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Two sections of a train track are 1 mile each. They are attached to each other forming a straight line. Each track expands 1.00 ft in length under the hot sun causing the track to buckle. If each section of track remains straight, how far does the midpoint deflect? (Answer in feet)

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General Physics RvTDLR 1 year 1 Answer 185 views 0

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Answer ( 1 )

  1. Before expansion, the 2 pieces of track are like this:
    A. . . M . . .B
    where M is mid-point where the tracks join. AM = BM = 1mile = 5280 ft.

    After expansion, the 2 pieces of track are like this:
    . . . . .P
    A. . . M . . .B
    where P is point where the now raised ends of the tracks join.
    AP = BP = 5280+1 ft = 5281 ft

    We want distance MP. Using Pythagoras:
    AP² = MP² + AM²
    5281² = MP² + 5280²
    MP² = 5281² – 5280²
    . . . . = 10561
    MP = √10561
    . . . = 103 ft

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