A car is traveling down a hill that makes an angle of 14° with the horizontal. The driver applies her brakes, and the wheels lock so that the car begins to skid. The coefficient of kinetic friction between the tires and the road is μK = 0.55.
To find the acceleration of the car while skidding down the hill, we can start by considering the forces acting on the car.
Since the car is on a hill, there are two components of the gravitational force acting on it: one that is parallel to the hill (mg*sinθ), and one that is perpendicular to the hill (mg*cosθ), where m is the mass of the car and θ is the angle of the hill.
The force of kinetic friction opposes the motion of the car and acts in the opposite direction of the parallel component of the gravitational force. The magnitude of the force of kinetic friction, Fk, can be calculated using the equation Fk = μK * N, where μK is the coefficient of kinetic friction and N is the normal force. In this case, the normal force is equal to the perpendicular component of the gravitational force, which is mg*cosθ.
Now we can calculate the acceleration of the car using Newton's second law, F = ma. The net force acting on the car is given by the difference between the parallel component of the gravitational force and the force of kinetic friction, so we have:
ma = mg*sinθ - Fk
Substituting the expressions for Fk and N, we get:
ma = mg*sinθ - μK * mg*cosθ
Dividing both sides of the equation by m gives us the acceleration, a:
a = g*sinθ - μK * g*cosθ
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Now we can plug in the values given in the question:
θ = 14°
μK = 0.55
g = 9.8 m/s^2
Using a scientific calculator, we can calculate:
a = 9.8 * sin(14°) - 0.55 * 9.8 * cos(14°)
Thus, the acceleration of the car while skidding down the hill can be determined by evaluating this expression.