Understanding the Forces
* Force of Friction: The force that prevents the car from slipping is static friction. Its maximum value is given by:
* F_friction = μ_s * F_normal
* Where:
* μ_s is the static coefficient of friction (0.55 in this case)
* F_normal is the normal force, which is equal to the car's weight (mg) on level ground.
* Force of Acceleration: This is the force that causes the car to accelerate. It's given by Newton's second law:
* F_acceleration = m * a
* Where:
* m is the mass of the car
* a is the acceleration
Maximum Acceleration
* At the limit of static friction: The car will start to slip when the force of acceleration exceeds the maximum force of static friction. This is when:
* F_acceleration = F_friction
* m * a = μ_s * m * g
* Solving for acceleration: Notice that the mass 'm' cancels out. We are left with:
* a = μ_s * g
* a = 0.55 * 9.8 m/s²
* a ≈ 5.4 m/s²
Therefore, the maximum acceleration a car can undergo on level ground with a static coefficient of friction of 0.55 is approximately 5.4 m/s².
