A ball (B) of mass mB hangs from two "ideal" ropes inside a small room as shown which is sitting on level ground on the surface of Earth. A perfectly vertical rope connects the ball to the ceiling at A and a second rope connects the ball to the ceiling at C and makes an angle θ with respect to the ceiling (note that 0∘<θ<90∘). Now suppose that the room is on a train which is undergoing constant acceleration to the right with magnitude at and that the orientation of the ropes stays the same. There are now two pretty tempting choic
A ball (B) of mass mB hangs from two "ideal" ropes inside a small room as shown which is sitting on level ground on the surface of Earth. A perfectly vertical rope connects the ball to the ceiling at A and a second rope connects the ball to the ceiling at C and makes an angle θ with respect to the ceiling (note that 0∘<θ<90∘).
Now suppose that the room is on a train which is undergoing constant acceleration to the right with magnitude at and that the orientation of the ropes stays the same. There are now two pretty tempting choices of observers we may want to use to apply Newton's Second Law. First, consider an observer who is at rest on the ground watching the train go by. If this observer applies Newton's Second Law to the ball, what expression would they determine for the magnitude of the tension TAB in terms of mB, θ, at and g?
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