What must be the radius of an unbanked (flat) curve so that a car can safely travel at a maximum speed of 39 m/s? The coefficient of static friction is 0.70.

m v^2/r = .7 m g

or
Ac = .7 g :)

39^2 / r = .7 (9.81)

r = 39^2/ (.7*9.81)

To determine the radius of an unbanked curve, we need to consider the maximum speed of the car and the coefficient of static friction.

The formula we can use here is the centripetal force formula:

F_c = (m * v^2) / r

Where:
F_c is the centripetal force (force towards the center of the circular path),
m is the mass of the car,
v is the velocity of the car, and
r is the radius of the curve.

In this case, we have the maximum speed (v = 39 m/s) and the coefficient of static friction (μ = 0.70). We can calculate the maximum centripetal force the car can safely handle using this friction coefficient.

F_f = μ * m * g

Where:
F_f is the maximum frictional force,
μ is the coefficient of static friction, and
g is the gravitational acceleration (approximately 9.8 m/s^2).

The maximum centripetal force F_c must be equal to or less than the maximum frictional force F_f to ensure the car can safely travel through the curve.

F_c ≤ F_f

Substituting the formulas:

(m * v^2) / r ≤ μ * m * g

Mass (m) cancels out on both sides of the inequality:

v^2 / r ≤ μ * g

Rearranging the formula:

r ≥ v^2 / (μ * g)

Now we can plug in the given values:

r ≥ (39 m/s)^2 / (0.70 * 9.8 m/s^2)

Calculating this expression will give us the minimum radius of the curve that ensures the car can safely travel at a maximum speed of 39 m/s.