An unbanked curve has a radius of curvature of 75m. On a winter day, with snow on the road, the coefficient of static friction between the tires of the car and the road is .23. What is the maximum speed with which the car can safely negotiate the curve?"

To determine the maximum speed the car can safely negotiate the curve, we can use the equation for centripetal force. The centripetal force required to keep an object moving in a curved path is provided by the static frictional force between the car's tires and the road.

The equation for centripetal force is:

F = (mv^2) / r

Where:
F is the centripetal force
m is the mass of the car
v is the velocity of the car
r is the radius of curvature

In this case, we need to find the maximum velocity (v) with which the car can safely negotiate the curve. To do this, we'll rearrange the equation to solve for v. The maximum velocity occurs when the static frictional force reaches its maximum value:

F_max = μ_s * N

Where:
F_max is the maximum static frictional force
μ_s is the coefficient of static friction
N is the normal force between the car and the road

The normal force (N) is equal to the weight of the car (mg), where g is the acceleration due to gravity.

Now, we can substitute the maximum static frictional force and the expression for the centripetal force into the equation:

μ_s * mg = (m * v^2) / r

Let's solve for v:

v^2 = (μ_s * g * r)

v = √(μ_s * g * r)

Given that the radius of curvature (r) is 75m and the coefficient of static friction (μ_s) is 0.23, we can substitute these values into the equation to find the maximum velocity (v).

v = √(0.23 * 9.8 * 75)

Calculating this value:

v ≈ 16.3 m/s

Therefore, the maximum speed with which the car can safely negotiate the curve is approximately 16.3 m/s.