A circular curve on a highway is designed for traffic moving at 27 m/s. The radius of the unbanked curve is 160 m. What is the minimum coefficient of friction between tires and the highway necessary to keep cars from sliding off the curve?

Question

A circular curve on a highway is designed for traffic moving at 27 m/s. The radius of the unbanked curve is 160 m. What is the minimum coefficient of friction between tires and the highway necessary to keep cars from sliding off the curve?

Is the friction static or kinetic? (type in the answer):

\mu =

The coeffienct of friction has to be which of the following for the car to stay on the curve?

A. greater than or equal to the value
B. less than or equal to the value
C. greater than or equal to the value
D. equal to the value
E. less than the value

Answer 1

F = m Ac = m v^2/r

also
F = mu m g
so
mu g = v^2/r
mu = v^2 /(g r)
in other words the ratio of centripetal acceleration to g

static, tires not slipping

A and C. You have a typo. They are the same

Answer 2

The coefficient of friction required to keep cars from sliding off the curve can be determined by considering the forces acting on the car as it moves around the circular curve. There are two main forces at play here: the force of gravity acting vertically downwards, and the centripetal force acting towards the center of the curve.

To find the minimum coefficient of friction needed, we can start by calculating the gravitational force acting on the car. The formula for gravitational force is given by:

F_gravity = m * g

where m is the mass of the car and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Next, we need to find the centripetal force required to keep the car on the curve. The centripetal force is given by:

F_centripetal = m * v^2 / r

where v is the velocity of the car and r is the radius of the curve. In this case, the velocity is given as 27 m/s and the radius is 160 m.

Now, we can equate the centripetal force to the gravitational force and solve for the coefficient of friction. The equation is:

F_centripetal = F_gravity

m * v^2 / r = m * g

The mass of the car cancels out on both sides of the equation, so we are left with:

v^2 / r = g

Now, we can rearrange the equation to solve for the minimum coefficient of friction (\mu):

\mu = v^2 / (r * g)

Plugging in the given values, we have:

\mu = (27 m/s)^2 / (160 m * 9.8 m/s^2)

Evaluating the expression, we find:

\mu ≈ 1.26

Since the coefficient of friction cannot be negative, the answer is not less than the value. Therefore, the correct answer is:

C. greater than or equal to the value