum The law of conservation of momentum states that‘In any group of objects that act uponeach other, the total momentum beforethe action equals the total momentumafter the action’ Applied to crash reconstruction, the action is thecollision between two vehicles and the objects are thetwo vehicles.10
Conservation of momentum Using Newton’s Second and Third Laws of Motion, anequation for conservation of momentum can bedeveloped. Conservation of momentum can be expressed as thefollowing equation:M1U1 M2U2 M1V1 M2V211
Equation ForConservation Of Momentum12
Example 1BAwestboundnorthboundGouge markji13
Example 1Gouge markji14
Coefficient of Restitution The coefficient of restitution, ϵ, is a measure of the“bounciness” of a collision between two objects: howmuch of the kinetic energy (KE) remains for theobjects to rebound from one another vs. how much islost as heat, or work done deforming the objects. It is defined as the ratio of relative speeds after andbefore an impact, taken along the line of the impact15
Coefficient of Restitution16
Coefficient of Restitution The cars have some coefficient of restitution, ϵ ; thatis, they try to go back to their original shape. But car-to car collisions are generally considered to beinelastic collisions, because cars do not bound. Oncethey are deformed, they essentially stay deformed. For typical collision speeds encountered in trafficcrash reconstruction cases, the ϵ can be considered aszero.17
Question What is the coefficient of restitution for the casediscussed in Example 1? ϵ 1, 0 ϵ 1, or ϵ 0?18
Impulse19
Impulse20
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Quiz 1 Consider a collision of a vehicle with a wall. Thediagram depicts the changes in velocity of the samewall. Indicate which case (A or B) has the greatestchange in velocity, greatest acceleration, greatestmomentum change, and the greatest impulse.Support each answer.22
Quiz 1 Greatest change in velocity? Greatest acceleration? Greatest momentum change? Greatest impulse?23
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Work, energy andspeed from damagein crash25
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Why Work & Energy? In crash reconstruction, many concepts associatedwith physics are used, especially those dealing withwork and energy. These concepts can be used to answer questionsconcerning speed estimates from skidmarks andvehicle damage, the effect of drag factor, and manyother issues.27
Work In physics, work is done when a force actson an object through a distance. Work is also a measure of what effect theforce has on changing the object. Theamount of change produced, i.e. theamount of work done, is reflected inchanges in the object’s velocity, position,size, shape, and so forth.28
Work A more quantitative description of the term work canbe established from the definition. Work (W) is equalto the product of the force (F) and the distance (d)through which the force acts, provided the force anddistance covered are in the same direction. This may be written in equation formW Fd In the metric system, the unit for work is Newtonmeter (N-m).29
Work Work is a scalar quantity, or the product of themagnitudes of force and distance. Being a scalar quantity, work has only magnitude andsign (positive or negative), but has no direction.30
Relationship BetweenWork and Energy By doing work, energy is transferred betweendifferent objects. The energy an object possesses is a measure of itsability to do work. The more energy an object has, themore work it can perform. Equations can be derived to calculate the amount ofenergy transferred between objects when work isdone under a variety of conditions.31
Types of EnergyType of energies normally used in crashreconstruction are: Kinetic Energy (KE) Potential Energy (PE)32
Kinetic Energy33
Kinetic Energy KE, like all energies, is a scalar quantity. KE of a given mass depends on the magnitude ofits velocity and not on the direction of travel. Acceleration rate is not a factor in KE. KE of a body depends on its mass and its velocity.It is not affected by how quickly the body reachesthat velocity.34
Potential Energy35
Gravitational Potential Energy36
Gravitational Potential Energy37
Elastic Potential Energy38
Elastic Potential Energy39
Conservation of Energy The law of conservation of energy statesthat when work is done and energy isconverted from one form into another, noenergy is created and no energy isdestroyed. The total amount remainsconstant.40
Equation ForConservation Of Energy Wfd, W weight of the vehicleF ma, a gf (refer drag factor notes)41
Quiz 242
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references Crash Reconstruction Unit, ‘Crash ReconstructionHandbook’, MIROS. Lynn B. Frike, “Traffic Accident Reconstruction’,Volume II of the Traffic Accident Manual,Notrhwestern University Traffic Institute, 1990. ISBN0-912642-07-6. son-1/Momentum-and-Impulse-Connection sof-Speed-in-Crash-Investigation44
Answers Quiz 145
Quiz 2 answer46
Conservation of momentum The law of conservation of momentum states that 'In any group of objects that act upon each other, the total momentum before the action equals the total momentum after the action' Applied to crash reconstruction, the action is the collision between two vehicles and the objects are the two vehicles. 10
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