Calculate the maximum acceleration of a car that is heading up a 5.5 degree slop

Question

Calculate the maximum acceleration of a car that is heading up a 5.5 degree slope (one that makes an angle of 5-5 degree with the horizontal and assuming up the slope is the positive direction) under the following road conditions. Assume that the car has four-wheel drive and that the coefficient of static friction is involved-that is, the tires are not allowed to slip during the acceleration. Randomized Variables theta = 5.5 degree Calculate the maximum acceleration of the car on dry concrete in m/s^2. Calculate the maximum acceleration of the car on wet concrete in m/s^2. Calculate the maximum acceleration of the car on ice in m/s^2, assuming that mu_s = 0.100, the same as for shoes on ice.

Explanation / Answer

max friction a_f = -µgcos = -µ * 9.8m/s² * cos5.5º = -9.75 µ

gravity component a_g = gsin = 9.8m/s² * sin5.5 = 0.939 m/s^2

net acceleration a = a_g + a_f

1) 0n dry concrete a = -5.886 m/s^2

2) on wet concrete a = -3.936 m/s^2

3) a = -0.036 m/s^2

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