Suppose that you need to measure whether a tabletop in a train is truly horizontal. If you use a spirit level, can you determine this when the train is moving down or up a grade? When the train is moving along a curve? (Hint: There are two horizontal components.)

							The spirit level consists of a solution which has a bubble inside the tube. The bubble stays at the marked center position of the level if the surface on which the spirit level is kept is horizontal. The bubble stays at the center (reference position) because equal amount of solution exist symmetrically along the length of the level.
The symmetrical distribution of solution around the position of bubble indicates that there is no net force on the solution and the weight of the solution is supported by the reaction from the table.
When the train starts to move up a grade, the forces run out of the balance and there is a net component of force on the solution which pushes the solution in the direction opposite to the direction of motion of train. This makes the bubble move in the direction of the train, and one can eventually know that the train is climbing the grade.
Similarly, when the train moves down the grade there is a net component of force on the solution which pushes the solution in the direction of the train. This makes the bubble to move opposite to the direction of motion of train and one can know from the change in bubble position that the train is moving down the grade.
When the train moves horizontally in a circular path, centrifugal forces act on the solution in the spirit level. This force will push the bubble away from the marked position, but the bubble stays in the center of the level.
Therefore from the change in bubble position, one can know that the train has moved on a curved path on a horizontal surface.