Car A uses tires for which the coefficient of static friction is 0.175 on a particular unbanked curve. The maximum speed at which the car can negotiate this curve is 28.3 m/s. Car B uses tires for which the coefficient of static friction is 0.740 on the same curve. The cars of the same weight. What is the maximum speed at which car B can negotiate the curve?
To find the maximum speed at which Car B can negotiate the curve, we need to use the coefficient of static friction and the weight of the car.
The maximum speed at which a car can negotiate a curve without slipping is determined by the centripetal force acting on the car. The centripetal force is given by the equation:
Fcentripetal = m * v^2 / r
Where:
- Fcentripetal is the centripetal force
- m is the mass of the car (assumed to be the same for both cars)
- v is the velocity of the car
- r is the radius of the curve (assumed to be the same for both cars)
The maximum centripetal force that Car B can experience is limited by the maximum static friction force, which can be calculated using the equation:
Ffriction = μs * N
Where:
- Ffriction is the maximum static friction force
- μs is the coefficient of static friction
- N is the normal force (equal to the weight of the car)
Since both cars are of the same weight, the normal force acting on both cars will be the same. Therefore, we can compare the maximum speed of Car B to that of Car A by using the maximum static friction force for Car B.
First, we need to calculate the maximum static friction force for Car B:
Ffriction = μs * N
Given that μs = 0.740 and N is the weight of the car, we can substitute these values into the equation to solve for Ffriction.
Now, we can equate the maximum static friction force to the centripetal force to find the maximum speed of Car B:
Ffriction = Fcentripetal
Substituting the respective equations for Ffriction and Fcentripetal, we get:
μs * N = m * v^2 / r
Next, we can solve for the maximum speed, v:
v^2 = (μs * N * r) / m
Taking the square root of both sides, we get:
v = √((μs * N * r) / m)
Now, we can substitute the given values for Car B (μs = 0.740), the weight of the car, and the radius of the curve to calculate the maximum speed at which Car B can negotiate the curve.