You are driving a 2520.0-kg car at a constant speed of 14.0 m/s along a wet, but straight, level road. As you approach an intersection, the traffic light turns red. You slam on the brakes. The car's wheels lock, the tires begin skidding, and the car slides to a halt in a distance of 26.2 m. What is the coefficient of kinetic friction between your tires and the wet road?

Question

You are driving a 2520.0-kg car at a constant speed of 14.0 m/s along a wet, but straight, level road. As you approach an intersection, the traffic light turns red. You slam on the brakes. The car's wheels lock, the tires begin skidding, and the car slides to a halt in a distance of 26.2 m. What is the coefficient of kinetic friction between your tires and the wet road?

Answer 1

Vf^2=Vi^2+2ad

solve for acceleration,a.
then, F=ma
mu*mg=ma
mu= a/g

Answer 2

To find the coefficient of kinetic friction between the tires and the wet road, we can use the following steps:

Step 1: Calculate the net force acting on the car.
The net force can be found using Newton's second law of motion:

F_net = mass × acceleration

Since the car comes to a halt, its acceleration is 0 m/s^2. Therefore, the net force acting on the car is:

F_net = mass × acceleration = mass × 0 = 0 N

Step 2: Identify the forces acting on the car.
There are two main forces acting on the car: the force of kinetic friction and the force of gravity.

The force of gravity is given by the equation:

F_gravity = mass × gravitational acceleration

where the gravitational acceleration is approximately 9.8 m/s^2.

Step 3: Calculate the force of gravity.
F_gravity = 2520.0 kg × 9.8 m/s^2 = 24756 N

Step 4: Calculate the force of kinetic friction.
Since the car is sliding to a halt, the force opposing its motion is the force of kinetic friction. The force of kinetic friction can be found using the equation:

F_kinetic friction = coefficient of kinetic friction × normal force

Step 5: Calculate the normal force.
The normal force is the force exerted by the road on the car, perpendicular to the surface. In this case, the normal force is equal to the force of gravity acting on the car.

Therefore, the normal force is 24756 N.

Step 6: Calculate the coefficient of kinetic friction.
Using the formula for the force of kinetic friction and the known values:

F_kinetic friction = coefficient of kinetic friction × normal force

0 N = coefficient of kinetic friction × 24756 N

Solve for the coefficient of kinetic friction:

coefficient of kinetic friction = 0 N / 24756 N ≈ 0

So the coefficient of kinetic friction between the tires and the wet road is approximately 0.