If a curve with a radius of 85 is perfectly banked for a car traveling 71 , what must be the coefficient of static friction for a car not to skid when traveling at 86 ?
The coefficient of static friction must be greater than or equal to 0.8.
To determine the coefficient of static friction required for a car not to skid on a banked curve, we can use the following equation:
μs = tan(θ)
where:
μs is the coefficient of static friction
θ is the angle of the banked curve
First, we need to calculate the angle of the banked curve.
θ = arctan(v² / (g * r))
where:
v is the velocity of the car
g is the acceleration due to gravity (approximately 9.8 m/s²)
r is the radius of the curve
Given:
v = 71 m/s
r = 85 m
Plugging in the values:
θ = arctan((71²) / (9.8 * 85))
θ ≈ arctan(5041 / 833)
Next, we can calculate the coefficient of static friction:
μs = tan(θ)
μs = tan(arctan(5041 / 833))
μs ≈ 5041 / 833
Therefore, the coefficient of static friction required for a car not to skid when traveling at 86 m/s on a perfectly banked curve with a radius of 85 m is approximately 6.06.
To determine the coefficient of static friction required for a car not to skid on a banked curve, we can use the following formula:
μ = tan(θ)
where μ is the coefficient of static friction and θ is the angle of banking of the curve. In this case, we need to find the coefficient of static friction when the car is traveling at a speed of 86 m/s.
First, let's find the angle of banking using the radius and speed of the car when it is perfectly banked:
θ = arctan(v^2 / (g * r))
where v is the speed of the car, g is the acceleration due to gravity, and r is the radius of the curve.
θ = arctan((71^2) / (9.8 * 85))
θ ≈ arctan(0.5672)
θ ≈ 29.57 degrees
Now, we can calculate the coefficient of static friction when the car is traveling at 86 m/s using the previously mentioned formula:
μ = tan(θ)
μ = tan(29.57°)
μ ≈ 0.582
Therefore, the coefficient of static friction required for the car not to skid when traveling at 86 m/s on a curve with a radius of 85 is approximately 0.582.