Understanding the Concepts
* Static Friction: This is the force that prevents an object from moving when a force is applied to it. The maximum static friction force is what we're interested in, as it represents the limit before the tires start slipping.
* Force of Friction: The force of friction is calculated as:
* F_friction = μ * F_normal
* Where:
* F_friction is the force of friction
* μ is the coefficient of friction (static in this case)
* F_normal is the normal force (equal to the car's weight in this situation)
* Newton's Second Law: This law states that the net force acting on an object is equal to its mass times its acceleration (F_net = m * a).
Calculation
1. Free Body Diagram: Imagine the car. The forces acting on it are:
* Weight (mg) acting downwards
* Normal force (N) acting upwards (equal in magnitude to the weight)
* Friction force (F_friction) acting horizontally (this is the force that accelerates the car)
2. Applying Newton's Second Law:
* Since the car is accelerating horizontally, we only consider the horizontal forces. The only horizontal force is the friction force, which is the net force causing the acceleration.
* Therefore, F_net = F_friction = m * a
3. Substituting Friction Force:
* F_friction = μ * F_normal = μ * mg (since F_normal = mg)
4. Solving for Acceleration:
* μ * mg = m * a
* a = μ * g
5. Plugging in Values:
* a = 0.78 * 9.8 m/s²
* a ≈ 7.64 m/s²
Conclusion:
The maximum acceleration the car can undergo with a coefficient of static friction of 0.78 is approximately 7.64 m/s².
Important Note: This calculation assumes that the car's weight is evenly distributed and that the coefficient of static friction is constant across all tires. In reality, these factors can vary, so the actual maximum acceleration might be slightly different.
