A train that is momentarily at rest, Newton's Laws

AI Thread Summary
A train traveling up a 3.73-degree incline at 3.25 m/s has its last car break free and coast without friction. To determine how long it takes for the last car to come to rest and the distance it travels before stopping, the acceleration must be calculated using the gravitational force component along the incline. The key point is that gravity is the only force acting on the car after it is released, allowing for the use of sine to find the acceleration. Understanding the relationship between velocity, acceleration, and distance is crucial for solving the problem. The discussion emphasizes the importance of correctly applying Newton's laws to analyze the motion of the car.
cloudage
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Homework Statement


A train is traveling up a 3.73 degrees incline at a speed of 3.25 m/s when the last car breaks free and begins to coast without friction.
a) How long does it take for the last car to come to rest momentarily?
b) How far did the last car travel before momentarily coming to rest?


Homework Equations





The Attempt at a Solution


I tried to draw the free body diagram, but since I have either mass or a force I don't know how to proceed. Momentarily at rest means that it's velocity is zero, but I don't know it's acceleration after the car has been released so I can't use the kinematics.
 
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cloudage said:

Homework Statement


A train is traveling up a 3.73 degrees incline at a speed of 3.25 m/s when the last car breaks free and begins to coast without friction.
a) How long does it take for the last car to come to rest momentarily?
b) How far did the last car travel before momentarily coming to rest?


Homework Equations





The Attempt at a Solution


I tried to draw the free body diagram, but since I have either mass or a force I don't know how to proceed. Momentarily at rest means that it's velocity is zero, but I don't know it's acceleration after the car has been released so I can't use the kinematics.
After the car is released, you should be able to find its acceleration. What net force acts on the car when it is released?
 
I got it, thank you very much! It would just be gravity acting on it, so I can find the component by using sine. Thanks!
 
cloudage said:
I got it, thank you very much! It would just be gravity acting on it, so I can find the component by using sine. Thanks!
Yes, and welcome to PF!
 

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