Posts Tagged ‘automobile’

Applying the Work-Energy Theorem to Braking Distance

Friday, January 29th, 2016

    I’m sometimes called upon to render an engineering expert opinion on auto accidents, and in our last blog we stretched this application to a scenario in which Santa’s sleigh collided with the opposing force of a strong wind.   At that time we used the Work-Energy Theorem to calculate the amount of food energy Rudolph and his team required to regain speed and get back on schedule.   Today we’ll use the Theorem to analyze the forces at play in another deer scenario and calculate the braking distance a car needs to avoid hitting one on the highway.

    The average sedan has a mass of about 1,500 pounds, or 680 kilograms.   In our example it’s driving down the highway at a speed, or velocity, of 30 miles per hour, which equates to it covering a distance of 13.3 meters, or just under 44 feet, per second.

    A deer jumps onto the highway, 60 meters in front of the car.   The alert driver slams on the brakes, which exert 1200 Newtons of stopping force on the car.   If you’ll recall from past blogs in this series, the Newton is the metric unit used to measure force.


 What Is Safe Braking Distance?What is Safe Braking Distance?


    Did Bambi survive?   Let’s use the Work-Energy Theorem to find out.   Here it is again,

F × d = ½ × m × [v22v12]

where, F is the braking force used to slow a car of mass m, from an initial velocity of v1 to a final velocity of v2 in a braking distance, d.   The car will eventually come to a complete stop as the driver attempts to avoid hitting the deer, so its final velocity, v2, will be zero.   The Work-Energy Theorem is most often stated in terms of metric units, the measuring unit of choice in the scientific community, and we’ll follow suit with our math.

    Inserting these values into the equation, we get,

[1200 Newtons] × d

 = ½ × [680 kilograms] × [(0)2 – (13.3 meters per second)2]

    Using algebra to solve for d, the braking distance, we arrive at,

d = ½ × [680 kilograms] ×  [(0)2 – (13.3 meters per second)2] ÷  [1200 Newtons]

d = 50.11 meters

    The car stopped 50.11 meters from the point when the driver slammed on his brakes, just about 10 meters short of hitting the deer.   Bambi lives to leap another day!

    Next time we’ll use the Work-Energy Theorem to assess the fate of the falling coffee mug we introduced in past blogs when we opened our discussion on the different forms of energy.


Copyright 2016 – Philip J. O’Keefe, PE

Engineering Expert Witness Blog



Wire Size and Electric Current

Sunday, March 13th, 2011
     Whether or not you live or work in a city, you are probably aware of rush hour traffic and how frustrating it can be.  As a matter of fact, this traffic is the number one reason many choose to live within cities providing public transportation.  Instead of watching the cars pile up in front of you, you can be checking your email or reading the paper.  And no matter where you live, you’ve probably encountered a narrow one-lane road at some time.  If this road were to be spotted with traffic lights and double parked cars, the resulting frustration would reach a new high, one which has you craving the freedom of a crowded three-lane expressway.  At least there’s the possibility of movement there.

      Generally, the wider the road and the fewer the impediments, the better traffic will flow.  The problems presented by vehicular traffic are analogous to those present in electrical wires.  For both, obstructions are impediments to flow.  You see, the thicker the metal is in a wire, the more electrical current it can carry.  But before we explore why, let’s see how electric wires are classified.

     If you’ve ever spent any time hanging around a hardware store looking at the goodies, you’ve probably come across wire gauge numbers, used to categorize wire diameter.  American Wire Gauge (AWG) is a standardized wire gauge system, used in North American industry since the latter half of the 19th Century.  Handy as it is, the AWG gauge numbering system seems to go against logic, because as a wire’s diameter increases, its gauge number decreases.  For example, a wire gauge number of 8 AWG has a diameter of 0.125 inches, while a gauge number of 12 AWG has a diameter of 0.081 inches.  To make things easier on those who need to know this type of information, wire diameter is tabulated for each AWG gauge number and readily available in engineering reference books.

      So what does this have to do with electric current?  To begin with, the larger the AWG number, the less current it can safely carry.  If we turn to an engineering reference book, and look up information relating to an 8 AWG insulated copper wire, we find that it can safely carry an electrical current of 50 amperes, while a 12 AWG insulated copper wire can safely carry only 25 amperes.  This information allows us to make important and relevant design decisions regarding a myriad of things, from electrical wiring in electronic devices, to appliances, automobiles, and buildings. 

      So, why are bigger wires able to carry more current?  Well, as you’ve heard me say before, no wire is a perfect conductor of electricity, but some metals, take copper for instance, are better conductors than others, say steel.  But even the best conductors are inherently full of impurities and imperfections that resist the flow of electricity.  This electrical resistance acts much like traffic lights and double parked cars that impede the flow of traffic.  The larger the diameter of the wire, the less electrical resistance is present.  The logic here is simple.  Wire that is larger allows more paths for electrical current to flow around impurities and imperfections.

      The congestion present in rush hour traffic results in travel delays and hot tempers, and heat is also present in electric wires that face resistance to electricity flow.  If the resistance to electric current flow is high enough, it can cause overheating.  Road rage within the wires is a possibility, and if the wires get hot enough, electrical insulation can melt and burn, creating a fire.  Known as the “Joule heating” effect, this phenomenon is responsible for its share of building fires.

      We’ll learn more about Joule heating and how wires are sized to keep electrical current flow within safe limits next week.  Until then, try to keep out of traffic.