a pendulum hanging from the ceiling of a train traveling with constant speed deviates 37 ° from the vertical when the train describes a curv

Question

a pendulum hanging from the ceiling of a train traveling with constant speed deviates 37 ° from the vertical when the train describes a curve of 60 m radius determines the train’s rapids

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Linh Đan 6 months 2021-08-19T19:27:06+00:00 1 Answers 3 views 0

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    2021-08-19T19:28:53+00:00

    Answer:

    21 m/s

    Explanation:

    There are three forces on the pendulum:

    Weight force mg pulling down,

    Vertical tension component Tᵧ pulling up,

    and horizontal tension component Tₓ pulling towards the center of the curve.

    Sum of forces in the y direction:

    ∑F = ma

    Tᵧ − mg = 0

    T cos 37° = mg

    T = mg / cos 37°

    Sum of forces in the centripetal direction:

    ∑F = ma

    Tₓ = mv²/r

    T sin 37° = mv²/r

    (mg / cos 37°) sin 37° = mv²/r

    g tan 37° = v²/r

    v = √(gr tan 37°)

    v = √(9.8 m/s² × 60 m × tan 37°)

    v = 21 m/s

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