Question

3.20 A section of a road with a constant 4% slope or grade (i.e., 4 ft vertically for each 100 ft horizontally) is to be paved. If the road is 32.000 ft wide and its total horizontal length is 1,200 ft, compute the road area to be paved.

3.21 Repeat Problem 3.20 if instead of having a 4% grade the road makes a 3 angle with the horizontal.

Answer 1

The problem involves using the coefficient of static friction along with the angle of incline to calculate a car's maximum possible acceleration on a slope under different road conditions.

Step-by-step explanation:

The student's question pertains to calculating the maximum acceleration of a car going up a slope with a specific grade under various road conditions. The calculations will involve the understanding of static friction and the forces at play when a car is on an inclined plane. With half the weight of the car supported by the drive wheels, the coefficient of static friction will ultimately dictate the maximum acceleration that can be achieved without the tires slipping. This concept is useful in engineering and physics to ensure that vehicle designs can handle various terrains and conditions safely.

The coefficient of static friction varies with the road condition. For example, the coefficient will be different for dry concrete, wet concrete, and ice. By knowing these coefficients and the angle of the slope, one can calculate the maximum force of friction and thus the maximum possible acceleration using Newton's second law of motion. This is a critical consideration for vehicle safety and performance.