How far did the train travel before stopping after detaching a compartment?

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Homework Help Overview

The problem involves a train moving up an incline at a 4-degree angle, with a focus on determining the distance traveled by the train after a compartment detaches while moving at a speed of 5 m/s. The original poster expresses confusion over their calculated distance of 0.09 m and seeks hints for a better approach.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to use kinematic equations by breaking down the speed into components and calculating vertical displacement, but questions the validity of their result. Another participant suggests a different interpretation of the problem, clarifying that it may refer to a train car detaching and discusses the conversion of kinetic energy to potential energy to find the height and distance along the incline.

Discussion Status

The discussion is active, with participants exploring different interpretations of the problem and offering guidance on how to approach the calculations. There is no explicit consensus, but a productive direction has been provided regarding energy conservation principles.

Contextual Notes

The original poster notes a lack of additional information, which may affect the clarity of the problem setup. The potential misunderstanding regarding whether a train or a train car is being referenced is also highlighted.

mrhobbes
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A train moving up an incline at 4 degrees has it's last train compartment detached. The train was moving at a speed of 5 m/s when the compartment breaks free. How far did the train get before the speed momentarily reaches zero?

No other information is given, but using all that was provided, I got a ridiculously small answer of 0.09 m. I got this by splitting up my speed into x and y components and then using the Vo(y) in the equation d= vf² - vo² / 2a to get my vertical displacement. I then used distance to get my inclined displacement by using sin 5 = y / r.

I checked the answer and it turns out that it was wrong. Could anyone give me any hints on how to solve the problem?

Thanks
 
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Welcome to PF.
The question doesn't make much sense as written. Perhaps it means a train CAR breaks free from the back of the train. Without engine. How far does the CAR go up the hill?

It's initial speed is 5 m/s. Since it is going up the hill, its KE will soon be converted into PE. You could begin with
initial KE = final PE
.5*mv² = mgh
and quickly find the height reached from the initial position. You'll have to convert that into a (larger) distance along the ramp with a bit of trigonometry. I'm getting a little more than 18 m.
 
Thank you so much. You were right.
 
Most welcome! Good luck with the next one.
 

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