Question

Calculate the maximum acceleration of a car that is heading up a 4.00° slope (one that makes an angle of 4.00° 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.)

(a) On dry concrete.
(b) On wet concrete.
(c) On ice, assuming that μs=0.100, the same as for shoes on ice.

Answer 1

The maximum acceleration of a car heading up a 4° slope under different road conditions can be calculated using the formula: Maximum acceleration = g * sin(θ) * μs, where g is the acceleration due to gravity, θ is the angle of the slope in radians, and μs is the coefficient of static friction. The maximum accelerations are calculated for dry concrete, wet concrete, and ice using the given coefficients of friction.

Step-by-step explanation:

To calculate the maximum acceleration of a car heading up a 4° slope under different road conditions, we need to consider the coefficient of static friction and the weight distribution. The maximum acceleration can be calculated using the formula:

Maximum acceleration = g * sin(θ) * μs

where g is the acceleration due to gravity (9.8 m/s²), θ is the angle of the slope in radians (4° = 0.07 radians), and μs is the coefficient of static friction.

(a) On dry concrete: Assuming the coefficient of static friction for dry concrete is μs = 1.0, the maximum acceleration is:

Maximum acceleration = 9.8 * sin(0.07) * 1.0 = 0.686 m/s²

(b) On wet concrete: Assuming the coefficient of static friction for wet concrete is μs = 0.6, the maximum acceleration is:

Maximum acceleration = 9.8 * sin(0.07) * 0.6 = 0.4116 m/s²

(c) On ice: Assuming the coefficient of static friction for ice is μs = 0.1, the maximum acceleration is:

Maximum acceleration = 9.8 * sin(0.07) * 0.1 = 0.0686 m/s²