Consider a car is heading down a 5.5° slope (one that makes an angle of 5.5° 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 coefficient of static friction is involved—that is, the tires are not allowed to slip during the deceleration. Use a coordinate system in which down the slope is positive acceleration.

Question

Rubber on dry concrete: static friction = 1.0
kinetic friction = 0.7
Rubber on wet concrete: static friction = 0.7
kinetic friction = 0.5
shoes on ice: static friction = 0.1
kinetic friction = 0.05

a) Calculate the maximum acceleration for the car on dry concrete in m/s2.
b) Calculate the maximum acceleration on wet concrete in m/s2.
c) Calculate the maximum acceleration for the car on ice in m/s2, assuming that μs = 0.100, the same as for shoes on ice.

Answer 1

forcedown-foreceup=Ma
mgSinTheta-mu*mgcosTheta=ma
a= g(sinTheta-mu*cosTheta)

Answer 2

9.8(1/2(1.00)costeta - sinteta)