a highway curve of radius 100 m, banked at an angle of 45 degrees, may be negotiated without friction at a speed of:

Question

a highway curve of radius 100 m, banked at an angle of 45 degrees, may be negotiated without friction at a speed of:

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Gia Bảo 5 years 2021-09-02T11:20:26+00:00 1 Answers 294 views 0

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  1. minhkhang
    0
    2021-09-02T11:22:13+00:00
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    A car making this turn is pulled downward by its own weight, and pushed up by the road at an angle of 45°, so by Newton’s second law,

    • the net horizontal force on the car is

    ∑ F = N cos(45°) = m a = m v ² / R

    • the net vertical force on the car is

    ∑ F = N sin(45°) – m g = 0

    where

    • N = magnitude of the normal force

    • m = mass of the car

    • a = v ² / R = centripetal acceleration of the car

    • v = tangential speed of the car

    • R = 100 m = radius of curvature

    • g = 9.8 m/s² = acceleration due to gravity

    From the net vertical force equation, we get

    N = m g / sin(45°)

    and substituting this into the net horizontal force equation and solving for v gives

    (m g / sin(45°)) cos(45°) = m v ² / R

    v = √(R g cos(45°) / sin(45°)) ≈ 31 m/s

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