How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95 km/h?
Answer the question please
a=v^2/r=(26)^2/85=8m/s
Ff=miuFn
ma=miu(mg)
a=miu(g)
8=miu9.8
miu=0.8
To determine the required coefficient of static friction between the tires and the road, we can start by analyzing the forces acting on the car as it rounds the curve.
When a car goes around a curve, it experiences a centrifugal force directed towards the center of the curve, which is balanced by the friction force between the tires and the road. The maximum value of the friction force is given by the product of the coefficient of static friction (μs) and the normal force (N).
First, let's convert the speed of the car from km/h to m/s:
95 km/h * (1/3.6 m/s per km/h) = 26.39 m/s (rounded to two decimal places)
Next, let's calculate the centrifugal force acting on the car. The centrifugal force is given by the equation Fc = (mv^2)/r, where m is the mass of the car, v is the velocity of the car, and r is the radius of the curve.
Assuming the mass of the car is 1000 kg and the radius of the curve is 85 m, the centrifugal force is:
Fc = (1000 kg) * (26.39 m/s)^2 / (85 m) = 8207.40 N (rounded to two decimal places)
Now, let's calculate the normal force acting on the car. The normal force is equal to the weight of the car, which is the product of the mass and the acceleration due to gravity (9.8 m/s^2).
The normal force is:
N = (1000 kg) * (9.8 m/s^2) = 9800 N
Finally, we can calculate the required coefficient of static friction using the equation:
Fc = μs * N
Rearranging the equation to solve for μs:
μs = Fc / N
Substituting the known values:
μs = 8207.40 N / 9800 N ≈ 0.84 (rounded to two decimal places)
Therefore, the coefficient of static friction between the tires and the road must be at least 0.84 for the car to round the level curve of radius 85 m at a speed of 95 km/h.