Acar is moving at 19 m/s along a curve on a horizontal plane with radius of curvature 49m.
the acceleration of gravity is 9.8 .
what is the required minimum coefficient of static friction between the road and the car’s tires to keep the car from skidding?

Minimum coefficient of static friction is 0.75

Velocity of car = 19 m/s

Radius of curvature = 49 meter

Acceleration of gravity = 9.8 m/s²

Minimum coefficient of static friction

Minimum coefficient of static friction = V² / rg

Minimum coefficient of static friction = 19² / [(49)(9.8)]

Minimum coefficient of static friction = 361 / [480.2]

Minimum coefficient of static friction = 0.7517

Minimum coefficient of static friction = 0.75

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Explanation:

Frictional Force

When the car is moving along the curve, it receives a force that tries to take it from the road. It's called centripetal force and the formula to compute it is:

The centripetal acceleration a_c is computed as

Where v is the tangent speed of the car and r is the radius of curvature. Replacing the formula into the first one

For the car to keep on the track, the friction must have the exact same value of the centripetal force and balance the forces. The friction force is computed as

The normal force N is equal to the weight of the car, thus

Equating both forces

Simplifying

Substituting the values

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