Question

a concrete highway curve of radius 60.0 m is banked at a 17.0 ∘ angle. What is the maximum speed with which a 1600kg rubber-tired car can take this curve without sliding? (Take the static coefficient of friction of rubber on concrete to be 1.0.)

Answer 1

The maximum speed at which the car can take the curve without sliding is 24.9 m/s.

Step-by-step explanation:

To find the maximum speed at which the car can take the curve without sliding, we need to consider the forces acting on the car. The two main forces are the gravitational force (mg) and the frictional force (f). The vertical component of the gravitational force provides the normal force (N), which is equal to mg. The horizontal component of the gravitational force provides the centripetal force (Fc), which is equal to mv^2/r, where m is the mass of the car, v is the velocity, and r is the radius of the curve.

Since the car is not sliding, the static friction force provides the necessary centripetal force. The maximum static friction force (fmax) is equal to the product of the normal force and the coefficient of static friction (μs), which in this case is 1.0. Setting the maximum static friction force equal to the centripetal force, we can solve for the maximum velocity:

fmax = μsN = μsmg

Fc = mv^2/r

Setting fmax equal to Fc:

μsmg = mv^2/r

Solving for v:

v = sqrt(μsgr)

Plugging in the given values, we get:

v = sqrt((1.0)(9.8 m/s^2)(60.0 m)) = 24.9 m/s