Relative motion of a dropping object on a moving train

AI Thread Summary
The discussion revolves around the relative motion of a bolt dropping in an accelerating train. The bolt's acceleration relative to the train is calculated as 10.4 m/s² at an angle of 19.7° south from vertical, while its acceleration relative to Earth is 9.8 m/s² downward. The confusion arises from the expectation that the bolt's acceleration should be purely vertical since it is dropped from the train. However, due to the train's northward acceleration, the bolt appears to move backward relative to the train. This highlights the importance of considering the frame of reference when analyzing motion in accelerating systems.
MechaMZ
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Homework Statement


A bolt drops from the ceiling of a train car that is accelerating northward at a rate of 3.50 m/s2.
(a) What is the acceleration of the bolt relative to the train car?
(b) What is the acceleration of the bolt relative to the Earth?

The Attempt at a Solution


(a)10.4 m/s2 at 19.7° to the south from the vertical
(b)9.8 m/s2 vertically downward


I don't understand why the acceleration in (a) is not vertically downward since it is relative to the train. As we could assume the train is not moving, then the motion should be vertically downward isn't?
 
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The train is accelerating. So the instant the bolt starts to drop you would see it going vertically downward if you were on the train. Now since the train is accelerating the bolt appears to be moving backwards since the train is speeding up but the bolt is not.
 
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