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

In summary, the problem involves a train traveling up a 3.73 degree incline at a speed of 3.25 m/s. The last car breaks free and begins to coast without friction. The question asks for the time it takes for the car to momentarily come to rest and the distance it travels before doing so. The solution involves finding the car's acceleration after it is released, which can be done by considering the net force acting on it. Using sine, the component of gravity can be found and used to solve the problem.
  • #1
cloudage
14
0

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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  • #2
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?
 
  • #3
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!
 
  • #4
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!
 

1. What is Newton's First Law?

Newton's First Law, also known as the Law of Inertia, states that an object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by an external force.

2. How does Newton's First Law apply to a train that is momentarily at rest?

In the case of a train that is momentarily at rest, Newton's First Law explains that the train will remain at rest unless an external force is applied, such as the force of the engine pushing the train forward.

3. What is Newton's Second Law?

Newton's Second Law, also known as the Law of Acceleration, states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass.

4. How does Newton's Second Law apply to a train that is momentarily at rest?

In the case of a train that is momentarily at rest, Newton's Second Law explains that for the train to begin moving, a net force must be applied to overcome its mass and inertia. This force is provided by the engine, causing the train to accelerate.

5. What is Newton's Third Law?

Newton's Third Law, also known as the Law of Action and Reaction, states that for every action, there is an equal and opposite reaction.

6. How does Newton's Third Law apply to a train that is momentarily at rest?

In the case of a train that is momentarily at rest, Newton's Third Law explains that as the engine applies a force to the train, the train exerts an equal and opposite force on the engine. This allows the train to overcome its inertia and begin moving.

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