On a curved roadway of radius 100 m, the suggested speed limit is 35 mph (approximately 16 m/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?

force friction=centripetal force

mg*mu=m*v^2/r
solve for mu

To determine the required coefficient of friction between a car's tires and the road for safe negotiation of a curved roadway, we can use the concept of centripetal force.

In this case, the centripetal force acting on the car is provided by the friction force between the tires and the road. The formula for centripetal force is:

F = (mv²) / r,

Where:
F = Centripetal force,
m = Mass of the car,
v = Velocity of the car,
r = Radius of the curved roadway.

We need to find the required coefficient of friction, denoted by μ, which can be calculated using the equation:

F = μN,

Where:
μ = Coefficient of friction,
N = Normal force (equal to the weight of the car).

To begin solving the problem, we will find the centripetal force acting on the car.

Given:
Radius (r) = 100 m,
Velocity (v) = 16 m/s.

First, we need to convert the speed from mph to m/s:
35 mph ≈ 16 m/s.

Now, we will calculate the centripetal force:

F = (m × v²) / r.

Plugging in the values:
F = (m × 16²) / 100.

Next, we need to express the mass of the car (m) in terms of the normal force (N). Since weight (W) = mass (m) × acceleration due to gravity (g), we can rewrite it as:

N = mg.

Now, we can substitute the value of the weight into the equation for the centripetal force:

F = μN = μmg.

Finally, we can set the equations for force equal to each other:

(16² × m) / 100 = μmg.

Rearranging the equation, we can solve for the coefficient of friction (μ):

μ = (16² × m) / (100g).

Please provide the mass of the car (m) in order to calculate the coefficient of friction required to safely negotiate the curve at the posted speed.