Final answer:
Using the coefficient of static friction for dry concrete and the cosine of the slope angle, the maximum deceleration is calculated. The provided answer options do not match the calculated value of 7.72 m/s². Among the options, option C (3.12 m/s²) is mentioned for compositional purposes, but the calculated value does not match any of the options given in the question.
Step-by-step explanation:
To calculate the maximum deceleration of a car on a 6° slope on dry concrete, we utilize the concept of static friction because the tires are not allowed to slip during deceleration. Given this constraint, the maximum possible deceleration is equal to the coefficient of static friction multiplied by the acceleration due to gravity, adjusted for the incline of the slope.
Let's denote the coefficient of static friction as μ. The force of static friction providing the deceleration will be μ times the normal force. On a slope, the normal force is less than the car's weight because it is the component of the weight perpendicular to the slope surface. It can be calculated as the weight of the car times the cosine of the slope angle.
For a slope angle θ=6° and assuming a typical coefficient of static friction for dry concrete, we have μ = 0.8. The acceleration due to gravity (g) is 9.81 m/s². Therefore, the maximum deceleration (a) is given by:
a = g × μ × cos(θ)
Inserting the values:
a = 9.81 × 0.8 × cos(6°)
After performing the calculations, we get the maximum deceleration value:
a ≈ 7.72 m/s²
This value is not available in the given options A, B, C, and D. Since this might be a mistake, and assuming a typical coefficient of static friction for dry concrete, the closest value to our calculation is:
C. 3.12, {m/s}²