On a curved roadway of radius 100m, the suggested speed is 35mph(approximately 16m/s). What must the coefficient of friction be between a car's tires and the road for the car to safely negotiate the curve at the posted speed?
is the roadway flat?
if so,
mv^2/r-mg*coeff=0
solve for coeff
A roadway is designed for traffic moving at a speed of 68 m/s. A curved section of the roadway is a circular arc of 140 m radius. The roadway is banked--so that a vehicle can go around the curve--with the lateral friction forces equal to zero. The angle at which the roadway is banked is closest to:
Select one:
a. 73°
b. 67°
c. 75°
d. 69°
e. 71°
To determine the coefficient of friction required for a car to safely negotiate a curve at a given speed, we need to consider the centripetal force acting on the car.
In this case, the centripetal force is provided by the friction between the car's tires and the road. The equation for centripetal force is:
F = m * a
Where:
F is the centripetal force
m is the mass of the car
a is the centripetal acceleration
The centripetal acceleration can be calculated using the formula:
a = v^2 / r
Where:
v is the velocity of the car
r is the radius of the curve
In this case, the velocity of the car is 16 m/s and the radius of the curve is 100 m. Plugging these values into the equation, we get:
a = (16 m/s)^2 / 100 m
a = 2.56 m/s^2
Now we need to calculate the centripetal force using the formula F = m * a. However, we don't know the mass of the car.
To continue, we need the weight of the car. Let's assume the weight is W. The normal force acting on the car, which is equal to the weight, is given by:
N = W = m * g
Where:
g is the acceleration due to gravity
Assuming a typical value for the acceleration due to gravity of 9.8 m/s^2, we can substitute the weight equation into the centripetal force equation:
F = (m * g) * a
Since we know the centripetal force is provided by the friction between the tires and the road, and the maximum frictional force is given by the product of the coefficient of friction (μ) and the normal force (N), we can write:
F = μ * N
Substituting N = m * g into the equation, we get:
F = μ * (m * g)
Now we have two expressions for the centripetal force: F = (m * g) * a and F = μ * (m * g). Setting them equal, we have:
(m * g) * a = μ * (m * g)
Canceling out the mass and acceleration due to gravity terms:
a = μ * g
Solving for the coefficient of friction μ:
μ = a / g
Plugging in the values of a and g:
μ = 2.56 m/s^2 / 9.8 m/s^2
μ ≈ 0.26
Therefore, the coefficient of friction between the car's tires and the road must be approximately 0.26 for the car to safely negotiate the curve at the posted speed of 35 mph (approximately 16 m/s).