Suppose the coefficient of static friction between the road and the tires on a car is 0.60 and the car has no negative lift. What speed will put the car on the verge of sliding as it rounds a level curve of 29.3 m radius?

rtew

13.39 To calculate the speed at which the car is on the verge of sliding as it rounds a level curve, we need to consider the forces acting on the car and use the centripetal force formula.

The centripetal force required to keep the car moving in a circle is provided by the friction force between the tires and the road. In this case, the maximum friction force is the product of the coefficient of static friction and the normal force acting on the car.

First, we need to calculate the normal force. In a level curve, the normal force is equal to the weight of the car, which is the mass of the car multiplied by the acceleration due to gravity.

Let's assume the mass of the car is m and the acceleration due to gravity is g.

Normal force (N) = m * g

Next, we can calculate the maximum friction force.

Friction force (Ff) = coefficient of static friction * Normal force (N)

Now, the centripetal force required to keep the car moving in a circle is given by:

Centripetal force (Fc) = (mass of the car * velocity^2) / radius

At the point of sliding, the maximum friction force is equal to the centripetal force. So we can equate the two:

Ff = Fc

Then, substitute the expressions for friction force and centripetal force:

coefficient of static friction * Normal force (N) = (mass of the car * velocity^2) / radius

Now, solve for velocity (v):

Velocity (v) = sqrt((coefficient of static friction * Normal force * radius) / mass of the car)

Given that the coefficient of static friction is 0.60 and the radius of the curve is 29.3 m, we can substitute these values into the formula.

Finally, without knowing the mass of the car, we are unable to obtain the exact speed at which it will slide.