Calculating velocity/acceleration from sway of an object.

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To determine how long it takes a train to travel 300 meters while accelerating from rest, the sway of the handles at a 32-degree angle from vertical can be analyzed. The horizontal component of the force on the handle is essential for calculating the train's acceleration. The relationship between gravitational acceleration and the train's horizontal acceleration can be expressed using the tangent of the angle: tan(32 degrees) equals the horizontal acceleration divided by gravitational acceleration. This approach allows for the calculation of the necessary acceleration to find the time taken for the train to cover the distance. Understanding these relationships is crucial for solving the problem effectively.
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Homework Statement


A train accelerates from rest causing the handles that hang from the roof to sway 32 degrees from vertical. How long will it take the train to travel 300metres.


Homework Equations





The Attempt at a Solution


All I know is that the horizontal component of the force vector on the handle would be used to find acceleration.
 
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Did you draw a Free Body Diagram for a typical handle? What is the relationship between the acceleration due to gravity and the horizontal acceleration of the train in terms of the hang angle?
 
Thanks for the reply.

Would it be tan32=?/g
With ? being the acceleration of the x component.
 
That sounds reasonable.
 

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