A 925 kg car rounds an unbanked curve at a speed of 25 m/s. If the radius of the curve is 72, what is the minimum coefficient of friction be

Question

A 925 kg car rounds an unbanked curve at a speed of 25 m/s. If the radius of the curve is 72, what is the minimum coefficient of friction between the car and the road required so that the car does not skid?

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Thu Giang 4 years 2021-09-02T00:26:16+00:00 1 Answers 198 views 0

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  1. Calantha
    0
    2021-09-02T00:27:46+00:00
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    Answer:

    \mu_s^{min}=0.885

    Explanation:

    The centripetal force is provided by the static friction between the car and the road, and always have to comply with f\leq\mu_sN, so we have:

    ma_{cp}=f\leq\mu_sN=\mu_smg

    Which means:

    a_{cp}=\frac{v^2}{r}\leq\mu_sg

    So we have:

    \frac{v^2}{gr}\leq\mu_s

    Which means that \frac{v^2}{gr} is the minimum value the coefficient of static friction can have, which for our values is:

    \mu_s^{min}=\frac{v^2}{gr}=\frac{(25m/s)^2}{(9.81m/s^2)(72m)}=0.885

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