Physics Behind a Train Accident

While I was procrastinating doing my work this week, I found an account called "historyphotographed" on Instagram, and started scrolling through it. Of the many interesting pictures, one stood out to me in particular of a locomotive suspended over a street after running off the end rails.

After seeing this image, I wondered what the locomotive's momentum was, and what force it had when it crashed into the wall. I was able to find an archived article in the Los Angeles Times about the accident, which took place on January 25, 1948. Today, the average Amtrak locomotive weighs about 150 tons, and the average Amtrak passenger car weighs about 65 tons. According to the article, the Santa Fe Diesel passenger train weighed about 300 tons, or 600,000 pounds. Additionally, the train was moving 2 to 3 miles per hour.

To calculate the momentum of the train, I used the equation:

m = 600,000 lbs or about 272,155 kg

v = approximately 2.5 mph or 1.12 meters per second

Therefore, the locomotive's momentum was about 304,814 kg*m / s.

To calculate the force at which the train struck the wall, I used the equation: 

Since the acceleration of the train was unknown, I used the equation:

F = m * (Δv/Δt) 

Δv = 1.12 meters per second
Δt = 54.5 seconds

I hypothesized that the train travelled a distance of 200 feet, or about 61 meters, between the station and the wall that it crashed into. Therefore, the Δt would be about 54.5 seconds.

By plugging in these values into the new equation for force, I found the force at which the train struck the wall to be about 5,593 N. 

Thankfully, the train was not moving quickly, and the wall was able to prevent the train from crashing onto the street below despite the force in which it hit the wall.