A truck drives with a constant linear speed v_iv i ​ v, start subscript, i, end subscript down a road with two curves. The first curve has a

Question

A truck drives with a constant linear speed v_iv i ​ v, start subscript, i, end subscript down a road with two curves. The first curve has a radius RRR and the second curve has a radius 3R3R3, R. How does the magnitude of the truck’s centripetal acceleration change after the radius increases? Choose 1 answer: Choose 1 answer: (Choice A) A Increases by factor of 333 (Choice B) B Decreases by factor of 999 (Choice C) C Decreases by factor of 333 (Choice D) D No change

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Khánh Gia 3 years 2021-08-12T12:44:12+00:00 1 Answers 13 views 0

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  1. Helga
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    2021-08-12T12:45:59+00:00
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    Answer:

    (C) Decreases by factor of 3

    Explanation:

    Centripetal acceleration is given by

    a = \dfrac{v^2}{r}

    where v is the linear velocity and r is the radius of the curve.

    Let the centripetal acceleration on the curve of radius R be a_1.

    Then

    a_1 = \dfrac{v_i^2}{R}

    Let the centripetal acceleration on the curve of radius 3R be a_2.

    Then

    a_2 = \dfrac{v_i^2}{3R} = \dfrac{1}{3}\dfrac{v_i^2}{R} = \dfrac{1}{3}a_1

    Here, we see that the acceleration decreases by a factor of 3.

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