what is the maximum speed at which automobile can round a curve of 100 ft radius on level if the coefficient of friction between the tires and the road is 0.35?
33.57 ft/s
Formula= mv^2/r=úN
ú-coefficient friction
N=mg
Given:
Radius=100ft
ú=0.35
Required: 100ft x 1m =30.48m
Velocit . 3.28ft
Solution:
mv^2/r=úmg - cancel m
v=√rúg
v=√(30.48m)(0.35)(9.8m/s^2)
v=10.22m/s
v=33.53ft/s
To find the maximum speed at which an automobile can round a curve, we can use the concept of centripetal force. The formula for centripetal force is:
F = (m * v^2) / r
Where:
F = Centripetal force
m = Mass of the automobile
v = Velocity of the automobile
r = Radius of the curve
In this case, we are given the radius of the curve as 100 ft (r = 100 ft) and the coefficient of friction between the tires and the road as 0.35.
The maximum value of the coefficient of friction represents the maximum allowable centripetal force. Therefore, we can equate the centripetal force to the maximum allowable force, which is given by:
Maximum allowable force = μ * m * g
Where:
μ = Coefficient of friction
m = Mass of the automobile
g = Acceleration due to gravity (approximately 32.2 ft/s^2)
By equating the centripetal force and the maximum allowable force, we get:
(m * v^2) / r = μ * m * g
Simplifying the equation by canceling out the mass (m) on both sides, we have:
v^2 / r = μ * g
Rearranging the equation to solve for the velocity (v), we get:
v = √(μ * g * r)
Now, we can substitute the given values into the formula to find the maximum speed at which the automobile can round the curve:
v = √(0.35 * 32.2 ft/s^2 * 100 ft)
Calculating this expression, we get:
v ≈ √(1127 ft^2/s^2)
v ≈ 33.6 ft/s
Therefore, the maximum speed at which the automobile can round the curve is approximately 33.6 ft/s (or 22.9 mph).
To determine the maximum speed at which an automobile can round a curve, we need to use the formula for centripetal force and equate it to the maximum friction force that the tires can provide.
The centripetal force (F) is equal to the frictional force (f) between the tires and the road, which can be calculated using the equation:
F = μ * N
Where:
F = centripetal force
μ = coefficient of friction between the tires and the road
N = normal force acting on the tires (equal to the weight of the car)
First, we need to calculate the normal force (N). The weight (W) of the car is given by:
W = m * g
Where:
m = mass of the car
g = acceleration due to gravity (approximately 9.8 m/s²)
Once we have the value of the normal force (N), we can calculate the centripetal force (F) using the formula:
F = (m * v²) / r
Where:
v = velocity of the car
r = radius of the curve
Now let's substitute the values given in the question:
μ = 0.35 (coefficient of friction)
r = 100 ft = 30.48 m (radius)
Assuming we do not have any additional information, such as the mass of the car, we cannot calculate the exact maximum speed since it depends on the car's mass.
However, when we solve for the maximum speed, we can express it in terms of the mass:
v = √((μ * g * r) / m)
You would need to know the mass of the car (m) in order to calculate the specific maximum speed it can traverse the curve.