Final answer
The maximum speed at which the car can take the curve is approximately 17.44 m/s.
Step-by-step explanation
The maximum speed a car can travel around a curve is determined by the force of static friction.
In this case, with a 1,200 kg car traveling on a curve with a 112 m radius and a coefficient of static friction between the tires and the road of 0.412, the formula to calculate the maximum speed is v = √(μ * g * r), where μ is the coefficient of static friction, g is the acceleration due to gravity, and r is the radius of the curve. Plugging in the values gives us v = √(0.412 * 9.81 m/s² * 112 m), resulting in a maximum speed of approximately 17.44 m/s.
The maximum speed at which the car can safely maneuver the curve without skidding is crucial in understanding the limitations imposed by friction between the tires and the road.
The coefficient of static friction indicates the maximum friction force that can be exerted between the tires and the road surface before sliding occurs. This calculation helps drivers and engineers comprehend the safe operating limits of a vehicle on a curve, preventing accidents due to excessive speed.
Understanding the physics behind a car's maximum speed on a curve assists in designing safer roads and vehicles while also aiding drivers in navigating curves at appropriate speeds, ensuring optimal safety.