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23 August, 18:33

A flat (unbanked) curve on a highway that has a radius of 50 m. A car rounds the curve. The car has mass 4,907 kg. The static coefficient of friction between the curve and the car is 0.35. What is the maximum speed of the car to prevent sliding?

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  1. 23 August, 22:25
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    maximum speed of the car to prevent sliding is 13.1m/s

    Explanation:

    Given data

    Radius of curve r=50m

    Mass of car m=4907kg

    Coefficient of friction u=0.35

    Limiting for R=?

    Hence limiting force R=ma

    R=4907*9.81

    R=48137.7N

    We know that the force to overcome friction is

    F=uR

    Hence

    F=0.35*48137.7

    F=16848.2N

    Centripetal force along the curve is given as

    Fc=mv²/r

    Fc = centripetal force

    m = mass

    v = velocity

    r = radius

    To solve for velocity we have to equate both force required to overcome friction and the centripetal force

    Fc=mv²/r=F=uR

    mv²/r=uR

    Making velocity subject of formula we have

    v²=u*r*R/m

    v² = (0.35*50*48137.7) / 4907

    v²=842409.75/

    v²=171.67

    v=√171.67

    v=13.1m/s
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