Stopping Distance for 25000kg Train Traveling at 18m/s: Conductor's Dilemma

[xbebegirlx]

a 25000kg train travel down a track at 18m/s. a cat wander onto the track 45m ahead of train, causing the conductor to slam on the brakes. The train skids to a stop. If the brakes can provide 75,000 Newtons of friction, will the conductor have enough stopping distance to avoid hitting the cat?

 

[rl.bhat]

Hi xbebegirlx, welcome to PF.
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[tomcue]

I would approach this scenario by first calculating the stopping distance of the train based on its mass, initial velocity, and the maximum friction force provided by the brakes. Using the equation for stopping distance (d = v^2/2a), where d is the stopping distance, v is the initial velocity, and a is the deceleration due to the friction force, I would get a stopping distance of 18.67 meters for the train.

Based on this calculation, it appears that the train would not have enough stopping distance to avoid hitting the cat, as the cat is 45 meters ahead of the train. However, it is important to note that this calculation assumes ideal conditions and does not take into account any other factors such as the reaction time of the conductor or the coefficient of friction between the train and the track.

In reality, the conductor may have a faster reaction time and be able to apply the brakes sooner, reducing the stopping distance of the train. Additionally, the coefficient of friction between the train and the track may vary depending on the condition of the track and the type of brakes being used.

Therefore, while the calculations suggest that the train may not have enough stopping distance to avoid hitting the cat, the actual outcome would depend on various factors and cannot be determined with absolute certainty. The conductor's dilemma highlights the importance of constantly monitoring and maintaining the condition of the train and track, as well as the need for quick and efficient decision-making in emergency situations.