Question

suppose a railroad is 5 kilometers and expands on a hot day by 15 cm in length. Approximately how many meters would the center of the rail rise above the ground?

Answer 1

13.4 m

Explanation:

For small angles, x, in radians,

tan(x) ≈ sin(x) = x

The actual deflected shape is parabolic, but it is approximated by an isosceles triangle with small equal angles.The extend length is 3 km + 12 cm, which is 3000 + 0.12 = 3000.12 m. Half of the extended length is 1500.06 m. Let h+ the rise of the center of the rail above ground. From the Pythagorean theorem, obtain h² + 1500² = 1500.6² h² = 1500.06² - 1500² = 180.004 h = 13.4 m, which is about 0.9% of the original length.