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29 July, 23:53

Certain suv ads claim that their vehicles can climb a slope of 45?. what is the minimum coefficient of static friction between the tires and the road for this to be possible?

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  1. 30 July, 01:23
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    First, you make a force body diagram to illustrate the problem. Then, apply Newton's laws of motion.

    Summation of forces along the y-direction:

    F = 0 (bodies at equilibrium) = Normal force - weight*cos45 = 0

    Normal force = wcos45

    Summation of forcesalong the x-direction:

    F = 0 (bodies at equilibrium) = Frictional force - weight*sin45 = 0

    x*Normal force - weight*sin45 = 0 (let x be the min coeff of static friction)

    x*weight*cos45 = weight*sin 45

    x = sin45/cos45 = 1

    Therefore, the minimum coefficient of static friction must be 1.
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