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We decided we could attach a mass to a string and attach the string to the ceiling. From inside the bus, it would look like this:

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...O

Ignore those dots. Theyre the only way I can space things over.

There are two forces acting on this mass: gravity and the tension of the string. From the Earth's referece frame, the mass is accelerating with the same acceleration as the bus, ie, horizontally. So the only force the causes the mass to accelerate is TsinA=ma where T is the tension is the string, A is the angle measured wrt the line perpendicular to the ceiling, and a is the acceleration of the bus (and ball). Also, TcosA-mg=0 since there is no acceleration in this direction. Dividing each by each yields a=gtanA.

From the reference frame of the bus, the mass is stationary. TsinA=0 and TcosA=mg. Dividing each by each yields 0=tanA or A=0. Does this spurious result come from the fact that the reference frames are noninertial with repsect to each other? How come the result is valid for one frame but not the other?