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Calculate the maximum deceleration of a car that is
Chapter 5, Problem 13(choose chapter or problem)
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.
Questions & Answers
QUESTION:
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.
ANSWER:
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 ,