An automobile with a tangential speed of 54.1 km/h follows a circular road that has a radius of 41.6 m. The automobile has a mass of 1260 kg. The pavement is wet and oily, so the coefficient of kinetic friction between the car's tires and the pavement is only 0.500.

1) Available force of friction: 6174 N

2) No

Explanation:

1)

The magnitude of the frictional force between the car's tires and the pavement of the road is given by

where

is the coefficient of friction

m is the mass of the car

g is the acceleration of gravity

For the car in this problem, we have:

(coefficient of friction)

m = 1260 kg (mass of the car)

Therefore, the force of friction is

2)

In order to mantain the car in circular motion, the force of friction must be at least equal to the centripetal force.

The centripetal force is given by

where

m is the mass of the car

v is the tangential speed

r is the radius of the curve

In this problem, we have

m = 1260 kg

is the tangential speed

r = 41.6 m is the radius of the curve

Therefore, the centripetal force is

Therefore, the force of friction is not enough to keep the car in the curve, since

the answer is a)

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