Final answer:
To calculate the maximum acceleration of a four-wheel drive car on a 4° slope, use Newton's second law incorporating static friction and gravity components. The four tires provide greater traction than two-wheel drive, resulting in higher possible accelerations.
Step-by-step explanation:
To calculate the maximum acceleration of a car with four-wheel drive heading up a 4° slope, we need to consider the coefficient of static friction (μs) for different road conditions. This calculation will give the maximum acceleration without the tires slipping.
- On dry concrete, the coefficient of static friction is typically high.
- On wet concrete, μs is lower due to the presence of water.
- On ice, μs is very low, around 0.100 for tires, which greatly reduces the possible acceleration.
For a car with four-wheel drive, unlike two-wheel drive, the entire weight of the car contributes to the frictional force that can be generated. Therefore, the fractions used in the two-wheel drive case should be adjusted accordingly, with all wheels now contributing equally to traction.
The maximum acceleration can be found using Newton's second law (F=ma), factoring in the force of gravity along the slope, the normal force, and the frictional force generated by all four tires. The formula for calculating this acceleration takes the form of:
a = (μs × N - m × g × sin(θ)) / m
Where N equals the normal force (m × g × cos(θ)), m is the mass of the car, g is the acceleration due to gravity, θ is the angle of the slope (4°), and a is the acceleration.
Using the relevant coefficients of static friction for each surface type and substituting into the formula will yield the maximum acceleration values. These values will be larger than the two-wheel case due to the increased traction.