Question 1 (20 marks) The Lac-Mégantic rail disaster occurred in the Eastern Tow

Question

Question 1 (20 marks) The Lac-Mégantic rail disaster occurred in the Eastern Townships of Québec, Canada, on July 6, 2013. In brief, a 74-car freight train, that was unattended, rolled down a slight grade toward downtown Lac-Mégantic. The train derailed in the downtown area, resulting in the explosion of multiple cars carrying fuel, and caused subsequent fires There were more than 40 people killed in the disaster and around half of the downtown area was destroyed. Imagine that you are tasked with investigating the aftermath of this disaster and consider: 9 How would you estimate the speed of the train when it reaches the downtown area if the brakes were NOT applied? Explain what parameters you would need to know to conduct your analysis and what assumptions you would need to make. (5 marks) a) b) How would your analysis change if the brakes WERE applied? What additional information would you need? Explain what parameters you would need to know to conduct your analysis and what assumptions you would need to make. (5 marks) c) If you knew the average force exerted by a single hand brake, how would you determine the number of hand brakes required to prevent the train from moving, assuming you know the grade of the slope that it is stopped upon? (5 marks) d) Assuming the derailment occurred on a curved portion of the track, explain the reason for the derailment as well as the effects of the radius of the curve and the train speed. (5 marks)

Explanation / Answer

a. let the speed of the train when it reached the downtown area be v

intitial speed of the train = 0

now, let the number of tyres in the train be n, each of mass m, radius r

then

force of friction on each tyre = f/n

hence

acceleration of the train = a

a = (Mg*sin(theta) - f)/M

also, f*r/n = 0.5mr^2*a/r

f/n = ma/2

f = nma/2

hence

Ma + nma/2 = Mg*sin(theta)

a = 2Mg*sin(theta)/(2M + nm)

hence

by knowing the distance between the downtown area and the initial point

mass of train = M

mass of each tyre = m

grade = theta

we can know acceleration of the train = a

and hence v = sqrt(2*a*d)

n - numebr of wheel son the train

b. if brakes were applied

then wqe need to know coefficeint of kinetic friction between the train wheels and the track

hence

let this coefficeint be u

then

force of frction f = uMgcos(theta) (where M is mass of train)

hence

a = (Mgsin(theta) - uMg*cos(theta))/M

a = g(sin(theta) - ucos(theta))

v = sqrt(2a*d)

c. if force of each hand brake = f'

then number of hand brakes required = n

then

nf' = Mg*sin(theta)

f' = Mg*sin(theta)/n

d. the train derailed because in the curved region of the track there is a limit above which vehicles cannot travel., due to the curvatiure of the track, there is a centrifugal force in the fram of reference of a moving train and this force causes the train to tip over and move outward of the track hence causing it to tip

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