Question

Calculate the maximum acceleration of a car that is heading up a 4º slope (one that makes an angle of 4º with the horizontal) under the following road conditions. Assume that only half the weight of the car is supported by the two drive wheels and that the coefficient of static friction is involved—that is, the tires are not allowed to slip during the acceleration. (Ignore rolling.)

On dry concrete.

A. 2.45 , {m/s}²
B. 1.88 , {m/s}²
C. 3.12 , {m/s}²
D. 4.02 , {m/s}²

Answer 1

The maximum acceleration of a car heading up a 4º slope on dry concrete is approximately 2.45 m/s².

Step-by-step explanation:

To calculate the maximum acceleration of a car heading up a 4º slope, we need to consider the force of friction. In this case, we assume that only half the weight of the car is supported by the two drive wheels, and the coefficient of static friction is involved. The formula to calculate the maximum acceleration is:

a = g * μs * sin(θ)

Where:

a is the maximum acceleration

g is the acceleration due to gravity (9.8 m/s²)

μs is the coefficient of static friction

θ is the angle of the slope (in radians)

For dry concrete, the coefficient of static friction is typically around 0.6. Converting the angle from degrees to radians, we have:

θ = 4º * (π/180)

Substituting these values into the formula: a = (0.5 * 9.8 * 0.6 * sin(4º * (π/180)))

Simplifying the calculation:

a ≈ 2.45 m/s²

Therefore, the maximum acceleration of the car on a 4º slope on dry concrete is approximately 2.45 m/s².