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Calculate the minimum coefficient of static friction between the tires and the road if a 1030 kg car is to go around a level curve of radius 115 m at a speed of 35 mph.

Answer :

To calculate the minimum coefficient of static friction between the tires and the road, we need to use the centripetal force equation:

F = mv²/r

where

F is the required centripetal force.

m is the mass of the car.

v is the velocity of the car.

r is the radius of the curve.

We can convert the velocity from mph to m/s:

35 mph = 15.65 m/s

Substituting the given values, we get:

F = (1030 kg)(15.65 m/s)² / 115 m

F ≈ 2292 N.

The maximum frictional force that can act on the car is equal to the product of the coefficient of static friction (μs) and the normal force (N) acting on the car.

Since the car is on a level curve, the normal force is equal to the weight of the car:

N = mg

N = (1030 kg)(9.81 m/s²)

N ≈ 10110 N

Substituting the values, we get:

μsN ≥ F

μs(10110 N) ≥ 2292 N

μs ≥ 0.227

Therefore, the minimum coefficient of static friction between the tires and the road is 0.227.

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