a car is traveling 25 ns^-1 around a level curve of radius 120 m. what is the minimum value of the coefficient of static friction µs between the tires and the road to prevent the car from skidding

To find the minimum value of the coefficient of static friction (µs) between the tires and the road, we need to consider the forces acting on the car as it travels around the curve.

The centripetal force is required to keep the car moving in a circular path. It is provided by the friction force between the tires and the road. If the friction force is not sufficient, the car will skid or slide off the road.

The formula for the centripetal force is given by:

Fc = mv² / r

Where:
- Fc is the centripetal force
- m is the mass of the car
- v is the velocity of the car
- r is the radius of the curve

In this case, we are given the velocity (v = 25 ns^-1) and the radius (r = 120 m). We can assume the mass of the car is canceled out in the calculation.

Fc = (25 ns^-1)² / (120 m)

Now, to find the minimum value of µs, we need to consider the maximum friction force, which occurs when the car is about to skid. At this point, the friction force reaches its maximum value: fs = µs * N.

Here, N represents the normal force, which equals the weight of the car: N = mg.

We need to compare the centrifugal force (Fc) with the maximum friction force (fs):

Fc = fs
(25 ns^-1)² / (120 m) = µs * mg

Simplifying further, since g (acceleration due to gravity) = 9.8 m/s²:

(25 ns^-1)² / 120 = µs * 9.8

µs = [(25 ns^-1)² / 120] / 9.8

Evaluating this expression will give us the minimum value of the coefficient of static friction (µs) required to avoid skidding on the curve.