You are driving a 2475.0 kg car at a constant speed of 10.0 m/s along an icy, but straight and level road. While approaching a traffic light, it turns red. You slam on the brakes, your wheels locks, the tires began skidding, and the car slides to halt in a distance of 28.0 m. What is the coefficient of sliding friction between your tires and the icy road?
Equate the work done against friction to the loss of kinetic energy. This will let you solve for the friction force. Divide that by the weight of the car to get the cefficient of sliding friction.
To find the coefficient of sliding friction between the tires and the icy road, we can use the equation:
μ = (m * g) / (m * g + F_normal)
Where:
μ is the coefficient of sliding friction,
m is the mass of the car (2475.0 kg),
g is the acceleration due to gravity (9.8 m/s²), and
F_normal is the normal force exerted on the car by the icy road.
To calculate F_normal, we need to consider the forces acting on the car during braking. When the brakes are applied and the wheels lock, the only horizontal force acting on the car is the force of friction opposing motion. This force is equal to the product of the coefficient of sliding friction (μ) and the normal force (F_normal).
Since the car comes to a halt and there is no vertical acceleration, the normal force is equal to the weight of the car, which can be calculated using the equation:
F_normal = m * g.
Let's calculate:
F_normal = 2475.0 kg * 9.8 m/s² = 24255 N.
Now, substituting this value into the equation for the coefficient of sliding friction:
μ = (m * g) / (m * g + F_normal)
= (2475.0 kg * 9.8 m/s²) / (2475.0 kg * 9.8 m/s² + 24255 N)
≈ 0.384.
Therefore, the coefficient of sliding friction between your tires and the icy road is approximately 0.384.