Inertial and Non-Inertial Frames of Reference Question

AI Thread Summary
A rubber stopper suspended in a subway car at an angle of 13 degrees from vertical indicates the train's deceleration. The tension in the string can be calculated using the formula T = (mass)(9.81) / cos(13 degrees). The horizontal component of tension relates to the acceleration of the train through the equation T sin(θ) = ma. By combining the equations for horizontal and vertical forces, the acceleration can be simplified to a = g tan(θ). This approach clarifies the relationship between the forces acting on the stopper and the train's acceleration.
Kaos_Griever
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Homework Statement


A rubber stopper of mass 25g is suspended by string from a handrail of a subway car traveling directly eastward. As the subway train nears a station, it begins to slow down, causing the stopper and string to hang at an angle of 13 degrees from the vertical. What is the acceleration of the train? Determine the magnitude of the tension in the string.

The attempt at a solution
Tension of String = (mass)(9.81) / cos 13 degrees
The Horizontal component of Tension = [(mass)(9.81) / cos 13 degrees] sin 13 degrees = (mass)(acceleration)
a = [[(mass)(9.81) / cos 13 degrees] sin 13 degrees] / mass
 
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That works. But simplify that answer!
 
I'm not sure how to simplify the answer because I do not have many values to use...
 
You have everything you need.

Cancel what can be canceled; use a single trig expression. Then evaluate to get the numerical answer.
 
Thank you very much! =D It took me a while to understand it.. I thought what I was doing was wrong.
 
Your solution is fine!

FYI, here's how I would do it:

Horizontal forces:
T\sin\theta = ma

Vertical forces:
T\cos\theta = mg

Combine (divide one by the other) to get:
a = g\tan\theta
 
Oh, thanks! I really appreciate your help.
 

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