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 a car needs to avoid hitting one on the highway.braking distanceThe 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 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.
Did Bambi survive? Let’s use the
v]_{1}^{2}where, m, from an initial velocity of v to a final velocity of _{1}vin a _{2 }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, vwill be zero. The _{2, } 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.Work-Energy TheoremInserting these values into the equation, we get, [1200
meters per second)]^{2} Using algebra to solve for
meters per second)] ÷^{2} [1200 Newtons]
The car stopped 50.11 meters from the point when the driver slammed on his Next time we’ll use the
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