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22 February, 12:59

A curve has a radius of 50 meters and is banked 5 degrees. The road is covered with ice and is frictionless. What is the maximum speed, in mph, a car can travel and negotiate the curve? A.) 15.65mph B.) 25.00mph C.) 65.00mph D.) 6.55mph E.) None of the above

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  1. 22 February, 15:04
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    E.) None of the above

    Explanation:

    Draw a free body diagram. There are two forces acting on the car. Normal force perpendicular to the road, and weight downward.

    Sum of the forces perpendicular to the road:

    ∑F = ma

    N - mg cos θ = 0

    N = mg cos θ

    Sum of the forces towards the center of the circle:

    ∑F = ma

    N sin θ = mv²/r

    mg cos θ sin θ = mv²/r

    g cos θ sin θ = v²/r

    v = √ (gr cos θ sin θ)

    Given r = 50 m and θ = 5°:

    v = √ (9.8 m/s² * 50 m * cos 5° * sin 5°)

    v = 6.52 m/s

    v = 14.6 mph
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