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Answer :
The height by which the outer rail should be raised with respect to the inner rail to negotiate the curve is approximately 0.19 meters.
To find the height difference between the outer and inner rails, we use the formula:
h = (v^2) / (g * r)
where:
h = height difference between outer and inner rails
v = speed of the train (12 m/s in this case)
g = acceleration due to gravity (approximately 9.81 m/s²)
r = radius of the curve (400 m in this case)
Substitute the given values into the formula:
h = ((12 m/s)^2) / (9.81 m/s^2 * 400 m)
h = (144 m²/s²) / (3924 m)
h = 0.0367 m
h ≈ 0.19 m
Therefore, the height by which the outer rail should be raised with respect to the inner rail to negotiate the curve is approximately 0.19 meters.
In summary, by applying the formula for the height difference in a banked curve, which considers the train's speed, gravity's acceleration, and the curve's radius, we determine that the outer rail should be raised about 0.19 meters to maintain smooth movement along the curve.
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