An Amtrak train bound from New York City to Savannah, Georgia derailed south of Philadelphia on 3rd April, 2016. According to the news article, it was going at 106mph (the speed limit on this section of track is 110mph) when the engineer saw a backhoe on the track and put the train into emergency braking with about 5 seconds to go. The impact derailed the lead engine of the train Reuters Problems: Braking will be approximately constant deceleration and dependent on the friction between the rims of the steel wheels and the steel rails. See next page for a list of relevant equations (which you have memorized anyway). How far away was the backhoe? In other words, how far would the train travel in 5 sec at 106mph (and not braking)? If the train were to stop before hitting the backhoe: 106mph to zero in the distance that you figure above, what would the deceleration need to be? If this stop were to be possible, what would the coefficient of friction (u) need to be? If the train is slowing down, does it still take 5 seconds to reach the backhoe? Hint: No The coefficient of friction for dry steel on dry steel is usually taken as 0.15. What is the maximum possible value of deceleration? Equations used in Constant Velocity s = vt, i.e. a = 0 Equations used in Constant Acceleration v = v + at S = Vot + 1at S = v = (v +vo) t 2 v + 2as F = ma Where: s = distance v = velocity Vo = initial velocity a = acceleration Fr=UN 5,280 ft = 1 mile mph x 22/15 = ft/sec Force and Acceleration, Friction Use consistent units! m = W/g Where m is mass and g is acceleration due to gravity. Use: g = 32.2ft/sec F, is the maximum available friction force u is the coefficient of Friction N is the Normal force, in this case W