A 1000 kg car is travelling on the highway at a constant speed of 110 km/h. The highway makes a turn that is banked at an angle of 10o and has a radius of 160 m. What is the coefficient of friction between the car tires and the pavement in the curve?
To find the coefficient of friction between the car tires and the pavement, we need to consider the forces acting on the car while it is making the turn.
First, let's calculate the gravitational force acting on the car. The gravitational force is given by the equation Fgravity = m * g, where m is the mass of the car and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Fgravity = (1000 kg) * (9.8 m/s^2) = 9800 N
Next, let's calculate the centripetal force required to keep the car moving in the curved path. The centripetal force is given by the equation Fcentripetal = m * v^2 / r, where m is the mass of the car, v is the velocity of the car, and r is the radius of the curved path.
Convert the velocity from km/h to m/s:
110 km/h = (110 km/h) * (1000 m/km) * (1 h/3600 s) = 30.56 m/s
Fcentripetal = (1000 kg) * (30.56 m/s)^2 / 160 m = 5838 N
The centripetal force is provided by the frictional force between the car tires and the pavement. Since the car is moving on a banked road, there is an additional vertically upward force component provided by the normal force. The equation to calculate the frictional force is Ffriction = Fcentripetal - Fnormal, where Fnormal = m * g * cos(theta), and theta is the angle of bank.
Fnormal = (1000 kg) * (9.8 m/s^2) * cos(10o) = 9643 N
Ffriction = 5838 N - 9643 N = -3805 N
The frictional force is directed towards the center of the curve in the opposite direction of motion. Since the direction of friction force is known, we can find the coefficient of friction using the equation Ffriction = mu * Fnormal, where mu is the coefficient of friction.
-3805 N = mu * 9643 N
mu = -3805 N / 9643 N = -0.394
The negative sign indicates that the frictional force is acting to the left, opposite to the direction of motion. However, the coefficient of friction is always a positive value, so the magnitude of the coefficient of friction is 0.394.
Therefore, the coefficient of friction between the car tires and the pavement in the curve is approximately 0.394.