Two iron rails, each 50 feet long, are laid end to end with no space between them. During the summer, the heat causes each rail to increase in length by 0.04 percent. Although this is a small increase, the lack of space at the joint makes the joint buckle upward. What distance upward will the joint be forced to rise? (Assume that each rail remains straight, and that the other ends of the rails are anchored. Round your answer to the nearest hundreth.

Question

Mathematics

Dominique Guzman

4 June, 03:43

Two iron rails, each 50 feet long, are laid end to end with no space between them. During the summer, the heat causes each rail to increase in length by 0.04 percent. Although this is a small increase, the lack of space at the joint makes the joint buckle upward. What distance upward will the joint be forced to rise? (Assume that each rail remains straight, and that the other ends of the rails are anchored. Round your answer to the nearest hundreth.

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Sebastian Thomas · Answer 1

You have to imagine o right triangle with one leg = 50 ft and the hypotenuse (to be calculated with the dilatation) and the 2nd leg, just the rise (or altitude).

The hypotenuse = 50 (1+0.04%) = 50.02 ft

te 1st leg = 50

Calculate the rise:

(hypotenuse) ² = (1st leg) ² + Rise (=2nd leg) ²

(50.02) ² = 50² + Rise²

Rise² = 2

and Rise = √2 = 1.414 ft