You are driving a 2570.0-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 24.6 m. What is the coefficient of kinetic friction between your tires and the wet road?
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To find the coefficient of kinetic friction between the tires and the wet road, we can use the following equation:
\( \mu_k = \frac{{F_{friction}}}{{F_{normal}}} \)
where:
\( \mu_k \) is the coefficient of kinetic friction,
\( F_{friction} \) is the force of friction,
\( F_{normal} \) is the normal force.
First, let's find the force of friction. The force of friction can be calculated using the formula:
\( F_{friction} = \mu_k \times F_{normal} \)
In this case, since the car is skidding and the wheels are locked, the force of friction is equal to the net force acting on the car.
The net force can be calculated using Newton's second law of motion:
\( F_{net} = m \times a \)
where:
\( F_{net} \) is the net force,
\( m \) is the mass of the car, and
\( a \) is the acceleration of the car.
In this case, the car comes to a halt, so the acceleration is equal to 0.
Therefore, the net force acting on the car is also 0, which means the force of friction is equal to 0.
Now, let's find the normal force. The normal force is the force exerted by the surface perpendicular to the car's weight.
In this case, the car is on a level road, so the normal force is equal to the weight of the car.
\( F_{normal} = m \times g \)
where:
\( g \) is the acceleration due to gravity (9.8 m/s^2).
Now we can substitute the values into the equation for the coefficient of kinetic friction:
\( \mu_k = \frac{{F_{friction}}}{{F_{normal}}} = \frac{0}{{m \times g}} \)
Substituting the given values into the equation:
\( \mu_k = \frac{0}{{2570.0 \, \text{kg} \times 9.8 \, \text{m/s}^2}} \)
Calculating this expression, we get:
\( \mu_k = 0 \)
Therefore, the coefficient of kinetic friction between the car's tires and the wet road is 0.