Problem 13PE

Calculate the maximum deceleration of a car that is heading down a 6º slope (one that makes an angle of 6º 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. (Ignore rolling.) Calculate for a car: (a) On dry concrete. (b) On wet concrete. (c) On ice, assuming that µs = 0.100 , the same as for shoes on ice.

Solution 13PE

Let us take the positive x- direction down the slope. The maximum deceleration of the car heading down a slope can be calculated by finding the net force Fx and using Newton’s second

law of motion. The free body diagram is as shown in the figure below

a.)

Step 1 of 4

The net force

Where, angle of inclination = 6o , g = acceleration due to gravity = 9.8 m/s2, s= coefficient of static friction between the tyre (rubber) and the road (concrete).

So, the maximum deceleration is ,