Calculate the maximum deceleration of a car that is heading down a 15 degree slo

Question

Calculate the maximum deceleration of a car that is heading down a 15 degree slope (one that makes an angle of 15 degree with the horizontal) under the following road conditions. You may assume that the weight of the car is evenly distributed on all four tires and that the static coefficient of friction is involved--that is, the tires are not allowed to slip during the deceleration. (a) on dry concrete m/s^2 (b) on wet concrete m/s^2 (C) On ice, assuming that mus = 0.100, the same as for shoes on ice m/s^2

Explanation / Answer

gravitational force Fg = m*g*sintheta

normal fore N = m*g*costheta

frictional force f = u*N = u*m*g*costheta

Fnet = Fg - f = m*g*(sintheta - u*costheta)

but Fnet = m*a

a = g*(sintheta - u*costheta)

part(a)

u = 1

a = 9.8*(sin15-cos15) = -6.92 m/s^2

part(b)

u = 0.3

a = 9.8*(sin15-(0.3*cos15)) = -0.303 m/s^2

part(c)

u = 0.1

a = 9.8*(sin15-(0.1*cos15)) = 1.6 m/s^2

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