Introduction to

Momentum & Energy Applications in

Crash Reconstruction

Engr. Iskandar Abdul Hamid

(IEM Reg. 22253), M.Sc (Mech)(Manchester UK), B.Eng (Mech)(UNITEN)

Research Officer

Crash Reconstruction Unit

MIROS 1

4th Malaysian Workshop on Crash Investigation & Injury Analysis

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

Example

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Background knowledge

required

Understanding of algebra

A grasp of trigonometry will make it easier

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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

Momentum applications in crash

reconstruction

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Why momentum?

To determine the velocities of vehicles when they first come into contact with each other.

To do this, it is necessary to understand how the vehicles moved from first contact to maximum engagement to separation and finally to their rest positions.

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Definition

Newton first expressed the notion of a body’s quantity of motion by multiplying the body’s mass by its velocity.

Momentum is a vector quantity. So it has magnitude and direction

International standard symbol is P

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Definition

Thus, the momentum of an object (or vehicle) is expressed by

P = mv

where P = momentum in N-sec

m = mass in kg

v = velocity in m/sec

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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.

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Conservation of momentum

Using Newton’s Second and Third Laws of Motion, an equation for conservation of momentum can be developed.

Conservation of momentum can be expressed as the following equation:

M1U1 + M2U2 = M1V1 + M2V2

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Equation For

Conservation Of Momentum

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Example 1

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i

j

Gouge mark

B

A

westbound

northbound

Example 1

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i

j

Gouge mark

Coefficient of Restitution

The coefficient of restitution, ϵ, is a measure of the “bounciness” of a collision between two objects: how much of the kinetic energy (KE) remains for the objects to rebound from one another vs. how much is lost as heat, or work done deforming the objects.

It is defined as the ratio of relative speeds after and before an impact, taken along the line of the impact

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Coefficient of Restitution

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Coefficient of Restitution

The cars have some coefficient of restitution, ϵ ; that is, they try to go back to their original shape.

But car-to car collisions are generally considered to be inelastic collisions, because cars do not bound. Once they are deformed, they essentially stay deformed.

For typical collision speeds encountered in traffic crash reconstruction cases, the ϵ can be considered as zero.

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Question

What is the coefficient of restitution for the case discussed in Example 1?

ϵ = 1,

0<ϵ<1, or

ϵ =0?

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Impulse

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Impulse

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Quiz 1 Consider a collision of a vehicle with a wall. The

diagram depicts the changes in velocity of the same wall. Indicate which case (A or B) has the greatest change in velocity, greatest acceleration, greatest momentum change, and the greatest impulse. Support each answer.

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Quiz 1

Greatest change in velocity?

Greatest acceleration?

Greatest momentum change?

Greatest impulse?

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Work, energy and speed from damage

in crash

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Why Work & Energy?

In crash reconstruction, many concepts associated with physics are used, especially those dealing with work and energy.

These concepts can be used to answer questions concerning speed estimates from skidmarks and vehicle damage, the effect of drag factor, and many other issues.

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Work

In physics, work is done when a force acts on an object through a distance.

Work is also a measure of what effect the force has on changing the object. The amount of change produced, i.e. the amount of work done, is reflected in changes in the object’s velocity, position, size, shape, and so forth.

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Work

A more quantitative description of the term work can be established from the definition. Work (W) is equal to the product of the force (F) and the distance (d) through which the force acts, provided the force and distance covered are in the same direction.

This may be written in equation form

W = Fd

In the metric system, the unit for work is Newton-meter (N-m).

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Work

Work is a scalar quantity, or the product of the magnitudes of force and distance.

Being a scalar quantity, work has only magnitude and sign (positive or negative), but has no direction.

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Relationship Between

Work and Energy

By doing work, energy is transferred between different objects.

The energy an object possesses is a measure of its ability to do work. The more energy an object has, the more work it can perform.

Equations can be derived to calculate the amount of energy transferred between objects when work is done under a variety of conditions.

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Types of Energy

Type of energies normally used in crash reconstruction are:

Kinetic Energy (KE)

Potential Energy (PE)

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Kinetic Energy

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Kinetic Energy

KE, like all energies, is a scalar quantity.

KE of a given mass depends on the magnitude of its 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 reaches that velocity.

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Potential Energy

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Gravitational Potential Energy

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Gravitational Potential Energy

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Elastic Potential Energy

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Elastic Potential Energy

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Conservation of Energy

The law of conservation of energy states that when work is done and energy is converted from one form into another, no energy is created and no energy is destroyed. The total amount remains constant.

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Equation For

Conservation Of Energy

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F = ma, a = gf (refer drag factor notes)

= Wfd, W = weight of the vehicle

Quiz 2

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references

Crash Reconstruction Unit, ‘Crash Reconstruction Handbook’, MIROS.

Lynn B. Frike, “Traffic Accident Reconstruction’, Volume II of the Traffic Accident Manual, Notrhwestern University Traffic Institute, 1990. ISBN 0-912642-07-6.

http://www.physicsclassroom.com/class/momentum/Lesson-1/Momentum-and-Impulse-Connection

https://www.arrivealive.co.za/Speeding-and-Analysis-of-Speed-in-Crash-Investigation

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Answers

Quiz 1

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Quiz 2 answer

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